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        <url>
          <loc>https://unidrills.com/video/t3m20stDwu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1078/t3m20stDwu.jpg</video:thumbnail_loc>

            <video:title>Tautomerism</video:title>

            <video:description><![CDATA[
Some isomers swap atoms to change their group. How does a hydrogen shift create a new functional class? We explain the dynamic equilibrium of tautomers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1078/t3m20stDwu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
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          <video:video>
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            <video:title>Definition</video:title>

            <video:description><![CDATA[
This lesson defines the standard form of a quadratic equation and its core components. You will learn to identify the variable, coefficients, and constants in a second-degree equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/887/69IAkoTJ_lk5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gxZgelzfU0OE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/gxZgelzfU0OE.jpg</video:thumbnail_loc>

            <video:title>Solution of differential equations (1)</video:title>

            <video:description><![CDATA[
Meaning of the solution of differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/gxZgelzfU0OE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CkalD8xvCxE2</loc>

          <video:video>
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            <video:title>Vector addition (2)</video:title>

            <video:description><![CDATA[
Parallelogram rule of addition of two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/CkalD8xvCxE2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vF6sXmdZJIC2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/10/vF6sXmdZJIC2.jpg</video:thumbnail_loc>

            <video:title>Internal division</video:title>

            <video:description><![CDATA[
Internal division of a line in a given ratio by a point.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/10/vF6sXmdZJIC2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2ylIPze2kAhB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/6/2ylIPze2kAhB.jpg</video:thumbnail_loc>

            <video:title>Kinds of vectors (2)</video:title>

            <video:description><![CDATA[
Equal and null vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/6/2ylIPze2kAhB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wCjvmuv5WDRi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/wCjvmuv5WDRi.jpg</video:thumbnail_loc>

            <video:title>Equation of a line II</video:title>

            <video:description><![CDATA[
Equation of a line in a two-dimensional cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/wCjvmuv5WDRi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yRQ_l9aVkWZg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/6/yRQ_l9aVkWZg.jpg</video:thumbnail_loc>

            <video:title>Kinds of vectors (3)</video:title>

            <video:description><![CDATA[
Unit vectors, like and unlike vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/6/yRQ_l9aVkWZg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1UGM6rE12sS9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/887/1UGM6rE12sS9.jpg</video:thumbnail_loc>

            <video:title>Roots or solutions</video:title>

            <video:description><![CDATA[
This lesson explains what a root is and how it serves as the solution to a quadratic equation. You will learn to identify these values and understand why they are the main focus of our work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/887/1UGM6rE12sS9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hNLYSuR8lAgh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/hNLYSuR8lAgh.jpg</video:thumbnail_loc>

            <video:title>Computer-aided handling</video:title>

            <video:description><![CDATA[
Computer-aided handling of complex numbers using Microsoft Excel.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/hNLYSuR8lAgh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VSJQmqm7Uocv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/6/VSJQmqm7Uocv.jpg</video:thumbnail_loc>

            <video:title>Kinds of vectors (1)</video:title>

            <video:description><![CDATA[
Free and localized vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/6/VSJQmqm7Uocv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QlhChENzA7bF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/QlhChENzA7bF.jpg</video:thumbnail_loc>

            <video:title>Cartesian coordinates</video:title>

            <video:description><![CDATA[
An introduction to the Cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/QlhChENzA7bF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/65-0LBshGnp_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/65-0LBshGnp_.jpg</video:thumbnail_loc>

            <video:title>Systems of unit</video:title>

            <video:description><![CDATA[
The SI system of units, the US customary units and conversion between them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/65-0LBshGnp_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_7wsSx5zXXJC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/8/_7wsSx5zXXJC.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and representation of position vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/8/_7wsSx5zXXJC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vxzXpijVx379</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/116/vxzXpijVx379.jpg</video:thumbnail_loc>

            <video:title>Neighborhoods</video:title>

            <video:description><![CDATA[
General neighborhoods and deleted neighborhoods.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/116/vxzXpijVx379.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/arC3RGbGRYjl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/arC3RGbGRYjl.jpg</video:thumbnail_loc>

            <video:title>Absolute values</video:title>

            <video:description><![CDATA[
Absolute values of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/arC3RGbGRYjl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NAH-kDRirH1V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/116/NAH-kDRirH1V.jpg</video:thumbnail_loc>

            <video:title>Disks</video:title>

            <video:description><![CDATA[
Open and closed disks.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/116/NAH-kDRirH1V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ueYEwz7KcXgw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/ueYEwz7KcXgw.jpg</video:thumbnail_loc>

            <video:title>Direction cosines</video:title>

            <video:description><![CDATA[
Meaning of direction cosines and the use of direction cosines to find the angle between two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/ueYEwz7KcXgw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jJd5ul_T7KnA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/jJd5ul_T7KnA.jpg</video:thumbnail_loc>

            <video:title>Arguments</video:title>

            <video:description><![CDATA[
General arguments and principal argument of a complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/jJd5ul_T7KnA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DCGxZdqHwAOb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/DCGxZdqHwAOb.jpg</video:thumbnail_loc>

            <video:title>Polar form</video:title>

            <video:description><![CDATA[
Polar form of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/DCGxZdqHwAOb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/njifwsln_5CF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/njifwsln_5CF.jpg</video:thumbnail_loc>

            <video:title>The quadratic formula</video:title>

            <video:description><![CDATA[
This lesson introduces the quadratic formula as the universal method for finding roots. You will learn to substitute coefficients into the formula to solve any quadratic equation, regardless of whether it can be factorised.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/njifwsln_5CF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dZryM2huLlCK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/198/dZryM2huLlCK.jpg</video:thumbnail_loc>

            <video:title>Spherical coordinates</video:title>

            <video:description><![CDATA[
Vector calculus properties in spherical coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/198/dZryM2huLlCK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oJgR-B9LLb1c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/oJgR-B9LLb1c.jpg</video:thumbnail_loc>

            <video:title>Slope of a line</video:title>

            <video:description><![CDATA[
Calculating the slope (gradient) of a line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/oJgR-B9LLb1c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zR0Dc7dTP_DN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/zR0Dc7dTP_DN.jpg</video:thumbnail_loc>

            <video:title>Inverse differentiation</video:title>

            <video:description><![CDATA[
Inverse functions reverse inputs. How do you find the derivative without solving for y explicitly? Learn the reciprocal rule shortcut.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/zR0Dc7dTP_DN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ea5OVPAWZxOm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/Ea5OVPAWZxOm.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Point charges are simple. How do you find potential for a charged rod or disc using integration? We replace summation with calculus to handle continuous charge distributions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/Ea5OVPAWZxOm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MjdG6ip6IGkq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/MjdG6ip6IGkq.jpg</video:thumbnail_loc>

            <video:title>Rational powers</video:title>

            <video:description><![CDATA[
How to find rational powers of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/MjdG6ip6IGkq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1cKlN1TgUlSH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/140/1cKlN1TgUlSH.jpg</video:thumbnail_loc>

            <video:title>Applications to conics</video:title>

            <video:description><![CDATA[
Applications of quadratic and canonical forms to conic sections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/140/1cKlN1TgUlSH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_01byGK0C_pn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/57/_01byGK0C_pn.jpg</video:thumbnail_loc>

            <video:title>Factorization</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by factorization.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/57/_01byGK0C_pn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SAD7CwdrGd_U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/SAD7CwdrGd_U.jpg</video:thumbnail_loc>

            <video:title>Midpoint of a line segment</video:title>

            <video:description><![CDATA[
Calculating the coordinates of the midpoint of a line segment in a Cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/SAD7CwdrGd_U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wgNAVVwfdS6O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/wgNAVVwfdS6O.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of the divergence of a vector field and solenoidality.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/wgNAVVwfdS6O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NQFkcEcziqkp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/NQFkcEcziqkp.jpg</video:thumbnail_loc>

            <video:title>Solving homogeneous equations with constant coefficients (1)</video:title>

            <video:description><![CDATA[
How to obtain the auxiliary equation of homogeneous equations with constant coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/NQFkcEcziqkp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pcIOtyp4Ozwz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/156/pcIOtyp4Ozwz.jpg</video:thumbnail_loc>

            <video:title>Mechanics, dynamics and kinetics</video:title>

            <video:description><![CDATA[
Meaning of mechanics, engineering mechanics, dynamics and kinetics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/156/pcIOtyp4Ozwz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xp96Hw5DKWCG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/xp96Hw5DKWCG.jpg</video:thumbnail_loc>

            <video:title>Distinct, identical or imaginary (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the discriminant to classify roots. You will learn to interpret the result to state whether solutions are real and distinct, identical, or imaginary without solving the equation. Solved: Determine the nature of the roots for the quadratic equation 2x^2 - 7x + 3 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/xp96Hw5DKWCG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y_LQY33LeYNB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/Y_LQY33LeYNB.jpg</video:thumbnail_loc>

            <video:title>The discriminant</video:title>

            <video:description><![CDATA[
This lesson defines the discriminant and explains its role in identifying the type of roots an equation has. You will learn to use the value of b² - 4ac to determine if solutions are real, equal, or non-real without solving the equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/Y_LQY33LeYNB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KK5IxD8vMq9Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/54/KK5IxD8vMq9Y.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning of functions and real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/54/KK5IxD8vMq9Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5PAqw_aO6bLk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/5PAqw_aO6bLk.jpg</video:thumbnail_loc>

            <video:title>Sum and product</video:title>

            <video:description><![CDATA[
This lesson defines the formulas for the sum and product of roots in terms of equation coefficients. You will learn to calculate these values directly without solving the quadratic equation itself.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/5PAqw_aO6bLk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UOIy4u2Hr5Wr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/UOIy4u2Hr5Wr.jpg</video:thumbnail_loc>

            <video:title>Fischer's projection</video:title>

            <video:description><![CDATA[
Fischer projections represent 3D chiral molecules on flat paper. How do you correctly assign R-S configuration when horizontal bonds project forward? We establish the vertical-group rule for accurate assignment.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/UOIy4u2Hr5Wr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l0LCOXAHRUQJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/l0LCOXAHRUQJ.jpg</video:thumbnail_loc>

            <video:title>Complex numbers</video:title>

            <video:description><![CDATA[
Meaning of complex numbers and their use.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/l0LCOXAHRUQJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0ZhPKqp6OFdj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/0ZhPKqp6OFdj.jpg</video:thumbnail_loc>

            <video:title>Properties of complex numbers</video:title>

            <video:description><![CDATA[
Some important properties of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/0ZhPKqp6OFdj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fKZTO_whJOK4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/108/fKZTO_whJOK4.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the curl of a vector field.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/108/fKZTO_whJOK4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CrY_9ycFOTUq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Thumbnails/115/CrY_9ycFOTUq.jpg</video:thumbnail_loc>

            <video:title>Euler's formula</video:title>

            <video:description><![CDATA[
The Euler formula and exponential form of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/A6MybVAaZ3/Previews/115/CrY_9ycFOTUq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_xv5l2sftmjv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/_xv5l2sftmjv.jpg</video:thumbnail_loc>

            <video:title>Symmetric identities (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to evaluate the sum of the reciprocals of roots using coefficients. You will learn to transform the expression into a ratio of the sum and product of roots to find the numerical value without solving the equation. Solved: Given that \alpha and \beta are the roots of 3x^2 - 7x + 2 = 0, find the value of \frac{1}{\alpha} + \frac{1}{\beta}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/_xv5l2sftmjv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rJpasEZ5f63g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/891/rJpasEZ5f63g.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
This lesson reviews all solution methods and analytical tools for quadratic equations. You will recap factorisation, the quadratic formula, discriminant properties, and root relationships to ensure a firm grasp of the entire course content.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/891/rJpasEZ5f63g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IIyzRj0WktV7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/222/IIyzRj0WktV7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector triple products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/222/IIyzRj0WktV7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_MOZ2ioGY9tm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/_MOZ2ioGY9tm.jpg</video:thumbnail_loc>

            <video:title>Symmetric identities (3)</video:title>

            <video:description><![CDATA[
This lesson shows how to evaluate advanced symmetric expressions like the sum of cubes of roots. You will learn to expand cubic algebraic identities to substitute the sum and product of roots and find the exact numerical result from the equation coefficients. Solved: If \alpha and \beta are the roots of x^2 - 4x + 1 = 0, calculate the value of \alpha^3 + \beta^3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/_MOZ2ioGY9tm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8KYYE4w7TGhD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/618/8KYYE4w7TGhD.jpg</video:thumbnail_loc>

            <video:title>L'Hopital's rule</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by L'Hopital's rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/618/8KYYE4w7TGhD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/owNryN4P5FuN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/owNryN4P5FuN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (15)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 4-Mg helicopter maneuvers a horizontal turn having a radius of curvature p=400m. Determine the lift force F_L required and the angle of the bank \theta when it is flying horizontally with a constant speed of v=40m/s. Show that \theta increases if v increases by also calculating \theta when v=60m/s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/owNryN4P5FuN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745931652801.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ZQiwnXHp5lk6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/156/ZQiwnXHp5lk6.jpg</video:thumbnail_loc>

            <video:title>Newton's second law</video:title>

            <video:description><![CDATA[
Newton's second law and inertial frames of reference.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/156/ZQiwnXHp5lk6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0tbVY4-0iwwy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/331/0tbVY4-0iwwy.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course, course outline, prerequisites and references.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/331/0tbVY4-0iwwy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7pUM7U4ouZpL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/7pUM7U4ouZpL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the method of undetermined coefficients. Solved: Solve the following:1 \frac {d^2y} {dx^2} = sin^{2}x2 \frac {dQ} {dt} + 4Q = 2cos 2t 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/7pUM7U4ouZpL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IdmWij1wRMF5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/59/IdmWij1wRMF5.jpg</video:thumbnail_loc>

            <video:title>Informal definition</video:title>

            <video:description><![CDATA[
Informal definition of continuity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/59/IdmWij1wRMF5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q7bBjR-gkRH7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/Q7bBjR-gkRH7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on gradients, directional derivatives and normals to surfaces. Solved: Obtain the gradient of \Phi(x,y,z)=xy^2z^3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/Q7bBjR-gkRH7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SZ9wXGTVawNC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/193/SZ9wXGTVawNC.jpg</video:thumbnail_loc>

            <video:title>Cartesian coordinates</video:title>

            <video:description><![CDATA[
Coordinate points, lines and surfaces on the Cartesian coordinate system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/193/SZ9wXGTVawNC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LNMGNehWCgwa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/57/LNMGNehWCgwa.jpg</video:thumbnail_loc>

            <video:title>Direct substitution</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by direct substitution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/57/LNMGNehWCgwa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lGbt8J4tQJsp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/57/lGbt8J4tQJsp.jpg</video:thumbnail_loc>

            <video:title>Theorems</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by use of fundamental theorems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/57/lGbt8J4tQJsp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/85vn7vnnK8HS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/85vn7vnnK8HS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the scalar triple product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/85vn7vnnK8HS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zsLWIQIREYv-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/57/zsLWIQIREYv-.jpg</video:thumbnail_loc>

            <video:title>Conjugates</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by use of conjugates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/57/zsLWIQIREYv-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fR_xNnhoeiXI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/fR_xNnhoeiXI.jpg</video:thumbnail_loc>

            <video:title>Indeterminate forms (2)</video:title>

            <video:description><![CDATA[
Indeterminate form 0*???.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/fR_xNnhoeiXI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vw9WsKqqdZH4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/Vw9WsKqqdZH4.jpg</video:thumbnail_loc>

            <video:title>Rectangular components</video:title>

            <video:description><![CDATA[
Definitions of position, velocity and acceleration of a particle in curvilinear motion using the Cartesian coordinate system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/Vw9WsKqqdZH4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8imENfSmxFQT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/8imENfSmxFQT.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Definition, notations and direction of the vector or cross product of two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/8imENfSmxFQT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yMUegNw7oWxh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/yMUegNw7oWxh.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: Determine the reactions at B and C when a=30mm. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/yMUegNw7oWxh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737104814998.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/f7b2IcomsZGh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/f7b2IcomsZGh.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 10-lb block is pressed against the spring so as to compress it 2 ft when it is at A. If the plane is smooth , determine the distance d, measured from the wall, to where the block strikes the ground. Neglect the size of the block. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/f7b2IcomsZGh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1746790036287.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/I-j_ASToidbE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/I-j_ASToidbE.jpg</video:thumbnail_loc>

            <video:title>Laplacian</video:title>

            <video:description><![CDATA[
Meaning of the Laplacian of scalar and vector fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/I-j_ASToidbE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HLOeqN-OuI7D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/HLOeqN-OuI7D.jpg</video:thumbnail_loc>

            <video:title>Directional derivative</video:title>

            <video:description><![CDATA[
Meaning of directional derivatives, their maximum values, and how they relate to gradients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/HLOeqN-OuI7D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_V3Y0W1wQ04S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/108/_V3Y0W1wQ04S.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of the curl of a vector field and irrotationality.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/108/_V3Y0W1wQ04S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ALs68b-rYesj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/108/ALs68b-rYesj.jpg</video:thumbnail_loc>

            <video:title>Illustration</video:title>

            <video:description><![CDATA[
Making sense of the curl of a vector field.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/108/ALs68b-rYesj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6RcCNbeC-9He</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/58/6RcCNbeC-9He.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on formal definition of infinite limits. Solved: Prove that \lim_{x\to0}\frac{1}{x^2}=\infty 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/58/6RcCNbeC-9He.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AYtLvKcVzcJM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/AYtLvKcVzcJM.jpg</video:thumbnail_loc>

            <video:title>The squeeze theorem (2)</video:title>

            <video:description><![CDATA[
Oscillating numerators over growing variables fail direct substitution at infinity. How do you trap the erratic term between two shrinking bounds to force the limit? Watch the squeeze theorem deliver the exact result. Solved: Evaluate \lim_{x \to \infty} \frac{\cos x}{x} using the Squeeze Theorem. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/AYtLvKcVzcJM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n5H6Exrk8i_o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/n5H6Exrk8i_o.jpg</video:thumbnail_loc>

            <video:title>Diastereomers</video:title>

            <video:description><![CDATA[
Stereoisomers with multiple chiral centres are not always mirror images. How do you classify pairs that differ at some but not all stereocentres? This lesson defines diastereomers and distinguishes them from enantiomers using structural analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/n5H6Exrk8i_o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IhXGqN6K3YCB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/60/IhXGqN6K3YCB.jpg</video:thumbnail_loc>

            <video:title>The max-min theorem</video:title>

            <video:description><![CDATA[
Understanding the max-min theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/60/IhXGqN6K3YCB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Tk_3VELWOPiw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/614/Tk_3VELWOPiw.jpg</video:thumbnail_loc>

            <video:title>Removable discontinuities</video:title>

            <video:description><![CDATA[
Meaning of removable and non-removable discontinuities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/614/Tk_3VELWOPiw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_Fz965n1H6ot</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/132/_Fz965n1H6ot.jpg</video:thumbnail_loc>

            <video:title>Maclaurin polynomials</video:title>

            <video:description><![CDATA[
Polynomial approximations of differentiable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/132/_Fz965n1H6ot.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Dy0QfYeT3T0Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/Dy0QfYeT3T0Y.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of higher-order derivatives and how to evaluate them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/Dy0QfYeT3T0Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MVqd5r6xH-_C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/615/MVqd5r6xH-_C.jpg</video:thumbnail_loc>

            <video:title>Quotients</video:title>

            <video:description><![CDATA[
Rule for differentiating the quotient of two functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/615/MVqd5r6xH-_C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vrkteOBdacHM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/58/vrkteOBdacHM.jpg</video:thumbnail_loc>

            <video:title>Formal definition</video:title>

            <video:description><![CDATA[
Formal (rigorous) definition of limits at infinity and infinite limits.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/58/vrkteOBdacHM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_AQvvhFzxtNf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/613/_AQvvhFzxtNf.jpg</video:thumbnail_loc>

            <video:title>Examples of continuous functions</video:title>

            <video:description><![CDATA[
Some examples of functions that are continuous everywhere in their domain of definition.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/613/_AQvvhFzxtNf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2sJjfN8rHDyt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/63/2sJjfN8rHDyt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on the Rolle's and mean-value theorems. Solved: Verify the mean-value theorem on the given interval, and find all values of x_o satisfying the conclusion:(a) f(x)=x^2-x;[3,5] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/63/2sJjfN8rHDyt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HM-CQqmxO8Se</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/HM-CQqmxO8Se.jpg</video:thumbnail_loc>

            <video:title>Solving problems</video:title>

            <video:description><![CDATA[
General mechanics problem solution approach.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/HM-CQqmxO8Se.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oRko4AX3PYzF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/oRko4AX3PYzF.jpg</video:thumbnail_loc>

            <video:title>Meso compounds</video:title>

            <video:description><![CDATA[
Molecules with chiral centres are not always optically active. Why do some compounds containing stereocentres remain achiral? This lesson explains meso compounds and identifies the internal plane of symmetry that cancels optical rotation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/oRko4AX3PYzF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b8ZIH39DfKEl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/b8ZIH39DfKEl.jpg</video:thumbnail_loc>

            <video:title>Velocity</video:title>

            <video:description><![CDATA[
Defining average and instantaneous values of speed and velocity for a particle undergoing rectilinear motion; implications of zero velocity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/b8ZIH39DfKEl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AQrKMCqzw3Xm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/AQrKMCqzw3Xm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of higher-order derivatives using the Leibnitz's formula. Solved: Obtain the nth derivative of (x^2+1)e^2x with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/AQrKMCqzw3Xm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i4GVYOYe__dm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/i4GVYOYe__dm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n\to \infty} \frac{3n+1}{7n-4} =\frac{3}{7} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/i4GVYOYe__dm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Nrf34bRhHMFS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/615/Nrf34bRhHMFS.jpg</video:thumbnail_loc>

            <video:title>Composites</video:title>

            <video:description><![CDATA[
Rules for differentiating composite functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/615/Nrf34bRhHMFS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rFyF24XKrTZi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/618/rFyF24XKrTZi.jpg</video:thumbnail_loc>

            <video:title>The squeeze theorem</video:title>

            <video:description><![CDATA[
Evaluating limits using the squeeze theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/618/rFyF24XKrTZi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Lqy5OXacZlvT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/57/Lqy5OXacZlvT.jpg</video:thumbnail_loc>

            <video:title>Graphing / use of calculator</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by graphing or use of a calculator.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/57/Lqy5OXacZlvT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nRC-qHNx42Fj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/200/nRC-qHNx42Fj.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and an overview of the course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/200/nRC-qHNx42Fj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hdII09HWmFgl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/66/hdII09HWmFgl.jpg</video:thumbnail_loc>

            <video:title>Kinds of sequences (1)</video:title>

            <video:description><![CDATA[
Positive, negative and alternating sequences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/66/hdII09HWmFgl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zev6_GyW4Sxw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/56/Zev6_GyW4Sxw.jpg</video:thumbnail_loc>

            <video:title>Formal definition</video:title>

            <video:description><![CDATA[
A formal (rigorous) definition of the limit of real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/56/Zev6_GyW4Sxw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EpT5NmYQNmx4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/132/EpT5NmYQNmx4.jpg</video:thumbnail_loc>

            <video:title>Taylor polynomials</video:title>

            <video:description><![CDATA[
Polynomial approximations of differentiable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/132/EpT5NmYQNmx4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_tsOY47c8MdT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1188/_tsOY47c8MdT.jpg</video:thumbnail_loc>

            <video:title>Nature of turning point</video:title>

            <video:description><![CDATA[
This lesson explains how the sign of the x-squared coefficient determines if a graph has a maximum or minimum turning point. You will learn to distinguish between a hill and a valley shape by inspecting the leading term of the equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1188/_tsOY47c8MdT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A60nXKoFPf74</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/A60nXKoFPf74.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n\to \infty} K=K 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/A60nXKoFPf74.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B19rAf0jC6Wo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/B19rAf0jC6Wo.jpg</video:thumbnail_loc>

            <video:title>Optical activity</video:title>

            <video:description><![CDATA[
Chiral compounds rotate plane-polarised light. How does rotation direction distinguish dextrorotatory from laevorotatory enantiomers? We define optical activity and link it to molecular handedness.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/B19rAf0jC6Wo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0CV_w0FPctSC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/195/0CV_w0FPctSC.jpg</video:thumbnail_loc>

            <video:title>Gradient</video:title>

            <video:description><![CDATA[
The gradient of a scalar in orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/195/0CV_w0FPctSC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hDZVRgw05CGZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/hDZVRgw05CGZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The system shown is at rest when a constant 30-lb force is applied to collar B,(a) If the force acts through the entire motion, determine the speed of collar B as it strikes the support at C.(b) After what distance d should the 30-lb force be removed if the collar is to reach support C with zero velocity? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/hDZVRgw05CGZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1746790766941.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ESFmhi9_vzYx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Thumbnails/387/ESFmhi9_vzYx.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of boundedness of a set of real numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Previews/387/ESFmhi9_vzYx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0YwNkA7CoYMW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/66/0YwNkA7CoYMW.jpg</video:thumbnail_loc>

            <video:title>Meaning</video:title>

            <video:description><![CDATA[
Meaning of sequences, and how they differ from progressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/66/0YwNkA7CoYMW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/g_NMULFlkADm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/60/g_NMULFlkADm.jpg</video:thumbnail_loc>

            <video:title>The intermediate-value theorem</video:title>

            <video:description><![CDATA[
Understanding the intermediate-value theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/60/g_NMULFlkADm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f3CwUunSN6W7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/f3CwUunSN6W7.jpg</video:thumbnail_loc>

            <video:title>Fundamental principles I</video:title>

            <video:description><![CDATA[
Fundamental concepts and principles on which the study of mechanics is based - the parallelogram law of addition of forces (vectors in general) and the principle of transmissibility of forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/f3CwUunSN6W7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZNqBKT012Wvf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/ZNqBKT012Wvf.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for the analysis of equilibrium of a rigid body under the action of forces in space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/ZNqBKT012Wvf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OHnzqixTZHE1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/65/OHnzqixTZHE1.jpg</video:thumbnail_loc>

            <video:title>Sum to infinity</video:title>

            <video:description><![CDATA[
Sum to infinity of various progressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/65/OHnzqixTZHE1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rrQhGBIzmF8n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/rrQhGBIzmF8n.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that a given sequence of real numbers can have at least one limit. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/rrQhGBIzmF8n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ln5BaxNbhS-v</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/62/Ln5BaxNbhS-v.jpg</video:thumbnail_loc>

            <video:title>Differentiability and its relation to continuity</video:title>

            <video:description><![CDATA[
How continuity and differentiability are related.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/62/Ln5BaxNbhS-v.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/10Rpiovrs7vH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/196/10Rpiovrs7vH.jpg</video:thumbnail_loc>

            <video:title>Some identities</video:title>

            <video:description><![CDATA[
Some vector product identities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/196/10Rpiovrs7vH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jI72EkKUs5JN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/692/jI72EkKUs5JN.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video provides a worked example for converting octal numbers to base 10. The same process and logic apply to all other number bases, reinforcing your understanding of the core conversion method.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/692/jI72EkKUs5JN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WfW7ZP909d6q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/97/WfW7ZP909d6q.jpg</video:thumbnail_loc>

            <video:title>Hyperboloids</video:title>

            <video:description><![CDATA[
Identifying hyperboloids - graphs and equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/97/WfW7ZP909d6q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JXwkBSTnUEFG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/135/JXwkBSTnUEFG.jpg</video:thumbnail_loc>

            <video:title>Polar coordinates</video:title>

            <video:description><![CDATA[
An overview of the polar coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/135/JXwkBSTnUEFG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ouy4OLazXTBL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/Ouy4OLazXTBL.jpg</video:thumbnail_loc>

            <video:title>Classification by variable substitution</video:title>

            <video:description><![CDATA[
Classification of quadric surfaces by variable substitution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/Ouy4OLazXTBL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d2b_W6XJKZmN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/197/d2b_W6XJKZmN.jpg</video:thumbnail_loc>

            <video:title>Laplacian (2)</video:title>

            <video:description><![CDATA[
The Laplacian of a vector field in orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/197/d2b_W6XJKZmN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/doU0-GtBH3Y7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/doU0-GtBH3Y7.jpg</video:thumbnail_loc>

            <video:title>Ellipse</video:title>

            <video:description><![CDATA[
Equation of an ellipse.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/doU0-GtBH3Y7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N1Xn0HUvzlS4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/96/N1Xn0HUvzlS4.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Introduction to transformation of coordinates by rotation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/96/N1Xn0HUvzlS4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4afS2cOGCMUD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/4afS2cOGCMUD.jpg</video:thumbnail_loc>

            <video:title>Three variables</video:title>

            <video:description><![CDATA[
Implicit differentiation of a function with two dependent variables and one independent variable using partial derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/4afS2cOGCMUD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/snK1kvpwDNPf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/133/snK1kvpwDNPf.jpg</video:thumbnail_loc>

            <video:title>Direct classification</video:title>

            <video:description><![CDATA[
Direct classification (identification) of quadric surfaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/133/snK1kvpwDNPf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Rl-9wQCXCiTl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/97/Rl-9wQCXCiTl.jpg</video:thumbnail_loc>

            <video:title>Ellipsoid</video:title>

            <video:description><![CDATA[
Identifying an ellipsoid - graph and equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/97/Rl-9wQCXCiTl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Nzhj6OGIsgwo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/83/Nzhj6OGIsgwo.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning and examples of equations in one variable, meaning root of an equation and zero of a function.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/83/Nzhj6OGIsgwo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bWmpfTtz2oh6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/97/bWmpfTtz2oh6.jpg</video:thumbnail_loc>

            <video:title>Cone</video:title>

            <video:description><![CDATA[
Identifying a cone - graph and equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/97/bWmpfTtz2oh6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nng9AmqaKa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/nng9AmqaKa.jpg</video:thumbnail_loc>

            <video:title>Exponential chain</video:title>

            <video:description><![CDATA[
Exponential functions repeat themselves when differentiated. How do you handle the inner linear term without losing the outer base? Watch the step-by-step solution to see the chain rule in action. Solved: Calculate the derivative of the function y = (e^{3x} + 5)^4 with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/nng9AmqaKa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3qUDOLyyGTyI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/692/3qUDOLyyGTyI.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video demonstrates how to convert hexadecimal numbers to base 10. We will walk through a complete worked example, solidifying the principles you've learned for converting any number base to denary.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/692/3qUDOLyyGTyI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0gaqI9KRnfqI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/692/0gaqI9KRnfqI.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson extends our conversion skills to numbers with decimal points. We will work through a practical example of converting a binary number with a fractional part to its base 10 equivalent. This is a crucial skill for real-world applications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/692/0gaqI9KRnfqI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vO9xi4Lr_pgv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/vO9xi4Lr_pgv.jpg</video:thumbnail_loc>

            <video:title>Mappings or functions</video:title>

            <video:description><![CDATA[
This lesson defines a function as a special relation where every input has exactly one output. You will learn to distinguish functions from ordinary relations and identify them using arrow diagrams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/vO9xi4Lr_pgv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WpPTbTw12LnX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/86/WpPTbTw12LnX.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
An overview of the theory of numerical integration methods.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/86/WpPTbTw12LnX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SANp16NqLdpW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/83/SANp16NqLdpW.jpg</video:thumbnail_loc>

            <video:title>Existence of a solution</video:title>

            <video:description><![CDATA[
Condition for the existence of a solution within an interval.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/83/SANp16NqLdpW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mrw62b6D8OeJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/222/mrw62b6D8OeJ.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Formal definition of the vector triple product or box product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/222/mrw62b6D8OeJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3Te9R6IvugaU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/3Te9R6IvugaU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: Block A has a mass of 60 kg and rests on block B, which has a mass of 30 kg. If the coefficients of static and kinetic friction are indicated in the figure, determine the largest horizontal force P which can be applied to block B so that block A does not slip on block B when block B slides. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/3Te9R6IvugaU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742300031517.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/LjK8h1_UHj8f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/83/LjK8h1_UHj8f.jpg</video:thumbnail_loc>

            <video:title>Bisection method</video:title>

            <video:description><![CDATA[
Bisection method of solution of equations in one variable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/83/LjK8h1_UHj8f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lAZiAsl-BdRJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/83/lAZiAsl-BdRJ.jpg</video:thumbnail_loc>

            <video:title>Overview of the bisection method</video:title>

            <video:description><![CDATA[
Advantages and disadvantages of the bisection method of solution of equations in one variable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/83/lAZiAsl-BdRJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XvaM3ifRy2uk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/XvaM3ifRy2uk.jpg</video:thumbnail_loc>

            <video:title>Newton's law of cooling</video:title>

            <video:description><![CDATA[
Modelling temperature change problems with first-order ordinary differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/XvaM3ifRy2uk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1mc8SIWJpdHR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/84/1mc8SIWJpdHR.jpg</video:thumbnail_loc>

            <video:title>Overview of Newton's method</video:title>

            <video:description><![CDATA[
Advantages and disadvantages of Newton's method solution of equations in one variable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/84/1mc8SIWJpdHR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WeXt0Sre3N_f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/WeXt0Sre3N_f.jpg</video:thumbnail_loc>

            <video:title>Symmetric suspension</video:title>

            <video:description><![CDATA[
Resolve tension in cables supporting a load at equal angles. This walkthrough applies free-body diagrams and equilibrium equations to find unknown force magnitudes. It provides the essential mathematical steps for solving symmetric suspension problems. Solved: 1. A 20.0\text{-kg} loudspeaker is hung from the ceiling by two cables, each making an angle of 30.0^{\circ} with the ceiling. Find the tension in each cable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/WeXt0Sre3N_f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XgRbt7Bs6AbR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/693/XgRbt7Bs6AbR.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson demonstrates converting denary numbers with decimal points to other bases. We will work through a complete example, applying the multiplication method to handle fractional parts and solidify your conversion skills.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/693/XgRbt7Bs6AbR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xN2wy3GLdKln</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/693/xN2wy3GLdKln.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to convert a denary number to an octal number. We'll use a worked example to apply the division method, reinforcing your ability to convert from base 10 to any other number base.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/693/xN2wy3GLdKln.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l35D7YiPSfgo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/197/l35D7YiPSfgo.jpg</video:thumbnail_loc>

            <video:title>Laplacian (1)</video:title>

            <video:description><![CDATA[
The Laplacian of a scalar field in orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/197/l35D7YiPSfgo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QrZWE1O14cG3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/QrZWE1O14cG3.jpg</video:thumbnail_loc>

            <video:title>Simple non-linear equations (1)</video:title>

            <video:description><![CDATA[
Solution of Bernoulli's ordinary differential equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/QrZWE1O14cG3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pV2VVuGLC1eN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/pV2VVuGLC1eN.jpg</video:thumbnail_loc>

            <video:title>Homogeneous equations</video:title>

            <video:description><![CDATA[
Solution of homogeneous differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/pV2VVuGLC1eN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A_QTHoCqo2OG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/A_QTHoCqo2OG.jpg</video:thumbnail_loc>

            <video:title>Linear differential equations</video:title>

            <video:description><![CDATA[
Solution linear differential equations with integrating factors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/A_QTHoCqo2OG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QLkVgalcaiHs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/QLkVgalcaiHs.jpg</video:thumbnail_loc>

            <video:title>Linear dependence</video:title>

            <video:description><![CDATA[
Understanding linear dependence of functions and the Wronskian.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/QLkVgalcaiHs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SeiKptA4cTy_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/SeiKptA4cTy_.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
An introduction to the vector equations of geometries.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/SeiKptA4cTy_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MjO3aH-jj_ht</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/135/MjO3aH-jj_ht.jpg</video:thumbnail_loc>

            <video:title>Spherical coordinates</video:title>

            <video:description><![CDATA[
An overview of the spherical coordinates system. Solved: Transform the equation x^2+y^2+2z^2-2x-3y-z=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/135/MjO3aH-jj_ht.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0yoi9H91TZAR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/618/0yoi9H91TZAR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of limits. Solved: Given that \lim_{x\to 0} \frac{e^{x} -1}{x}=1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/618/0yoi9H91TZAR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FU5eglUfNEow</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/FU5eglUfNEow.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n\to \infty}\frac{1}{n^2 +1}=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/FU5eglUfNEow.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gGHPhZSrby3Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/216/gGHPhZSrby3Z.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the coordinates of a vector with respect to a given basis of its vector space. Solved: Let v = (5,3,4) \epsilon \mathbb{R^3} and basis S= {(1, -1, 0), (1, 1, 0), (0, 1, 1)}. Find the coordinate of v relative to the basis S, [v]_s 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/216/gGHPhZSrby3Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FcdvALBnXrzU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/FcdvALBnXrzU.jpg</video:thumbnail_loc>

            <video:title>Numerical and symbolic solutions</video:title>

            <video:description><![CDATA[
Meaning and the need for numerical and symbolic solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/FcdvALBnXrzU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BVHjD9_FGrlN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/BVHjD9_FGrlN.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
What are differential equations?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/BVHjD9_FGrlN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R8rdVY7VTnqj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/R8rdVY7VTnqj.jpg</video:thumbnail_loc>

            <video:title>Ordinary and partial differential equations</video:title>

            <video:description><![CDATA[
Classification of differential equations into ordinary and partial differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/R8rdVY7VTnqj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q_pjQ8Qcp_vH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/Q_pjQ8Qcp_vH.jpg</video:thumbnail_loc>

            <video:title>Order of differential equations</video:title>

            <video:description><![CDATA[
Meaning of the order of differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/Q_pjQ8Qcp_vH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bhf49iOb8V4J</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/bhf49iOb8V4J.jpg</video:thumbnail_loc>

            <video:title>Newton's second law of motion</video:title>

            <video:description><![CDATA[
Worked examples on Newton's second law of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/bhf49iOb8V4J.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uWRT1uoOvnBK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/uWRT1uoOvnBK.jpg</video:thumbnail_loc>

            <video:title>Oblique trajectories</video:title>

            <video:description><![CDATA[
Determining the oblique trajectories of a family of curves.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/uWRT1uoOvnBK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O6Vngds1ypla</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/O6Vngds1ypla.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning, matrix representation and homogeneity of systems of linear equations  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/O6Vngds1ypla.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8qQ-ayDoAJnE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/8qQ-ayDoAJnE.jpg</video:thumbnail_loc>

            <video:title>Nonhomogeneous systems</video:title>

            <video:description><![CDATA[
Conditions for existence of different forms of solutions for nonhomogeneous systems of linear equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/8qQ-ayDoAJnE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5SC66IM-bvjW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/5SC66IM-bvjW.jpg</video:thumbnail_loc>

            <video:title>Non-homogeneous equations</video:title>

            <video:description><![CDATA[
Solution of non-homogeneous differential equations reducible to homogeneous form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/5SC66IM-bvjW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a8goieecBJ7D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/a8goieecBJ7D.jpg</video:thumbnail_loc>

            <video:title>Buffer solutions</video:title>

            <video:description><![CDATA[
This lesson explains how buffer solutions resist changes in pH when small amounts of acid or base are added. You will learn the composition of acidic and basic buffers and the chemical mechanisms behind their action. Master these principles to understand pH stability in biological and industrial systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/a8goieecBJ7D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/08dCKa_g1EIB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/103/08dCKa_g1EIB.jpg</video:thumbnail_loc>

            <video:title>Scalars, vectors and tensors</video:title>

            <video:description><![CDATA[
Meaning and examples of scalars, tensors and vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/103/08dCKa_g1EIB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AC1Uap-IRN6E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/103/AC1Uap-IRN6E.jpg</video:thumbnail_loc>

            <video:title>Levi-Civita</video:title>

            <video:description><![CDATA[
Levi-Civita notation and its use.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/103/AC1Uap-IRN6E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Tk1bEKU5GA5E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/Tk1bEKU5GA5E.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
Worked examples on the method of variation of parameters. Solved: Solve the following:1 y^{""} + y = tan x2 (x^2 + 1)y^{""} - 2xy' + 2y = 6(x^2 + 1)^2, given that y_c = c_1 {x} + c_2(x^2 + 1) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/Tk1bEKU5GA5E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s1xxnICwwRid</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/s1xxnICwwRid.jpg</video:thumbnail_loc>

            <video:title>Rank and nullity of a matrix</video:title>

            <video:description><![CDATA[
Meaning of rank and nullity of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/s1xxnICwwRid.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IXqg40R1zF_X</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/696/IXqg40R1zF_X.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video provides another worked example, this time solving a word problem involving number base multiplication. You will learn how to apply the learned principles to real-world scenarios, preparing you for complex exams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/696/IXqg40R1zF_X.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c7Ftx4YwkmvX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/696/c7Ftx4YwkmvX.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson provides a step-by-step worked example for multiplying numbers in other bases. You will learn the core rules and techniques, preparing you to solve more complex problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/696/c7Ftx4YwkmvX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eddtnWimAACE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/eddtnWimAACE.jpg</video:thumbnail_loc>

            <video:title>Matrix multiplication</video:title>

            <video:description><![CDATA[
How to multiply a matrix by another matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/eddtnWimAACE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BaANamqi4Ek9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/BaANamqi4Ek9.jpg</video:thumbnail_loc>

            <video:title>Properties of matrix addition</video:title>

            <video:description><![CDATA[
Commutativity, associativity, identity and inverse in the operation of addition of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/BaANamqi4Ek9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vno7biskYbA6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/vno7biskYbA6.jpg</video:thumbnail_loc>

            <video:title>More special matrices (4)</video:title>

            <video:description><![CDATA[
Unitary matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/vno7biskYbA6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qKJ0120Ufxdp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/qKJ0120Ufxdp.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning of elementary transformations - elementary row and column operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/qKJ0120Ufxdp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sz3eDGBZf2kF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/sz3eDGBZf2kF.jpg</video:thumbnail_loc>

            <video:title>Orthogonal trajectories</video:title>

            <video:description><![CDATA[
Determining the orthogonal trajectories of a family of curves.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/sz3eDGBZf2kF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tt_DQeWGe6lM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/tt_DQeWGe6lM.jpg</video:thumbnail_loc>

            <video:title>More special matrices (2)</video:title>

            <video:description><![CDATA[
Orthogonal matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/tt_DQeWGe6lM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rPnfa-kmHmA3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/rPnfa-kmHmA3.jpg</video:thumbnail_loc>

            <video:title>Row echelon form (1)</video:title>

            <video:description><![CDATA[
Meaning of a row echelon form of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/rPnfa-kmHmA3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XukKV19O27cG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/XukKV19O27cG.jpg</video:thumbnail_loc>

            <video:title>Adjoints</video:title>

            <video:description><![CDATA[
Definition of the adjoint of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/XukKV19O27cG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sQRBD-rb-NSO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/sQRBD-rb-NSO.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of eigenvalues and eigenvectors of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/sQRBD-rb-NSO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2yBiChd8FTCV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/2yBiChd8FTCV.jpg</video:thumbnail_loc>

            <video:title>Fundamental principles II</video:title>

            <video:description><![CDATA[
Fundamental concepts and principles on which the study of mechanics is based - Newton's three laws of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/2yBiChd8FTCV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IE2yTj4rMpP1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/IE2yTj4rMpP1.jpg</video:thumbnail_loc>

            <video:title>Steric factor</video:title>

            <video:description><![CDATA[
Electron maps do not tell the whole story. How does physical bulk block a reaction site even when electronics favour it? See how shape dictates chemical fate.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/IE2yTj4rMpP1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vN5NGpRob6Gd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/vN5NGpRob6Gd.jpg</video:thumbnail_loc>

            <video:title>Characteristic polynomials of degrees 2 and 3</video:title>

            <video:description><![CDATA[
Calculating characteristic polynomials of matrices of orders 2 and 3.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/vN5NGpRob6Gd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zdgeyA_fMV7i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/zdgeyA_fMV7i.jpg</video:thumbnail_loc>

            <video:title>Polynomials of matrices</video:title>

            <video:description><![CDATA[
Meaning of polynomials of matrices, and how to evaluate them by direct multiplication.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/zdgeyA_fMV7i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-GCCreoyjykX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/140/-GCCreoyjykX.jpg</video:thumbnail_loc>

            <video:title>Definitions</video:title>

            <video:description><![CDATA[
Meaning of quadratic and canonical forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/140/-GCCreoyjykX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U_fHD7IOBxHb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/U_fHD7IOBxHb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on identifying differential equations and their solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/U_fHD7IOBxHb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kc_qJxgrmR3P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/Kc_qJxgrmR3P.jpg</video:thumbnail_loc>

            <video:title>Cayley-Hamilton theorem</video:title>

            <video:description><![CDATA[
Statement of Cayley-Hamilton theorem; calculating the inverse of a matrix using Cayley-Hamilton theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/Kc_qJxgrmR3P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fmCSNF76GIqv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/fmCSNF76GIqv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on identifying differential equations and their solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/fmCSNF76GIqv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9RWeuJhdLdp6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/9RWeuJhdLdp6.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of diagonalization of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/9RWeuJhdLdp6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uPM8orcYyB6u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/uPM8orcYyB6u.jpg</video:thumbnail_loc>

            <video:title>Acceleration</video:title>

            <video:description><![CDATA[
Defining average and instantaneous acceleration for a particle undergoing rectilinear motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/uPM8orcYyB6u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cAV5Q83I-rJ6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/140/cAV5Q83I-rJ6.jpg</video:thumbnail_loc>

            <video:title>The coefficient matrix</video:title>

            <video:description><![CDATA[
How to obtain the [symmetric] coefficient matrix for quadratic and canonical forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/140/cAV5Q83I-rJ6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/24TphHL9BKtZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/151/24TphHL9BKtZ.jpg</video:thumbnail_loc>

            <video:title>Uniform velocity</video:title>

            <video:description><![CDATA[
Meaning of uniform motion and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/151/24TphHL9BKtZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xaUvFlNyoY-_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/xaUvFlNyoY-_.jpg</video:thumbnail_loc>

            <video:title>Fundamental principles III</video:title>

            <video:description><![CDATA[
Fundamental concepts and principles on which the study of mechanics is based - Newton's law of universal gravitation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/xaUvFlNyoY-_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SvkhdmFdVrBp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/SvkhdmFdVrBp.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on computing matrix inverses. Solved: Solve for x, y, and z using matrix inverse of3x - 2y + 2z = 10x + 2y - 3z = -14x + y + 2z = 3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/SvkhdmFdVrBp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/acAYP1vdgR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/acAYP1vdgR.jpg</video:thumbnail_loc>

            <video:title>Resonance stability ranking</video:title>

            <video:description><![CDATA[
Not all resonance forms are equal. How do charge location and octet completion decide the major contributor? Watch to rank stability with confidence. Solved: Rank the following resonance structures in order of increasing stability based on formal charge distribution.CH_2=CH-CH=CH_2CH_2=CH-CH=CH_2 \leftrightarrow CH_2^+-CH=CH-CH_2^- 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/acAYP1vdgR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FbIsnauwEc_U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/698/FbIsnauwEc_U.jpg</video:thumbnail_loc>

            <video:title>Problems</video:title>

            <video:description><![CDATA[
This lesson provides another set of miscellaneous problems to solve. You will combine all number base concepts???conversion, addition, subtraction, and multiplication???to master complex questions and reinforce your skills.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/698/FbIsnauwEc_U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ppxpcrf6LeGZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/Ppxpcrf6LeGZ.jpg</video:thumbnail_loc>

            <video:title>Engineering mechanics</video:title>

            <video:description><![CDATA[
Meaning of engineering, and the need for engineering mechanics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/Ppxpcrf6LeGZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/85t3tx5BQF0e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/85t3tx5BQF0e.jpg</video:thumbnail_loc>

            <video:title>Perpendicular vectors</video:title>

            <video:description><![CDATA[
Scalar products of perpendicular vectors and unit vectors; scalar product of two vectors in terms of their mutually-perpendicular components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/85t3tx5BQF0e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ONAoxpEF2fZd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/ONAoxpEF2fZd.jpg</video:thumbnail_loc>

            <video:title>Polynomials of matrices</video:title>

            <video:description><![CDATA[
Evaluating polynomials of matrices by diagonalization.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/ONAoxpEF2fZd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ob66HPg7Dydt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/Ob66HPg7Dydt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: At a given instant, the 20-lb block A is moving downwards with a speed of 6 ft/s. Determine its speed 2 s later if block B has a weight of 4 lb and the coefficient of kinetic friction between it and the inclined plane is \mu_k = 0.2. Neglect the mass of the pulleys and cord. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/Ob66HPg7Dydt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742306009496.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/yj9J8jbyPjAN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/yj9J8jbyPjAN.jpg</video:thumbnail_loc>

            <video:title>Factorisation</video:title>

            <video:description><![CDATA[
This lesson explains the factorisation method for solving quadratic equations by breaking the expression into linear factors. You will learn to use the zero-product property to find the roots efficiently when an equation is easily factorable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/yj9J8jbyPjAN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/647BmV_8OtVi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/647BmV_8OtVi.jpg</video:thumbnail_loc>

            <video:title>Particles and rigid bodies</video:title>

            <video:description><![CDATA[
Differences between particles and rigid bodies in the study of mechanics of rigid bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/647BmV_8OtVi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6lkBJ0nykLLx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/6lkBJ0nykLLx.jpg</video:thumbnail_loc>

            <video:title>Mechanics</video:title>

            <video:description><![CDATA[
Meaning and branches of mechanics; meaning and branches of the mechanics of rigid bodies - statics and dynamics; meaning and branches of dynamics - kinematics and kinetics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/6lkBJ0nykLLx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZHRhc9jFlJUr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/11/ZHRhc9jFlJUr.jpg</video:thumbnail_loc>

            <video:title>Onto a plane</video:title>

            <video:description><![CDATA[
Analysis of the projection of a vector on a plane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/11/ZHRhc9jFlJUr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2hEe4m5-Y9Wk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/2hEe4m5-Y9Wk.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning of rectilinear motion; defining the position, distance and displacement of a particle undergoing rectilinear motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/2hEe4m5-Y9Wk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rGV2i5JI04</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1085/rGV2i5JI04.jpg</video:thumbnail_loc>

            <video:title>Rate law basics</video:title>

            <video:description><![CDATA[
Reaction speed depends on reactant concentrations. How do you link rate to concentration mathematically without guessing the exponents? This lesson derives the rate law and defines reaction order precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1085/rGV2i5JI04.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nxUQM98jsjhd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/147/nxUQM98jsjhd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of motion of a rigid body undergoing general plane motion by locating an instantaneous centre of zero velocity. Solved: The attached wheels roll without slipping on the plates A and B, which are moving in opposite directions as shown. If v_A = 60 mm/s to the right and v_B = 200 mm/s to the left, determine the speed for the center O and the point P for the position shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/147/nxUQM98jsjhd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744986679451.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/YbDSbhzM6B0Q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/YbDSbhzM6B0Q.jpg</video:thumbnail_loc>

            <video:title>Suspension and pull</video:title>

            <video:description><![CDATA[
Resolve forces for loads at unequal angles or under horizontal pull. Use free-body diagrams and vector resolution to solve equilibrium equations for unknown tensions. Apply mathematical steps to calculate force magnitudes and verify cable safety limits. Solved: 3. A body of mass m is hung from a fixed point by a string. A horizontal force P is applied to the body until the string makes an angle \theta with the vertical. If the system is in equilibrium, find the values of P and the tension T of the string. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/YbDSbhzM6B0Q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nTxPO3lIGIdC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/nTxPO3lIGIdC.jpg</video:thumbnail_loc>

            <video:title>Linear dependence</video:title>

            <video:description><![CDATA[
Examining the linear dependence (or coplanarity) of three vectors by their scalar triple product.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/nTxPO3lIGIdC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TesuvqqbL8jM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/222/TesuvqqbL8jM.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the vector triple product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/222/TesuvqqbL8jM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0mPWpKktBoEV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/0mPWpKktBoEV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of two-variable real-valued functions. Solved: Evaluate \lim_{(x,y)\to(5, 1)} \frac {xy} {x + y} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/0mPWpKktBoEV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V7go6AoUYIk6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/V7go6AoUYIk6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of two-variable real-valued functions. Solved: Evaluate \lim_{\substack{x\to 0 \\ y\to 0}} \frac{x^2 y}{x^4+ y^2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/V7go6AoUYIk6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F05oTaCLeeHu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/F05oTaCLeeHu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of two-variable real-valued functions. Solved: Evaluate \lim_{\substack{x\to 0 \\ y\to 0}} \frac{x^2 y^3}{x^2 + y^2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/F05oTaCLeeHu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9QsJd5hIYssc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/9QsJd5hIYssc.jpg</video:thumbnail_loc>

            <video:title>Circle</video:title>

            <video:description><![CDATA[
Equation of a circle.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/9QsJd5hIYssc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gixXksdzM0vr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/gixXksdzM0vr.jpg</video:thumbnail_loc>

            <video:title>Purity check</video:title>

            <video:description><![CDATA[
Separation is not enough; you must verify. How do sharp melting and boiling points prove a sample is pure? Watch to confirm your results.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/gixXksdzM0vr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/36wvGEc5wVXt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/36wvGEc5wVXt.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/36wvGEc5wVXt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dGdlwbBx9ibG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/dGdlwbBx9ibG.jpg</video:thumbnail_loc>

            <video:title>Wall and string</video:title>

            <video:description><![CDATA[
Calculate tension and normal force for a sphere held against a smooth wall. Use free-body diagrams and equilibrium equations to resolve forces and find unknown magnitudes. This walkthrough shows the exact steps for solving static contact problems. Solved: 4. A uniform sphere of mass m is held against a smooth vertical wall by a string. The string is attached to the wall such that the sphere remains in equilibrium. Calculate the tension in the string and the normal force exerted by the wall on the sphere. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/dGdlwbBx9ibG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c0fL8wyzEu7O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/c0fL8wyzEu7O.jpg</video:thumbnail_loc>

            <video:title>Worked examples II</video:title>

            <video:description><![CDATA[
Worked examples on the equation of a hyperbola. Solved: 1 Sketch the hyperbola -\frac{x^2}{4} +\frac{y^2}{9} =12 Sketch the hyperbolax^2-9y^2-4x-54y-86=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/c0fL8wyzEu7O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SFLo0LikXLCg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/SFLo0LikXLCg.jpg</video:thumbnail_loc>

            <video:title>Worked examples IV</video:title>

            <video:description><![CDATA[
Worked examples on the equation of a circle. Solved: 1 Sketch x^2+y^2=42 Sketchx^2+y^2-6x+4y+9=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/SFLo0LikXLCg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_NDWzJMP0c7a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/_NDWzJMP0c7a.jpg</video:thumbnail_loc>

            <video:title>Hyperbolic forms</video:title>

            <video:description><![CDATA[
Hyperbolic integrands mix with inverse hyperbolic results from algebraic radicals. How do you scale sinh terms versus recognise the sum of squares pattern? We resolve both forms with precise standard rules. Solved: Evaluate the indefinite integral \int \left( 3 \sinh (4x) + \frac{1}{\sqrt{x^{2} + 9}} \right) dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/_NDWzJMP0c7a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aWqZEAOvawtw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/95/aWqZEAOvawtw.jpg</video:thumbnail_loc>

            <video:title>Worked examples III</video:title>

            <video:description><![CDATA[
More worked examples graphing in 3 dimensions. Solved: Graph x^2+y^2=4 in R2 and R3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/95/aWqZEAOvawtw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8soL9Jky9e9n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/103/8soL9Jky9e9n.jpg</video:thumbnail_loc>

            <video:title>Kronecker delta</video:title>

            <video:description><![CDATA[
Kronecker delta notation and its use.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/103/8soL9Jky9e9n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mpFKCzFAbyWm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/mpFKCzFAbyWm.jpg</video:thumbnail_loc>

            <video:title>Pull at constant speed</video:title>

            <video:description><![CDATA[
Learn how to calculate the coefficient of kinetic friction for a suitcase moving at a constant speed. You will resolve the pulling force into horizontal and vertical components to balance the forces acting on the body. This example shows how to use the equations of equilibrium in practice. Solved: 6. A traveller pulls a 20.0\text{-kg} suitcase across a horizontal floor at a constant speed using a strap held at an angle 35.0^{\circ} above the horizontal. If the pulling force is 35.0\text{N}, calculate the coefficient of kinetic friction \mu_k. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/mpFKCzFAbyWm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U3Rf3OXYE0ve</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/105/U3Rf3OXYE0ve.jpg</video:thumbnail_loc>

            <video:title>Vector fields</video:title>

            <video:description><![CDATA[
Meaning and examples of vector fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/105/U3Rf3OXYE0ve.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Am7VU38LayH0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/Am7VU38LayH0.jpg</video:thumbnail_loc>

            <video:title>Vector addition (1)</video:title>

            <video:description><![CDATA[
Triangle rule of addition of two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/Am7VU38LayH0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AHOjHWPM2Tkl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/AHOjHWPM2Tkl.jpg</video:thumbnail_loc>

            <video:title>Laws of vector algebra</video:title>

            <video:description><![CDATA[
Laws (properties) of vector addition and scalar multiplication.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/AHOjHWPM2Tkl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vaVkNXur2w9i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/vaVkNXur2w9i.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the divergence of vector fields and some Laplacian. Solved: Show that the vector \vec{F}=3y^2z\mathbf{i}-8x^2z\mathbf{j}+\sin x\mathbf{k} is solenoidal 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/vaVkNXur2w9i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/u3oU9TUqVNxC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/103/u3oU9TUqVNxC.jpg</video:thumbnail_loc>

            <video:title>Einstein's summation</video:title>

            <video:description><![CDATA[
Einstein's summation convention and its use.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/103/u3oU9TUqVNxC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DJgEB_ZzDDU6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/DJgEB_ZzDDU6.jpg</video:thumbnail_loc>

            <video:title>Common techniques</video:title>

            <video:description><![CDATA[
How do you separate solids from liquids or isolate pure crystals from impurities? Watch to master filtration, centrifuging, recrystallisation, and sublimation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/DJgEB_ZzDDU6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_FXvVBXYC41V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/_FXvVBXYC41V.jpg</video:thumbnail_loc>

            <video:title>Radical conversion</video:title>

            <video:description><![CDATA[
Roots cannot be integrated directly. How do you convert a radical into a fractional power for the standard rule? This walkthrough demonstrates the exact conversion and calculation. Solved: Find\int \sqrt[3]{x} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/_FXvVBXYC41V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H1HJUdfCl3c6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/H1HJUdfCl3c6.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating determinants by row and column operations. Solved: Evaluate the followinga. \begin{pmatrix} 100 & 101 & 102 \\101 &102 & 103 \\102 & 103 & 104\end{pmatrix} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/H1HJUdfCl3c6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dHbuiuxjJEbk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/dHbuiuxjJEbk.jpg</video:thumbnail_loc>

            <video:title>More worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating determinants by row and column operations. Solved: Evaluate \begin{pmatrix} 2 &5&-3&-2\\ -2&-3&2&-5\\1&3&-2&2\\-1&-6&4&3\end{pmatrix} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/dHbuiuxjJEbk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xef9-IO9ayPk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/xef9-IO9ayPk.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on elementary row operations. Solved: Determine the rank and nullity of the matrix A =\begin{pmatrix} 1&2&-3&0\\2&4&-2&-2\\3&6&-4&3\end{pmatrix} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/xef9-IO9ayPk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D_V5lu-yhiDq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/104/D_V5lu-yhiDq.jpg</video:thumbnail_loc>

            <video:title>Scalar products (2)</video:title>

            <video:description><![CDATA[
Scalar product of two vectors - using sign notations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/104/D_V5lu-yhiDq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IXFpOncH6Wf6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/104/IXFpOncH6Wf6.jpg</video:thumbnail_loc>

            <video:title>Vector products (1)</video:title>

            <video:description><![CDATA[
Vector product of two vectors - using their magnitudes and angle, and using their Cartesian components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/104/IXFpOncH6Wf6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/70mL-kg2J7mA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/70mL-kg2J7mA.jpg</video:thumbnail_loc>

            <video:title>Dependent motion (1)</video:title>

            <video:description><![CDATA[
Dependent motion of connected bodies and how to relate their positions, velocities and accelerations when the connecting cable(s) is (are) aligned with the direction(s) of motion of the bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/70mL-kg2J7mA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bb5X_r-TKc5U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/215/bb5X_r-TKc5U.jpg</video:thumbnail_loc>

            <video:title>Intersections</video:title>

            <video:description><![CDATA[
Bases and dimensions of the sum and intersection of two subspaces of a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/215/bb5X_r-TKc5U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JN9GUxsT5AXA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/11/JN9GUxsT5AXA.jpg</video:thumbnail_loc>

            <video:title>On another vector</video:title>

            <video:description><![CDATA[
Meaning of projection; analysis of the projection of a vector on another vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/11/JN9GUxsT5AXA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SRCP2v4eWimp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/SRCP2v4eWimp.jpg</video:thumbnail_loc>

            <video:title>Two bodies on a surface (2)</video:title>

            <video:description><![CDATA[
General approach for force-acceleration analysis of absolute and relative motion of bodies in contact, for two bodies on a surface.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/SRCP2v4eWimp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V_A_cFCxZ7aM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/V_A_cFCxZ7aM.jpg</video:thumbnail_loc>

            <video:title>Steam distillation</video:title>

            <video:description><![CDATA[
How do you purify heat-sensitive compounds without burning them? Watch to see how steam and Dalton’s law lower boiling points safely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/V_A_cFCxZ7aM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/46VcvuOu0aGP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/46VcvuOu0aGP.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: The firing mechanism of a pinball machine consists of a plunger P having a mass of 0.25 kg and a spring of stiffness 200 N/m. When s = 0, the spring is compressed 50 mm. If the arm is pulled back such that s= 100 mm and released, determine the speed of the 0.3-kg pinball B just before the plunger strikes the stop, i.e, s = 0. Assume all surfaces of contact to be smooth. The ball moves in the horizontal plane. Neglect friction, the mass of the spring, and the rolling motion of the ball. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/46VcvuOu0aGP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747071911435.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/FWaWkPyuL0bU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/FWaWkPyuL0bU.jpg</video:thumbnail_loc>

            <video:title>Rational function split</video:title>

            <video:description><![CDATA[
Complex fractions block direct integration. How do you split the numerator to separate each term? This walkthrough shows the division and power conversion for easy calculation. Solved: Find the indefinite integral \int \frac{x + 5}{\sqrt{x}} dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/FWaWkPyuL0bU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MvYYBMxrSpHu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/133/MvYYBMxrSpHu.jpg</video:thumbnail_loc>

            <video:title>What if cross-product terms exist?</video:title>

            <video:description><![CDATA[
The implication, and how to identify surfaces, when defined with cross-product terms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/133/MvYYBMxrSpHu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z4DPVKDyYRan</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/97/Z4DPVKDyYRan.jpg</video:thumbnail_loc>

            <video:title>Paraboloids</video:title>

            <video:description><![CDATA[
Identifying paraboloids - graphs and equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/97/Z4DPVKDyYRan.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DYccVreCImSX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/617/DYccVreCImSX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on the proof of limits of functions. Solved: Prove that \lim_{x\to 2}x^2=4 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/617/DYccVreCImSX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GYF0RLwXTbnl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/543/GYF0RLwXTbnl.jpg</video:thumbnail_loc>

            <video:title>Erratic motion</video:title>

            <video:description><![CDATA[
Meaning of erratic motion and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/543/GYF0RLwXTbnl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/anm2pTwst_gx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/105/anm2pTwst_gx.jpg</video:thumbnail_loc>

            <video:title>Scalar fields</video:title>

            <video:description><![CDATA[
Meaning and examples of scalar fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/105/anm2pTwst_gx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VNkZVplTZcgv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/VNkZVplTZcgv.jpg</video:thumbnail_loc>

            <video:title>Transcendentals of matrices</video:title>

            <video:description><![CDATA[
Evaluating exponentials, logarithms, sines, cosines, etc., of matrices - by diagonalization.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/VNkZVplTZcgv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zYsEbXhWWNSL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/151/zYsEbXhWWNSL.jpg</video:thumbnail_loc>

            <video:title>Uniform acceleration</video:title>

            <video:description><![CDATA[
Meaning of uniformly-accelerated motion and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/151/zYsEbXhWWNSL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CgoO3870Jn9B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/CgoO3870Jn9B.jpg</video:thumbnail_loc>

            <video:title>Analysis of steam distillation</video:title>

            <video:description><![CDATA[
How do vapour pressure and molar mass dictate the yield of steam distillation? Watch to master the ratio formula and selection criteria.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/CgoO3870Jn9B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yJgPAkU_OeZK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/yJgPAkU_OeZK.jpg</video:thumbnail_loc>

            <video:title>Eigenvalue inspection</video:title>

            <video:description><![CDATA[
Predicting the nature of a quadric surface by inspection of the eigenvalues of its symmetric coefficient matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/yJgPAkU_OeZK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pCxeaMXZkdJW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/pCxeaMXZkdJW.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and illustration of the components of a vector along arbitrary directions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/pCxeaMXZkdJW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F1nIxQmgGvE7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/108/F1nIxQmgGvE7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the curl of a vector field. Solved: Given that \vec{H}=3y^4\mathbf{i}-\cos x\mathbf{j}+e^{3x^2}\mathbf{k}. Find curl \vec{H}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/108/F1nIxQmgGvE7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/47xThxHBaNpE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/47xThxHBaNpE.jpg</video:thumbnail_loc>

            <video:title>Variable-separable equations</video:title>

            <video:description><![CDATA[
Solution of variable-separable differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/47xThxHBaNpE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lvHIoOROdbBm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/108/lvHIoOROdbBm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the curl of a vector field. Solved: Show that {(xyz})^6(x^\alpha\mathbf{i}+y^\alpha\mathbf{j}+z^\alpha\mathbf{k}) is irrational, then either b=0 or \alpha=-1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/108/lvHIoOROdbBm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PtXUH-CserY4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/108/PtXUH-CserY4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the curl of a vector field. Solved: Show that \nabla\times\left(\frac{\vec{r}}{r^2}\right)=\vec0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/108/PtXUH-CserY4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i2MWbLBPyMIQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/80/i2MWbLBPyMIQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on partial derivatives of composite functions. Solved: If f(u)=sinu and u=\sqrt{x^2+y^2}, find \frac{\partial f}{\partial x} and \frac{\partial f}{\partial y}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/80/i2MWbLBPyMIQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UafdNjWBX3jP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/UafdNjWBX3jP.jpg</video:thumbnail_loc>

            <video:title>Level curves and surfaces</video:title>

            <video:description><![CDATA[
Meaning of level curves and surfaces, and their relation to the gradient.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/UafdNjWBX3jP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IKJnYPSdO4p8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/IKJnYPSdO4p8.jpg</video:thumbnail_loc>

            <video:title>General solution of homogeneous equations</video:title>

            <video:description><![CDATA[
Linearly-independent solutions and the general solution of homogeneous linear second-order differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/IKJnYPSdO4p8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nYb4DkdPfukv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/215/nYb4DkdPfukv.jpg</video:thumbnail_loc>

            <video:title>Sums</video:title>

            <video:description><![CDATA[
Meaning of the sum of two subspaces of a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/215/nYb4DkdPfukv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9M3EoaBPEGnN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/9M3EoaBPEGnN.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity (5)</video:title>

            <video:description><![CDATA[
Radical quotients at negative infinity hide a sign trap. How do you pull the variable from the root while keeping the correct sign? Watch the absolute value step settle the limit. Solved: Evaluate \lim_{x \to -\infty} \frac{\sqrt{4x^2 + 1}}{x + 3}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/9M3EoaBPEGnN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OQT3zr_NzU9Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/OQT3zr_NzU9Z.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on general curvilinear motion concepts. Solved: A particle travels along the curve from A to B in 5s. It takes 8s for it to go from B to C and 10s to go from C to A. Determine the average speed when it goes around the closed path. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/OQT3zr_NzU9Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742210254882.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/N7aa29_h25Rr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/N7aa29_h25Rr.jpg</video:thumbnail_loc>

            <video:title>Rough ramp</video:title>

            <video:description><![CDATA[
This lesson calculates the minimum and maximum forces required to keep an object still on a rough ramp. You will determine the force range that prevents sliding by resolving gravity and static friction components. Solved: 2. A crate of mass 25.0\text{ kg} rests on a rough ramp inclined at \theta = 30.0^{\circ}. The coefficient of static friction between the crate and the ramp is \mu_s = 0.30. A worker pushes on the crate with a force P. (a) Calculate the minimum force P_{\text{min}} required to prevent the crate from sliding down the ramp. (b) Calculate the maximum force P_{\text{max}} the worker can apply before the crate starts sliding up the incline. (c) What is the full range of values of P for which the crate is stationary? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/N7aa29_h25Rr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n82YNRkGqac0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/n82YNRkGqac0.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Master the qualitative logic of Le Chateliers principle to predict how dynamic systems counteract external stresses. You will establish the fundamental framework for determining equilibrium shifts in response to changes in concentration, pressure, and temperature.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/n82YNRkGqac0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Hnl7PFfElmP5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/8/Hnl7PFfElmP5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on position vectors. Solved: Prove that the medians of a triangle are concurrent. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/8/Hnl7PFfElmP5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QwN2kBjL_Zc2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/QwN2kBjL_Zc2.jpg</video:thumbnail_loc>

            <video:title>Solving homogeneous equations with constant coefficients (2)</video:title>

            <video:description><![CDATA[
How to obtain the general solution of homogeneous equations with constant coefficients from the roots of the auxiliary equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/QwN2kBjL_Zc2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5wS6Wg-oUZ21</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/5wS6Wg-oUZ21.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating first and higher-order partial derivatives using the general methods of differentiation. Solved: Given that f(x, y, z) = e^{2z}cos(xy), obtain \frac {\partial f} {\partial x}, \frac {\partial f} {\partial y} and \frac {\partial f} {\partial z}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/5wS6Wg-oUZ21.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kW6J-do9r4Hm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/104/kW6J-do9r4Hm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on scalar and vector products using sign functions. Solved: Prove that (\vec{c}\times\vec{b})\times\vec{a}=\vec{a}\times(\vec{b}\times\vec{c}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/104/kW6J-do9r4Hm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vc9JAC6fSL6m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/Vc9JAC6fSL6m.jpg</video:thumbnail_loc>

            <video:title>Principle of conservation of energy</video:title>

            <video:description><![CDATA[
Conditions under which mechanical energy is conserved - their implications and equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/Vc9JAC6fSL6m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/opDi6rcsh-k2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/opDi6rcsh-k2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/opDi6rcsh-k2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/78gxgKO4xU88</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/78gxgKO4xU88.jpg</video:thumbnail_loc>

            <video:title>Potential energy</video:title>

            <video:description><![CDATA[
Meaning of energy, potential energy and an introduction to conservative forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/78gxgKO4xU88.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7mBKTRwXT915</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/7mBKTRwXT915.jpg</video:thumbnail_loc>

            <video:title>Conservation of linear momentum</video:title>

            <video:description><![CDATA[
Conditions under which linear momentum is conserved, and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/7mBKTRwXT915.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yg-Nnqrb2kGI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/yg-Nnqrb2kGI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: The 50-kg crate is stationary when the force P is applied. Determine the resulting acceleration of the crate if(a) P = 0, (b) P = 150 N, (c) P = 300 N. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/yg-Nnqrb2kGI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742297553466.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/DBHx11eXk51x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/86/DBHx11eXk51x.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on integration by the trapezoidal rule. Solved: Evaluate I = \int_{0}^{\frac 1 2}{\frac {dx} {\sqrt{1 - x}}} using the trapezoidal rule with five ordinates. Find the exact value of I. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/86/DBHx11eXk51x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CUHpnij4Ji1w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/85/CUHpnij4Ji1w.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on numerical integration. Solved: Suppose f(0) = 1.0000, f(0.25) = 0.8000, f(0.50) = \alpha, f(0.75) = 0.5714 and f(1.0) = 0.5000. Find \alpha if the Simpson's one-third rule with n = 4 gives the value 0.6932 for \int_{0}^{1}f(x)dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/85/CUHpnij4Ji1w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y6UwIY_1e-4A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/85/y6UwIY_1e-4A.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on numerical integration. Solved: For a function f(x), the trapezoidal rules gives \int_{2}^{18} f(x)dx = 10 sq. units. If f(2) = 12c, f(6) = 1, f(10) = 2, f(14) = 3, f(18) = 5c^2, find the possible values of c. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/85/y6UwIY_1e-4A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VLB9qq-pDx7o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/VLB9qq-pDx7o.jpg</video:thumbnail_loc>

            <video:title>Conservative forces</video:title>

            <video:description><![CDATA[
A closer look at conservative forces and their properties.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/VLB9qq-pDx7o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gjcl8onvho5m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/Gjcl8onvho5m.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of impact; types of impact based on the orientations of line of impact and velocities of the bodies involved.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/Gjcl8onvho5m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0X3B6Jsh44Pm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/0X3B6Jsh44Pm.jpg</video:thumbnail_loc>

            <video:title>Work and kinetic energy</video:title>

            <video:description><![CDATA[
Relation between work done by a force and the change in kinetic energy of the body it works on.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/0X3B6Jsh44Pm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NU-dikt223Nl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/NU-dikt223Nl.jpg</video:thumbnail_loc>

            <video:title>Coefficient of restitution</video:title>

            <video:description><![CDATA[
Meaning and determination of the coefficient of restitution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/NU-dikt223Nl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9uOZS3678S1Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/9uOZS3678S1Z.jpg</video:thumbnail_loc>

            <video:title>Selectors</video:title>

            <video:description><![CDATA[
This lesson covers how to target HTML elements. We will explain element, class, and ID selectors, which are the primary tools for applying styles to your page.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/9uOZS3678S1Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/djC2_6ItT3Bl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/djC2_6ItT3Bl.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General analysis procedure for motion of particles under conservative forces by considering the conservation of mechanical energy in the system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/djC2_6ItT3Bl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iaTgDdyt1yRK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/iaTgDdyt1yRK.jpg</video:thumbnail_loc>

            <video:title>One body on a surface</video:title>

            <video:description><![CDATA[
General approach for force-acceleration analysis of absolute and relative motion of bodies in contact, for one body on a surface.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/iaTgDdyt1yRK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D0HIpsLvg2ii</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/D0HIpsLvg2ii.jpg</video:thumbnail_loc>

            <video:title>Connected bodies</video:title>

            <video:description><![CDATA[
Calculate the mass needed to stop a block from sliding down a slope. You will balance tension, gravity, and friction to keep connected objects at rest on both smooth and rough surfaces. Solved: 8. Block A of mass 10.0\text{ kg} rests on an incline angled at 45.0^{\circ} to the horizontal. It is connected by a light, inextensible string that passes over a frictionless pulley to a hanging bucket B of mass m_B. (a) Calculate the mass m_B of bucket B required to hold block A in place, assuming the incline is smooth.(b) If the incline is rough (with \mu_s = 0.40), calculate the minimum mass of bucket B required to prevent block A from sliding down the incline. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/D0HIpsLvg2ii.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uht_YLwq8N8S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/13/uht_YLwq8N8S.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Formal definition of the scalar or dot product of two vectors, and its relation to the projection of a vector on another vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/13/uht_YLwq8N8S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8XxxSj7jXwhu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/8XxxSj7jXwhu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: A tank car is stopped by two spring bumpers A and B having a stiffness of k_A = 15(10^3) lb/ft and k_B = 20(10^3) lb/ft, respectively. Bumper A is attached to the car, whereas bumper B is attached to the wall. If the car has a weight of 25(10^3) lb and is freely coasting at 3 ft/s, determine the maximum deflection of each spring at the instant the bumpers stop the car. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/8XxxSj7jXwhu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747311201263.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/b-9vWxv9K5a0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/b-9vWxv9K5a0.jpg</video:thumbnail_loc>

            <video:title>Conjugates</video:title>

            <video:description><![CDATA[
Conjugates of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/b-9vWxv9K5a0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xnqoexRG7r4J</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/202/xnqoexRG7r4J.jpg</video:thumbnail_loc>

            <video:title>Representation</video:title>

            <video:description><![CDATA[
Representation of a complex number on the Argand plane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/202/xnqoexRG7r4J.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b9PTKqwLRDs_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/196/b9PTKqwLRDs_.jpg</video:thumbnail_loc>

            <video:title>Curl</video:title>

            <video:description><![CDATA[
The curl of a vector field in orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/196/b9PTKqwLRDs_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SS2usP2eeYvm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/SS2usP2eeYvm.jpg</video:thumbnail_loc>

            <video:title>Work of a constant force</video:title>

            <video:description><![CDATA[
Calculating the work done by a force of constant magnitude and direction in rectilinear motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/SS2usP2eeYvm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TFxBDI02URwr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/TFxBDI02URwr.jpg</video:thumbnail_loc>

            <video:title>Multiplication</video:title>

            <video:description><![CDATA[
Multiplication of complex numbers in polar form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/TFxBDI02URwr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NbgzjzvxszlK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/NbgzjzvxszlK.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of the gradient of a scalar field, potential or gradient fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/NbgzjzvxszlK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DBcSefMyCo-L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/194/DBcSefMyCo-L.jpg</video:thumbnail_loc>

            <video:title>Arc length</video:title>

            <video:description><![CDATA[
Arc length (length element) in orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/194/DBcSefMyCo-L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aalCCmpORIC3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/194/aalCCmpORIC3.jpg</video:thumbnail_loc>

            <video:title>Right-handed systems</video:title>

            <video:description><![CDATA[
Meaning of right-handed systems, and the implication of right-handedness for vector products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/194/aalCCmpORIC3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Yakub3M0iTJy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/Yakub3M0iTJy.jpg</video:thumbnail_loc>

            <video:title>Direction cosines</video:title>

            <video:description><![CDATA[
Relationships between the scalar product, direction cosines of vectors and the angle between two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/Yakub3M0iTJy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LM0XNrd225jK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/196/LM0XNrd225jK.jpg</video:thumbnail_loc>

            <video:title>Divergence</video:title>

            <video:description><![CDATA[
The divergence of a vector field in orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/196/LM0XNrd225jK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vV3d7mBRs_5J</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/vV3d7mBRs_5J.jpg</video:thumbnail_loc>

            <video:title>Division</video:title>

            <video:description><![CDATA[
Division of complex numbers in polar form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/vV3d7mBRs_5J.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/51D4KymLtu_4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/12/51D4KymLtu_4.jpg</video:thumbnail_loc>

            <video:title>Weighted mean</video:title>

            <video:description><![CDATA[
Meaning and analysis of the weighted mean of a number of points.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/12/51D4KymLtu_4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vu6Zjs5RfzuA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/Vu6Zjs5RfzuA.jpg</video:thumbnail_loc>

            <video:title>Equality</video:title>

            <video:description><![CDATA[
Equality (and inequality) of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/Vu6Zjs5RfzuA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K3dp_0uWfZHl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/95/K3dp_0uWfZHl.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
An introduction to the 3-dimensional Cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/95/K3dp_0uWfZHl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0w0MTe_oyMA7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/0w0MTe_oyMA7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: A circular plate of 120-mm radius is supported by two bearings A and B with a constant angular velocity of 26rad/s. Knowing that, at the instant considered, the velocity of point C is directed to the right, determine the velocity and acceleration of point E. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/0w0MTe_oyMA7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743850573247.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/uVSueY1QIS40</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/uVSueY1QIS40.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Determine the coordinate direction angles of F_1 and indicate them on the figure. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/uVSueY1QIS40.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739793600109.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/SoTO43IEHCeE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/80/SoTO43IEHCeE.jpg</video:thumbnail_loc>

            <video:title>Chain rule</video:title>

            <video:description><![CDATA[
Chain rule of differentiation for partial derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/80/SoTO43IEHCeE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HvhKl6c_iQzM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/205/HvhKl6c_iQzM.jpg</video:thumbnail_loc>

            <video:title>Multiplication, division and powers</video:title>

            <video:description><![CDATA[
Multiplication, division and powers of complex numbers in exponential form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/205/HvhKl6c_iQzM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JH2x4AIEvIHN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/205/JH2x4AIEvIHN.jpg</video:thumbnail_loc>

            <video:title>Representation</video:title>

            <video:description><![CDATA[
The Eulerian representation of a complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/205/JH2x4AIEvIHN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pvn7ws-4j1fG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/541/Pvn7ws-4j1fG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on problems involving derivation of the definition of a linear map from some known images. Solved: Suppose T: \mathbb{R}^2 \to P_2 is linear, such that T(1, 1) = 2 - 3x + x^2 and T(2, 3) = 1 - x^2. Find T(-1, 2) and T(a, b). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/541/Pvn7ws-4j1fG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/988Yja2dtvUv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/988Yja2dtvUv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving algebraic relations. Solved: Pegs A and B are restricted to move in the elliptical slots due to the motion of the slotted link. If the link moves with a constant speed of 10 m/s, determine the magnitudes of the velocity and acceleration of peg A when x = 1m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/988Yja2dtvUv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742212992358.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/LbQdkk3viL9-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/208/LbQdkk3viL9-.jpg</video:thumbnail_loc>

            <video:title>Expression</video:title>

            <video:description><![CDATA[
General expression for logarithms of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/208/LbQdkk3viL9-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qyo9COdly3RU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/qyo9COdly3RU.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties and identities of algebra of complex numbers and their conjugates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/qyo9COdly3RU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ojAnMQEemQRw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/207/ojAnMQEemQRw.jpg</video:thumbnail_loc>

            <video:title>Expressions</video:title>

            <video:description><![CDATA[
Expressions for hyperbolic Sine and Cosine using complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/207/ojAnMQEemQRw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lsrDr5GiUZic</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/lsrDr5GiUZic.jpg</video:thumbnail_loc>

            <video:title>Parallel vectors</video:title>

            <video:description><![CDATA[
Vector product of parallel and anti-parallel (like and unlike) vectors and unit vectors; vector product of two vectors in terms of their Cartesian components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/lsrDr5GiUZic.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4f3fAIm8XOml</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/4f3fAIm8XOml.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the scalar triple product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/4f3fAIm8XOml.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iGG8KtgFkltm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/iGG8KtgFkltm.jpg</video:thumbnail_loc>

            <video:title>Geometric meaning</video:title>

            <video:description><![CDATA[
A geometric interpretation of the magnitude of a cross product of two vectors as the area of some parallelogram.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/iGG8KtgFkltm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y3ITPCYxdH5h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/y3ITPCYxdH5h.jpg</video:thumbnail_loc>

            <video:title>Vector addition (3)</video:title>

            <video:description><![CDATA[
Polygon rule of vector addition.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/y3ITPCYxdH5h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TWEcH-SdMG27</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/156/TWEcH-SdMG27.jpg</video:thumbnail_loc>

            <video:title>Forces and reactions (1)</video:title>

            <video:description><![CDATA[
Meaning and modelling of forces and reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/156/TWEcH-SdMG27.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A27-cDUTsjL9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/A27-cDUTsjL9.jpg</video:thumbnail_loc>

            <video:title>Equality</video:title>

            <video:description><![CDATA[
Equality of complex numbers in polar form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/A27-cDUTsjL9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5MXMEBF9NKs9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/5MXMEBF9NKs9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/5MXMEBF9NKs9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dgktcGnzUqgK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/dgktcGnzUqgK.jpg</video:thumbnail_loc>

            <video:title>Axioms, conjectures, theorems, etc.</video:title>

            <video:description><![CDATA[
Meaning and examples of axioms, conjectures, theorems, lemma, corollary, theory, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/dgktcGnzUqgK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MNUx7MnQsCXX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/MNUx7MnQsCXX.jpg</video:thumbnail_loc>

            <video:title>De-Moivre's theorem</video:title>

            <video:description><![CDATA[
Statement and proof of De-Moivre's theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/MNUx7MnQsCXX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YFC697mIgTbi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/YFC697mIgTbi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The force F, acting in a constant direction on the 20-kg block, has a magnitude which varies with the positions s of the block. Determine how far the block must slide before its velocity becomes 15m/s. When s=0 the block is moving to the right at v=6m/s. The coefficient of the kinetic friction between the block and the surface is u_k=0.3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/YFC697mIgTbi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1746533576468.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/aZoL5xwHHiLu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/aZoL5xwHHiLu.jpg</video:thumbnail_loc>

            <video:title>Smooth horizontal floor</video:title>

            <video:description><![CDATA[
Learn how to calculate the acceleration of a crate being pulled across a smooth horizontal floor. You will apply Newton's second law to relate the constant horizontal force and mass to the resulting motion. This walkthrough demonstrates the basic application of F = ma in a frictionless system. Solved: 1. A 40.0\text{-kg} crate is pulled across a smooth horizontal floor by a constant horizontal force of 120\text{N}. Calculate the acceleration of the crate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/aZoL5xwHHiLu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UqnKAYlYdDWj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/UqnKAYlYdDWj.jpg</video:thumbnail_loc>

            <video:title>Solution of weak bases</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the pOH and pH of weak base solutions using the base dissociation constant, Kb. You will learn to use ICE tables to find hydroxide ion concentrations and convert these values to pH. Follow these worked examples to master weak base equilibrium arithmetic. Solved: For illustration: Dimethylamine has K_b value of 5.9 \times 10^{-4}. Calculate the pH of a 1.5M solution of this base 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/UqnKAYlYdDWj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/q7U-Ro1J-Vsi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/q7U-Ro1J-Vsi.jpg</video:thumbnail_loc>

            <video:title>Powers</video:title>

            <video:description><![CDATA[
Powers of complex numbers in polar form and an introduction to De-Moivre's theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/q7U-Ro1J-Vsi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZUwzf60cq-mA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/202/ZUwzf60cq-mA.jpg</video:thumbnail_loc>

            <video:title>Properties of the modulus</video:title>

            <video:description><![CDATA[
Properties of the modulus of a complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/202/ZUwzf60cq-mA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sEpm4jAJMqnA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/sEpm4jAJMqnA.jpg</video:thumbnail_loc>

            <video:title>Representation</video:title>

            <video:description><![CDATA[
Representation of a complex number in polar coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/sEpm4jAJMqnA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3u1JoCwFwZGD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/3u1JoCwFwZGD.jpg</video:thumbnail_loc>

            <video:title>Vector spaces</video:title>

            <video:description><![CDATA[
Definition of [linear] vector spaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/3u1JoCwFwZGD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RFAIU6-w3Dte</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/RFAIU6-w3Dte.jpg</video:thumbnail_loc>

            <video:title>Roots</video:title>

            <video:description><![CDATA[
How to find all roots of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/RFAIU6-w3Dte.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nGBy5XSbefkp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/nGBy5XSbefkp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/nGBy5XSbefkp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w4xcQd0tdWCA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/216/w4xcQd0tdWCA.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of the coordinates of a vector with respect to a given basis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/216/w4xcQd0tdWCA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FI0kmCK7S4oM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/FI0kmCK7S4oM.jpg</video:thumbnail_loc>

            <video:title>The quadratic formula</video:title>

            <video:description><![CDATA[
This lesson shows how to use the quadratic formula to solve an equation. You will learn to correctly substitute values for a, b, and c into the formula to find the numerical roots. Solved: Apply the quadratic formula to find the roots of the equation 3x^2 - 10x + 3 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/FI0kmCK7S4oM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/urMMTqIuxxOp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/urMMTqIuxxOp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: A baseball pitching machine "throws" baseballs with a horizontal velocity v_o. Knowing the height h varies between 788 mm and 1068 mm, determine(a) the range of values of v_o,(b) the values of \alpha corresponding to h = 788 mm and h = 1068 mm. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/urMMTqIuxxOp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742213642187.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0jdt5vDvwOS2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/0jdt5vDvwOS2.jpg</video:thumbnail_loc>

            <video:title>Blocks in contact</video:title>

            <video:description><![CDATA[
Calculate the contact force between two blocks pushed across a smooth surface. You will treat the blocks as a single system to find acceleration before isolating one block to solve for the internal force. This walkthrough applies Newton's second and third laws to coupled particles. Solved: 4. Two blocks with masses 4.00\text{ kg} and 6.00\text{ kg} are placed in contact on a smooth horizontal surface. A horizontal force of 25.0\text{ N} is applied to the 4.00\text{-kg} block. Find the magnitude of the contact force exerted by the 4.00\text{-kg} block on the 6.00\text{-kg} block. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/0jdt5vDvwOS2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lYYusrjr89RZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/214/lYYusrjr89RZ.jpg</video:thumbnail_loc>

            <video:title>Column space</video:title>

            <video:description><![CDATA[
Meaning and illustration of the column space of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/214/lYYusrjr89RZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9ccfKhX7dbmU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/9ccfKhX7dbmU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: A tennis player strikes the tennis ball with her racket while the ball is still rising. The ball speed before impact with the racket is v_1=15m/s and after impact its speed is v_2=22m/s with directions as shown in the figure. If the 60-g ball is in contact with the racket for 0.05 s, determine the magnitude of the average force R exerted by the racket on the ball. Find the angle \beta made by R with the horizontal. Comment on the treatment of the ball weight during the impact. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/9ccfKhX7dbmU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748266251371.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ESRxTCQPoutc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/ESRxTCQPoutc.jpg</video:thumbnail_loc>

            <video:title>Solving equations with unknown index (1)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving equations where the unknown variable is an index. You will learn to express both sides of an equation in a common base to equate powers directly and solve for x using the fundamental laws of indices. Solved: 1. Solve for x in(\sqrt[3]{2})^{2-x} = 2^{x^2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/ESRxTCQPoutc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gqdC0R8P4shi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/205/gqdC0R8P4shi.jpg</video:thumbnail_loc>

            <video:title>Taylor's series</video:title>

            <video:description><![CDATA[
Review of Taylor's series expansion of sine, cosine and exponential functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/205/gqdC0R8P4shi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zlmtCj7WPnob</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/221/zlmtCj7WPnob.jpg</video:thumbnail_loc>

            <video:title>Change of bases (1)</video:title>

            <video:description><![CDATA[
How a change of the domain basis affects the matrix representation of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/221/zlmtCj7WPnob.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SX6YccVAcrmm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/SX6YccVAcrmm.jpg</video:thumbnail_loc>

            <video:title>Thin-layer chromatography</video:title>

            <video:description><![CDATA[
Spots tell the truth. How does the Rf ratio reveal a compound’s identity on silica? Watch to read TLC plates like a pro.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/SX6YccVAcrmm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4AN8Zosz4xdl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/4AN8Zosz4xdl.jpg</video:thumbnail_loc>

            <video:title>Ideal gas equation (1)</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates precise application of the Ideal Gas Equation, PV = nRT, to calculate unknown pressure, volume, temperature, or moles. We detail the correct use of the gas constant and essential unit conversions for all variables. Master this universal equation for ideal gas analysis. Solved: (i) What is the mass of 5.60\text{L} of gaseous oxygen (\text{O}_2) at 100^\circ\text{C} and 0.500 \text{ atm}?(ii) 500\text{ml} of a gas weighs 0.838\text{g} measured at 27^\circ\text{C} and 650\text{mm} of pressure. What is its molecular weight?(iii) What is the density of gaseous \text{SO}_2 at 47^\circ\text{C} and 62.4\text{ cm} pressure? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/4AN8Zosz4xdl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mxbklG3HuN7g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/mxbklG3HuN7g.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on polynomials and transcendentals of matrices. Solved: Given A=\left[ \begin{array}{ccc} 1 & 2 \\ 2 & 1 \\ \end{array} \right] , evaluate (a) f(A) if f(x)=x^{10}-5x^5+3(b) e^A 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/mxbklG3HuN7g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_6WJeo6MPxLq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/_6WJeo6MPxLq.jpg</video:thumbnail_loc>

            <video:title>The Atwood machine</video:title>

            <video:description><![CDATA[
Calculate the acceleration of two masses connected by a string over a frictionless pulley. You will set up simultaneous equations using Newton's second law for each mass to solve for the system acceleration. This walkthrough demonstrates the analysis of coupled particles in vertical motion. Solved: 5. Two masses 3.00\text{ kg} and 5.00\text{ kg} are connected by a light, inextensible string passed over a frictionless pulley. Calculate the magnitude of the acceleration of the masses when the system is released from rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/_6WJeo6MPxLq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iTAfLXZse1Sd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/iTAfLXZse1Sd.jpg</video:thumbnail_loc>

            <video:title>Properties (1)</video:title>

            <video:description><![CDATA[
Some properties of linear maps.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/iTAfLXZse1Sd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CpCpzF6z_t0-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/219/CpCpzF6z_t0-.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and illustration of the image of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/219/CpCpzF6z_t0-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kU0fQCINdviH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/218/kU0fQCINdviH.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and illustration of the kernel of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/218/kU0fQCINdviH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z9Sz6ZsJZ9BR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/z9Sz6ZsJZ9BR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: During a brake test, the rear-engine car is stopped from an initial speed of 100 km/h in a distance of 50 m. If it is known that all four wheels contribute equally to the braking force, determine the braking force F at each wheel. Assume a constant deceleration for the 1500-kg car. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/z9Sz6ZsJZ9BR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742297846495.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/oG63JImOeRf8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/oG63JImOeRf8.jpg</video:thumbnail_loc>

            <video:title>Constant angular acceleration</video:title>

            <video:description><![CDATA[
Equations of angular motion of a rigid body undergoing rotation about a fixed axis when its angular acceleration is constant.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/oG63JImOeRf8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2eU_4yCVwLRy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/2eU_4yCVwLRy.jpg</video:thumbnail_loc>

            <video:title>Undetermined coefficients</video:title>

            <video:description><![CDATA[
Solution of non-homogeneous second-order linear ordinary differential equations by the method of undetermined coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/2eU_4yCVwLRy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vhweICmi3hdS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/vhweICmi3hdS.jpg</video:thumbnail_loc>

            <video:title>Frictionless contacts, cables, etc.</video:title>

            <video:description><![CDATA[
Reactions at frictionless contacts, cables, springs, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/vhweICmi3hdS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P2gL1RoDVb9t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/296/P2gL1RoDVb9t.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components. Solved: The tension in the four cables are equal: |T_1| = |T_2| = |T_3| = |T_4| = T. Determine the value of T so that the four cables exert a total force of 25,000-lb magnitude on the support. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/296/P2gL1RoDVb9t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739470573074.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/b9DS_dUpRaOv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/b9DS_dUpRaOv.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/b9DS_dUpRaOv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f0QDOzeNPlai</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/f0QDOzeNPlai.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components. Solved: The boy of mass 40kg is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r=1.5m, \theta=(0.7t)rad and z=(-0.5t)m, where t is in seconds. Determine the components of force F_r,F_\theta and F_z. Which the slide exerts on him at the instant t=2s. Neglect the size of the boy. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/f0QDOzeNPlai.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1746108007807.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/HyCrp_Lbl29d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/HyCrp_Lbl29d.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: A bowling ball is cast on the "alley" with a backspin \omega=10rad/s of while its center O has a forward velocity of v_0=3m/s . Determine the velocity of the contact point A in contact with the alley. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/HyCrp_Lbl29d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744973536969.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/QnvzjX9OLJpC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mqcR3AmTzO/Thumbnails/990/QnvzjX9OLJpC.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Establish your operational framework for MTH 101 by aligning your study objectives with the NUC CCMAS syllabus requirements. This orientation ensures technical compliance with Nigerian University standards while optimizing your use of the student-led learning system for maximum academic efficiency.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mqcR3AmTzO/Previews/990/QnvzjX9OLJpC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cyJzyOTUvLLH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/cyJzyOTUvLLH.jpg</video:thumbnail_loc>

            <video:title>Angular displacement</video:title>

            <video:description><![CDATA[
Angular motion parameters for a rigid body rotating about a fixed axis - angular position and displacement.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/cyJzyOTUvLLH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dgzKuOwszjhS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/dgzKuOwszjhS.jpg</video:thumbnail_loc>

            <video:title>Vector products (2)</video:title>

            <video:description><![CDATA[
Review of the vector or cross product of vectors - rectangular components of vector products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/dgzKuOwszjhS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oQcBe7Vs20g7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/oQcBe7Vs20g7.jpg</video:thumbnail_loc>

            <video:title>Equation of a plane</video:title>

            <video:description><![CDATA[
Equation of a plane - vector and standard forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/oQcBe7Vs20g7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ycaEq25DaPG5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/ycaEq25DaPG5.jpg</video:thumbnail_loc>

            <video:title>Ideal gas equation (2)</video:title>

            <video:description><![CDATA[
This problem walkthrough further demonstrates precise application of the Ideal Gas Equation, PV = nRT, to calculate unknown pressure, volume, temperature, or moles. We detail the correct use of the gas constant and essential unit conversions for all variables. Master this universal equation for ideal gas analysis. Solved: (i) What is the pressure in a 30.0\text{L} tank that contains 3.03\text{ kg} of \text{O}_2 at 23^\circ\text{C}? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/ycaEq25DaPG5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PKCTZNtJukPT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/PKCTZNtJukPT.jpg</video:thumbnail_loc>

            <video:title>Table-pulley system</video:title>

            <video:description><![CDATA[
Calculate the acceleration of a system where a block on a rough horizontal table is connected to a hanging mass. You will apply Newton's second law to each mass individually to solve for the common acceleration while accounting for kinetic friction. This example shows how to analyse coupled particles. Solved: 6. A 4.00-kg block rests on a rough horizontal table where \mu_k = 0.20. It is connected by a string over a pulley to a 2.00-kg mass hanging vertically. Find the acceleration of the 2.00-kg mass. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/PKCTZNtJukPT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dK4IQHdykjnP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/dK4IQHdykjnP.jpg</video:thumbnail_loc>

            <video:title>Differential relations</video:title>

            <video:description><![CDATA[
Angular motion parameters for a rigid body rotating about a fixed axis - differential relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/dK4IQHdykjnP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iLR79YobG-fd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/iLR79YobG-fd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: Determine the velocity of the center of gravity G of the connecting rod at the instant shown. Piston P is moving upwards with a velocity of 300 in./s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/iLR79YobG-fd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744985515434.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/2srT0ZGYsOqe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/2srT0ZGYsOqe.jpg</video:thumbnail_loc>

            <video:title>Existence</video:title>

            <video:description><![CDATA[
Conditions for the existence of the limit of a function of several variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/2srT0ZGYsOqe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mvVSI18RZ1Tj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/mvVSI18RZ1Tj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: If the slider block A is moving downward at v_A = 4 m/s, determine the velocity of point E at the instant shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/mvVSI18RZ1Tj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744985701032.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/hk4We61vmD2S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/hk4We61vmD2S.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: In the engine system shown, l = 160 mm and b = 60 mm. Knowing that crank AB rotates with a constant angular velocity of 1000 rpm clockwise, determine the velocity of the piston P and the angular velocity of the connecting rod when \theta = 60^\circ. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/hk4We61vmD2S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744985271590.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/DIa-bGsu7t61</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/DIa-bGsu7t61.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n\to \infty}\frac{1}{n}=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/DIa-bGsu7t61.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xuFkC8KNnDhl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/xuFkC8KNnDhl.jpg</video:thumbnail_loc>

            <video:title>Angular velocity</video:title>

            <video:description><![CDATA[
Angular motion parameters for a rigid body rotating about a fixed axis - angular velocity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/xuFkC8KNnDhl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NMN4Z4AfU02s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/NMN4Z4AfU02s.jpg</video:thumbnail_loc>

            <video:title>Rigid-body motion (4)</video:title>

            <video:description><![CDATA[
Overview of different kinds of rigid-body motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/NMN4Z4AfU02s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oPvKq9ymq0lo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/oPvKq9ymq0lo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion. Solved: A projectile is fired from point A with an initial velocity v_o. (a) Show that the radius of curvature of the trajectory of the projectile reaches its minimum level at the highest point B of the trajectory(b) Denoting by \theta the angle formed by the trajectory and the horizontal at a given point C, show that the radius of curvature of the trajectory at C is p = \rho_{min}/cos^3\theta. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/oPvKq9ymq0lo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742218197186.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/eogTftrRlahj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/eogTftrRlahj.jpg</video:thumbnail_loc>

            <video:title>Angular acceleration</video:title>

            <video:description><![CDATA[
Angular motion parameters for a rigid body rotating about a fixed axis - angular acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/eogTftrRlahj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/foqGDgDNuObW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/foqGDgDNuObW.jpg</video:thumbnail_loc>

            <video:title>Spaces</video:title>

            <video:description><![CDATA[
Meaning, representations and examples of sets and spaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/foqGDgDNuObW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/esHN9WE1HnYK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/210/esHN9WE1HnYK.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Definition of vector subspaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/210/esHN9WE1HnYK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F9rjjd7nGlSi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/F9rjjd7nGlSi.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/F9rjjd7nGlSi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dEviQPCOhxo_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/dEviQPCOhxo_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: A small grinding wheel is attached to the shaft of an electric motor which has a rated speed of 3600rpm. When the power is turned on, the unit reaches its rated speed in 5s, and when the power is turned off, the unit coasts to rest in 70s. Assuming uniformly accelerated motion, determine the number of revolutions that the motor executes (a) in reaching its rated speed (b) in coasting to rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/dEviQPCOhxo_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743769661780.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xyItiq4aNUmJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/xyItiq4aNUmJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: The angular acceleration of a body which is rotating about a fixed axis is given by \alpha =-kw^2 , where the constant k=0.1 (no units) . Determine the angular displacement and the time elapsed when the angular velocity has been reduced to one third its initial value\omega_0=12rad\s 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/xyItiq4aNUmJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mMXhS3HXG2Uc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/mMXhS3HXG2Uc.jpg</video:thumbnail_loc>

            <video:title>Faraday's second law</video:title>

            <video:description><![CDATA[
Faraday's second law compares the mass of different substances released by the same quantity of electricity. This lesson explains how chemical equivalent weights determine these proportions when cells are connected in series. It is the basis for comparing different electrolytes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/mMXhS3HXG2Uc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tsN9y0fua3tY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/53/tsN9y0fua3tY.jpg</video:thumbnail_loc>

            <video:title>Rationals and irrationals</video:title>

            <video:description><![CDATA[
A closer look at differences between rational and irrational numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/53/tsN9y0fua3tY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BYq7XhdeCTjf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/BYq7XhdeCTjf.jpg</video:thumbnail_loc>

            <video:title>Other chromatography techniques</video:title>

            <video:description><![CDATA[
TLC is just the start. How do column and gas chromatography scale up separation for pure grams or volatile mixes? Watch to understand these.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/BYq7XhdeCTjf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cbumgXXq-Zaz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/cbumgXXq-Zaz.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: The 6-m pole ABC is acted upon by a 455-N force as shown. The pole is held by a ball and socket joint at A and by two cables BD and BE. For a=3m, determine the tension in each cable and the reaction at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/cbumgXXq-Zaz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1737453884107.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/69nVhlchce1j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/214/69nVhlchce1j.jpg</video:thumbnail_loc>

            <video:title>Row space</video:title>

            <video:description><![CDATA[
Meaning and illustration of the row space of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/214/69nVhlchce1j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uZycb_FXNNzX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/147/uZycb_FXNNzX.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of motion of a rigid body undergoing general plane motion by locating an instantaneous centre of zero velocity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/147/uZycb_FXNNzX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HHzOUU6RIFNL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/HHzOUU6RIFNL.jpg</video:thumbnail_loc>

            <video:title>Speed at maximum point</video:title>

            <video:description><![CDATA[
Calculate the speed of a toy car at the top of a circular loop using energy conservation. This walkthrough explains how to find the vertical height change and equate the potential energy loss to the final kinetic energy. Solved: A frictionless toy car is released from rest at a height of 6.0 \, m and enters a vertical circular loop of radius 1.5 \, m. Calculate the speed of the car when it reaches the highest point of the loop. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/HHzOUU6RIFNL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WTPUZUKvBUBu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/WTPUZUKvBUBu.jpg</video:thumbnail_loc>

            <video:title>Linear combination</video:title>

            <video:description><![CDATA[
Meaning of linear combination.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/WTPUZUKvBUBu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pveVZdIvK21x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/aNaQYVEiEu/Thumbnails/165/pveVZdIvK21x.jpg</video:thumbnail_loc>

            <video:title>Forces and reactions (2)</video:title>

            <video:description><![CDATA[
How to obtain different forces and reactions in a given system, for use in free-body diagrams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/aNaQYVEiEu/Previews/165/pveVZdIvK21x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W35cF33hfAsA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/W35cF33hfAsA.jpg</video:thumbnail_loc>

            <video:title>Vector equations</video:title>

            <video:description><![CDATA[
Scalar equations of motion of a point on a rigid body undergoing rotation about a fixed axis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/W35cF33hfAsA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YAjTLOOjM3Cp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/YAjTLOOjM3Cp.jpg</video:thumbnail_loc>

            <video:title>Solution of linear equations</video:title>

            <video:description><![CDATA[
Solving linear equations with matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/YAjTLOOjM3Cp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/p4AwhLHily68</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Thumbnails/177/p4AwhLHily68.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Introduction to modelling of translational mechanical systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Previews/177/p4AwhLHily68.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i8gSX-TO3Onh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/526/i8gSX-TO3Onh.jpg</video:thumbnail_loc>

            <video:title>Diagonalizing symmetric matrices</video:title>

            <video:description><![CDATA[
Theorems on diagonalization of symmetric matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/526/i8gSX-TO3Onh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/flpBPaXBnnCW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/213/flpBPaXBnnCW.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of basis and dimension of a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/213/flpBPaXBnnCW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PWVmjeDz5BLi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Thumbnails/292/PWVmjeDz5BLi.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Derivation of the Lagrange's equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Previews/292/PWVmjeDz5BLi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QA2qvUyBIt7w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/QA2qvUyBIt7w.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: A 250\times400-mm plate of mass 12kg and a 300-mm-diameter pulley are welded to axle AC that is supported by bearings at A and B. For \beta=30^{\circ}, determine (a) the tension in the cable, (b) the reaction at A and B. Assuming that the bearing at B does not exert any axial thrust. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/QA2qvUyBIt7w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1737468223291.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/cQIVOnTGCrJT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/6/cQIVOnTGCrJT.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of scalars, vectors and tensors; representation of a vector by a directed line segment.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/6/cQIVOnTGCrJT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FEJCBsKCWV7a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/FEJCBsKCWV7a.jpg</video:thumbnail_loc>

            <video:title>Illustration</video:title>

            <video:description><![CDATA[
Making sense of the gradient of a scalar - its implications and how it relates to the derivative of single-variable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/FEJCBsKCWV7a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jYiLIktIwY3k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/jYiLIktIwY3k.jpg</video:thumbnail_loc>

            <video:title>Curvilinear motion</video:title>

            <video:description><![CDATA[
Meaning of curvilinear motion; general definitions of position, displacement, velocity and acceleration for a particle undergoing curvilinear motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/jYiLIktIwY3k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rVawpo4Pu3Tm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/rVawpo4Pu3Tm.jpg</video:thumbnail_loc>

            <video:title>Compound surds</video:title>

            <video:description><![CDATA[
This lesson explains compound surds as expressions combining rational and irrational parts through addition or subtraction. You will also learn the conditions for the equality of two compound surds, where rational and irrational components must be compared and equated separately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/rVawpo4Pu3Tm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/54lCeHdM4CpH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/54lCeHdM4CpH.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
When is a force said to do work on a particle? What are the different formulas for calculating the work of a force?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/54lCeHdM4CpH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uzNyVmMgdKTp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/uzNyVmMgdKTp.jpg</video:thumbnail_loc>

            <video:title>Exponential functions</video:title>

            <video:description><![CDATA[
Evaluation of limits of exponential functions at infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/uzNyVmMgdKTp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HMtMGtztYq5_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/10/HMtMGtztYq5_.jpg</video:thumbnail_loc>

            <video:title>Collinearity</video:title>

            <video:description><![CDATA[
Meaning of collinearity and the algebraic condition for collinearity of three points.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/10/HMtMGtztYq5_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1MrKrk1cpQgH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/1MrKrk1cpQgH.jpg</video:thumbnail_loc>

            <video:title>Equation of a line I</video:title>

            <video:description><![CDATA[
Equation of a line in a two-dimensional cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/1MrKrk1cpQgH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KPwjTYNxNXDT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/KPwjTYNxNXDT.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: The uniform load has a mass of 600kg and is lifted using a uniform30-kg strongback beam BAC and the four ropes. Determine the tension in each rope and the force that must be applied at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/KPwjTYNxNXDT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738572149678.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/8K1glqzKKCoq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/8K1glqzKKCoq.jpg</video:thumbnail_loc>

            <video:title>Linear and non-linear differential equations</video:title>

            <video:description><![CDATA[
Identifying linear and non-linear differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/8K1glqzKKCoq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/25Lbv6DTGt0l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/58/25Lbv6DTGt0l.jpg</video:thumbnail_loc>

            <video:title>Informal definition</video:title>

            <video:description><![CDATA[
Informal definition of limits at infinity and infinite limits.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/58/25Lbv6DTGt0l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xKsPQT1tAf8E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/xKsPQT1tAf8E.jpg</video:thumbnail_loc>

            <video:title>Collinearity</video:title>

            <video:description><![CDATA[
Re-examining the collinearity of two vectors (three points) in the light of cross products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/xKsPQT1tAf8E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XlJ6jURyn8h6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/403/XlJ6jURyn8h6.jpg</video:thumbnail_loc>

            <video:title>Review (2)</video:title>

            <video:description><![CDATA[
Review of key concepts on convergence of infinite series - power series.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/403/XlJ6jURyn8h6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jkzN5bp908uM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/76/jkzN5bp908uM.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Formal and informal definitions of continuity of two-variable real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/76/jkzN5bp908uM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4JoxcnjKhUwP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/4JoxcnjKhUwP.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Establish your roadmap for mastering the real number system and advanced algebraic operations. This lesson defines the course scope and the technical precision required for engineering and quantitative analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/4JoxcnjKhUwP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6z_EjxseeJWr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/6z_EjxseeJWr.jpg</video:thumbnail_loc>

            <video:title>Conjugate surds</video:title>

            <video:description><![CDATA[
Conjugate surds are pairs of expressions that differ only by the sign between their terms. Multiplying these pairs results in a rational number, a property essential for removing roots from the denominators of complex fractions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/6z_EjxseeJWr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c579Dh_8IeNh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/c579Dh_8IeNh.jpg</video:thumbnail_loc>

            <video:title>Force vectors</video:title>

            <video:description><![CDATA[
Representation of forces using directed line segments.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/c579Dh_8IeNh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oH0xNNr3ccG4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/195/oH0xNNr3ccG4.jpg</video:thumbnail_loc>

            <video:title>Base vectors</video:title>

            <video:description><![CDATA[
Contravariant base vectors in orthogonal curvilinear coordinates, their relation to the covariant base vectors, and their vector product identities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/195/oH0xNNr3ccG4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e3MymX1sbHdI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/e3MymX1sbHdI.jpg</video:thumbnail_loc>

            <video:title>Fundamental concepts (4)</video:title>

            <video:description><![CDATA[
Newton's law of gravitation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/e3MymX1sbHdI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tFAct3BNXb0S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/403/tFAct3BNXb0S.jpg</video:thumbnail_loc>

            <video:title>Review (3)</video:title>

            <video:description><![CDATA[
Review of key concepts on convergence of infinite series - tests of convergence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/403/tFAct3BNXb0S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/az3XMq9zhBEB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/193/az3XMq9zhBEB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on orthogonality, scale factors and Jacobian of transformation of curvilinear coordinate systems. Solved: The parabolic coordinate system (u,v,\Phi) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/193/az3XMq9zhBEB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W91zzk0em6TK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/W91zzk0em6TK.jpg</video:thumbnail_loc>

            <video:title>Fundamental concepts (3)</video:title>

            <video:description><![CDATA[
Newton's laws of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/W91zzk0em6TK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oDmU1mbw0vaQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/86/oDmU1mbw0vaQ.jpg</video:thumbnail_loc>

            <video:title>Trapezoidal rule</video:title>

            <video:description><![CDATA[
Integration by the trapezoidal rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/86/oDmU1mbw0vaQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y6wuFytMM4WP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/Y6wuFytMM4WP.jpg</video:thumbnail_loc>

            <video:title>Rationalising denominators</video:title>

            <video:description><![CDATA[
This lesson covers direct and sequential rationalisation to remove radicals from denominators. You will learn to use conjugates in single or multiple stages to systematically eliminate roots until the denominator becomes a single rational number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/Y6wuFytMM4WP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9hbdpWF02-wg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/9hbdpWF02-wg.jpg</video:thumbnail_loc>

            <video:title>Scalar equations</video:title>

            <video:description><![CDATA[
Scalar equations of motion of a point on a rigid body undergoing rotation about a fixed axis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/9hbdpWF02-wg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gpAYOosO39iF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/gpAYOosO39iF.jpg</video:thumbnail_loc>

            <video:title>Inexact differential equations</video:title>

            <video:description><![CDATA[
Inexact differential equations and their solutions with integrating factors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/gpAYOosO39iF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RsK0MJvyyu7W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/RsK0MJvyyu7W.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
This lesson explains the fundamental laws governing surds, specifically how to split or combine roots during multiplication and division. You will learn the rules for handling products and quotients of radicals to ensure accurate algebraic manipulation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/RsK0MJvyyu7W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yOv5vrUDT7gc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/192/yOv5vrUDT7gc.jpg</video:thumbnail_loc>

            <video:title>Definitions</video:title>

            <video:description><![CDATA[
Defining the gradient, divergence, curl and Laplacian using sign conventions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/192/yOv5vrUDT7gc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8Ve64r2SOwd0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/65/8Ve64r2SOwd0.jpg</video:thumbnail_loc>

            <video:title>Geometric progressions</video:title>

            <video:description><![CDATA[
Meaning, examples, and descriptions of geometric progressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/65/8Ve64r2SOwd0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2RoLgmNJCjwb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/2RoLgmNJCjwb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: Link OA rotates with a clockwise angular velocity \omega=7rad/sec . Determine the velocity of point B for the position \theta=30^\circ . Use the values b=3.2in., d=4in, and h=1.2in. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/2RoLgmNJCjwb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744970997738.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5d8EsLwJbn-Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/85/5d8EsLwJbn-Y.jpg</video:thumbnail_loc>

            <video:title>Simpson's rule</video:title>

            <video:description><![CDATA[
Integration by Simpson's 1/3 rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/85/5d8EsLwJbn-Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Bwn53Oxncpq3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/Bwn53Oxncpq3.jpg</video:thumbnail_loc>

            <video:title>Conical pendulum</video:title>

            <video:description><![CDATA[
Calculate the speed of a mass revolving in a horizontal circle while suspended from a string. You will resolve the tension into vertical and horizontal components to balance weight and provide centripetal force. This walkthrough applies circular dynamics to a conical pendulum system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/Bwn53Oxncpq3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uruPvfms7paP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/uruPvfms7paP.jpg</video:thumbnail_loc>

            <video:title>Scalar multiplication</video:title>

            <video:description><![CDATA[
Scalar multiplication of linear maps and its linearity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/uruPvfms7paP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_JEwc3_lyKIF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/_JEwc3_lyKIF.jpg</video:thumbnail_loc>

            <video:title>Equivalent weight</video:title>

            <video:description><![CDATA[
Equivalent weight is the mass of a substance related to its electrochemical equivalent via the Faraday constant. This lesson explains how to link these two values to calculate the total mass released during electrolysis. It provides the theoretical bridge between electrical charge and chemical mass.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/_JEwc3_lyKIF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_gyLQ5W2myD6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/_gyLQ5W2myD6.jpg</video:thumbnail_loc>

            <video:title>Using a calculator</video:title>

            <video:description><![CDATA[
Calculators approximate limits numerically. What if rounding errors or oscillating outputs hide the true value? Watch to spot when the tool helps or misleads.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/_gyLQ5W2myD6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mzyPKZ_1HXaR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/mzyPKZ_1HXaR.jpg</video:thumbnail_loc>

            <video:title>Potential energy</video:title>

            <video:description><![CDATA[
Potential energy is the stored energy an object has due to its position or state. This lesson defines gravitational potential energy using height and elastic potential energy using spring compression to show how work is stored for later motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/mzyPKZ_1HXaR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZosUYtlYmqoi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/105/ZosUYtlYmqoi.jpg</video:thumbnail_loc>

            <video:title>Visualization</video:title>

            <video:description><![CDATA[
Visualizing some plane vector fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/105/ZosUYtlYmqoi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nasuWw1sd7Bm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/nasuWw1sd7Bm.jpg</video:thumbnail_loc>

            <video:title>Dependent motion (2)</video:title>

            <video:description><![CDATA[
Dependent motion of connected bodies and how to relate their positions, velocities and accelerations when the connecting cable(s) is (are) not aligned with the direction(s) of motion of the bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/nasuWw1sd7Bm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wNuPsTFc2quh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/wNuPsTFc2quh.jpg</video:thumbnail_loc>

            <video:title>General solution of non-homogeneous equations</video:title>

            <video:description><![CDATA[
General solution of non-homogeneous linear second-order differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/wNuPsTFc2quh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5EJJArorQRvK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/5EJJArorQRvK.jpg</video:thumbnail_loc>

            <video:title>Radioactive decay</video:title>

            <video:description><![CDATA[
Modelling radioactive decay with first-order ordinary differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/5EJJArorQRvK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ADKxjWqyDmqE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/386/ADKxjWqyDmqE.jpg</video:thumbnail_loc>

            <video:title>Area and centroid</video:title>

            <video:description><![CDATA[
Calculation of area and centroid of a region R in a plane by double integration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/386/ADKxjWqyDmqE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VGMuFk-WiAab</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/VGMuFk-WiAab.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the vector product of two vectors and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/VGMuFk-WiAab.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZLm3Echst8eM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/ZLm3Echst8eM.jpg</video:thumbnail_loc>

            <video:title>Illustration</video:title>

            <video:description><![CDATA[
Making sense of the divergence of a vector field.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/ZLm3Echst8eM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gXD4ciGNhYuB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/100/gXD4ciGNhYuB.jpg</video:thumbnail_loc>

            <video:title>Change of variables</video:title>

            <video:description><![CDATA[
How to evaluate double integrals by change of variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/100/gXD4ciGNhYuB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zhwldz_A4y_C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/620/Zhwldz_A4y_C.jpg</video:thumbnail_loc>

            <video:title>What if everything fails?</video:title>

            <video:description><![CDATA[
Examining limits for which the L'Hospital's rule fails.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/620/Zhwldz_A4y_C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HxkIxgwDoO16</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/HxkIxgwDoO16.jpg</video:thumbnail_loc>

            <video:title>Completing the square</video:title>

            <video:description><![CDATA[
This lesson explains the process of transforming a quadratic expression into a perfect square trinomial. You will learn to use this method to solve equations that cannot be easily factorised and to prepare for deriving the quadratic formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/HxkIxgwDoO16.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rJIHSO5k_8y2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/59/rJIHSO5k_8y2.jpg</video:thumbnail_loc>

            <video:title>Continuity on an interval</video:title>

            <video:description><![CDATA[
Continuity of a function on an interval in its domain.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/59/rJIHSO5k_8y2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O_re2AiXH3tR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/O_re2AiXH3tR.jpg</video:thumbnail_loc>

            <video:title>Projectile motion</video:title>

            <video:description><![CDATA[
Application of the concepts of rectangular components for curvilinear motion to problems of projectile motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/O_re2AiXH3tR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N1OofTTjDb8x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/N1OofTTjDb8x.jpg</video:thumbnail_loc>

            <video:title>Normal and tangential components</video:title>

            <video:description><![CDATA[
Position, speed, velocity, acceleration and radius of curvature of the trajectory of a particle in curvilinear motion, using components normal and tangential to the trajectory.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/N1OofTTjDb8x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OGkpxvhZJlJk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/OGkpxvhZJlJk.jpg</video:thumbnail_loc>

            <video:title>Cartesian components (1)</video:title>

            <video:description><![CDATA[
Components of a vector in two-dimensional Cartesian coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/OGkpxvhZJlJk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D3LYJ6UJtgzB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/D3LYJ6UJtgzB.jpg</video:thumbnail_loc>

            <video:title>Conservative forces</video:title>

            <video:description><![CDATA[
Work done by a conservative force depends only on the starting and ending points, not the path taken. This lesson explains why gravity and springs allow energy to be stored and recovered without loss.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/D3LYJ6UJtgzB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9lexm0WIgCI0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/9lexm0WIgCI0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: The pin P is constrained to move along the curve defined by the lemniscate r = (4 sin 2\theta) ft. If the angular position of the slotted arm OA is defined by \theta = (3t^\frac 3 2) rad, where t is in seconds, determine the magnitude of the velocity and acceleration of P when \theta = 60^\circ. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/9lexm0WIgCI0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742220884296.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/saDPv-VsRdPz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/56/saDPv-VsRdPz.jpg</video:thumbnail_loc>

            <video:title>Informal definition</video:title>

            <video:description><![CDATA[
An informal definition of the limit of real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/56/saDPv-VsRdPz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8zE11ReRfYE8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/8zE11ReRfYE8.jpg</video:thumbnail_loc>

            <video:title>General conics and degeneracy</video:title>

            <video:description><![CDATA[
Visualizing the conic sections and degeneracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/8zE11ReRfYE8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z8tUoaVQoXKZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/59/z8tUoaVQoXKZ.jpg</video:thumbnail_loc>

            <video:title>Continuity at an interior point</video:title>

            <video:description><![CDATA[
Continuity at an interior point of the domain of a function.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/59/z8tUoaVQoXKZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wUkD9HifdGHa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/wUkD9HifdGHa.jpg</video:thumbnail_loc>

            <video:title>Indeterminate forms (3)</video:title>

            <video:description><![CDATA[
Indeterminate forms involving powers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/wUkD9HifdGHa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/usBhdnzdD-qw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/132/usBhdnzdD-qw.jpg</video:thumbnail_loc>

            <video:title>Taylor and Maclaurin series</video:title>

            <video:description><![CDATA[
Infinite series representation of differentiable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/132/usBhdnzdD-qw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sxHiYLSw_WzL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/63/sxHiYLSw_WzL.jpg</video:thumbnail_loc>

            <video:title>The mean-value theorem</video:title>

            <video:description><![CDATA[
The mean-value theorem and its implications  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/63/sxHiYLSw_WzL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/947BsxP8fsJT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/947BsxP8fsJT.jpg</video:thumbnail_loc>

            <video:title>Symmetric and orthogonal matrices</video:title>

            <video:description><![CDATA[
Meaning and examples of symmetric and orthogonal matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/947BsxP8fsJT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7x9qhb7cn69K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/887/7x9qhb7cn69K.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson introduces the standard quadratic form and its practical applications in engineering and finance. It provides a concise summary of the topics and solution methods covered throughout this course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/887/7x9qhb7cn69K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QkX7WGjfTQTB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/QkX7WGjfTQTB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the vector product of two vectors and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/QkX7WGjfTQTB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n531gBXen62o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/n531gBXen62o.jpg</video:thumbnail_loc>

            <video:title>Leibniz's formula</video:title>

            <video:description><![CDATA[
Evaluating higher-order derivatives of a product of functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/n531gBXen62o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Hxl5Ct25xsHS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/Hxl5Ct25xsHS.jpg</video:thumbnail_loc>

            <video:title>Symmetric distributions</video:title>

            <video:description><![CDATA[
Symmetry simplifies integration. How does constant distance from a ring to its axis reduce the potential integral? We pull constants out to solve it instantly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/Hxl5Ct25xsHS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4YenZV_UQ9ft</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/97/4YenZV_UQ9ft.jpg</video:thumbnail_loc>

            <video:title>Quadric cylinders</video:title>

            <video:description><![CDATA[
Elliptic, circular, hyperbolic and parabolic cylinders.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/97/4YenZV_UQ9ft.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/91GharjI_pb_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/91GharjI_pb_.jpg</video:thumbnail_loc>

            <video:title>Rationalising denominators (3)</video:title>

            <video:description><![CDATA[
This walkthrough explains sequential rationalisation for denominators containing multiple radicals. You will learn to apply conjugates in successive stages to systematically eliminate every root until the denominator becomes a single rational number. Solved: 5. Simplify \frac{2}{\sqrt{2} + \sqrt{3} - 1}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/91GharjI_pb_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aP9dqY7j4S_A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/aP9dqY7j4S_A.jpg</video:thumbnail_loc>

            <video:title>Modulus function</video:title>

            <video:description><![CDATA[
Evaluation of the limits of functions with non-rationalizable radicals at infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/aP9dqY7j4S_A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4bBs8wxh-QxM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/4bBs8wxh-QxM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: At time t = 0, the baseball player releases a ball with the initial conditions shown in the figure. Determine the quantities r, \dot r, \ddot r, \theta, \dot \theta, and \ddot \theta, all relative to the x-y coordinate system shown, at time t = 0.5 sec. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/4bBs8wxh-QxM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742222381536.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/6kpl3WbfP3Zw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/6kpl3WbfP3Zw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: A car is travelling along the circular curve of radius r = 300 ft. At the instant shown, its angular rate of rotation is \dot \theta = 0.4 rad/s which is increasing at the rate of \ddot \theta = 0.2r ad/s^2. Determine the magnitudes of the car's velocity and acceleration at this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/6kpl3WbfP3Zw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742221801324.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Kl3CbKNIkcMi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/Kl3CbKNIkcMi.jpg</video:thumbnail_loc>

            <video:title>Rectangular components</video:title>

            <video:description><![CDATA[
Meaning of rectangular components of a force.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/Kl3CbKNIkcMi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/o26qxYbroIAZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/o26qxYbroIAZ.jpg</video:thumbnail_loc>

            <video:title>Cartesian components (2)</video:title>

            <video:description><![CDATA[
Components of a vector in three-dimensional Cartesian coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/o26qxYbroIAZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RIzg2_aiWkn_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/RIzg2_aiWkn_.jpg</video:thumbnail_loc>

            <video:title>Exact differential equations</video:title>

            <video:description><![CDATA[
Solution of exact differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/RIzg2_aiWkn_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b07YeV_cg2jV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/b07YeV_cg2jV.jpg</video:thumbnail_loc>

            <video:title>Electric circuits</video:title>

            <video:description><![CDATA[
Modelling electric circuit problems with first-order ordinary differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/b07YeV_cg2jV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RhVXrpKKiSGr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/RhVXrpKKiSGr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: An automobile travels to the right at a constant speed of 48mi/h. If diameter of a wheel is 22in., determine the velocities of points B,C,D, and E on the rim of the wheel. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/RhVXrpKKiSGr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743853770780.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JKMzI7akUn3m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/JKMzI7akUn3m.jpg</video:thumbnail_loc>

            <video:title>Our approach</video:title>

            <video:description><![CDATA[
The learning process, methodology and references for this course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/JKMzI7akUn3m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HyfxVW_BFw6c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/HyfxVW_BFw6c.jpg</video:thumbnail_loc>

            <video:title>Rationalising denominators (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step process of removing a single radical from the denominator of a fraction. You will learn to multiply by a suitable surd to convert the irrational bottom into a whole number, ensuring the final expression is in its simplest standard form. Solved: 3. Simplify \frac{15}{4\sqrt{3}}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/HyfxVW_BFw6c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rHr8rNO9EY4d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/rHr8rNO9EY4d.jpg</video:thumbnail_loc>

            <video:title>Transformation of coordinates</video:title>

            <video:description><![CDATA[
Detecting transformed coordinates with variable substitutions using orthogonal diagonalizing matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/rHr8rNO9EY4d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qeHGprv3jAqL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/qeHGprv3jAqL.jpg</video:thumbnail_loc>

            <video:title>Functions</video:title>

            <video:description><![CDATA[
Examples of vector spaces - space of functions and its operators.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/qeHGprv3jAqL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ziKFKY2x-7Oy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/103/ziKFKY2x-7Oy.jpg</video:thumbnail_loc>

            <video:title>Orthogonal and orthonormal bases</video:title>

            <video:description><![CDATA[
Meaning of orthogonal and orthonormal bases of a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/103/ziKFKY2x-7Oy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GlWD-OaWXedf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/GlWD-OaWXedf.jpg</video:thumbnail_loc>

            <video:title>Relative motion</video:title>

            <video:description><![CDATA[
Relative position, velocity and acceleration for two particles in rectilinear motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/GlWD-OaWXedf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x9vcQ0TjHAX-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/x9vcQ0TjHAX-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/x9vcQ0TjHAX-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uYm0xtnLTZEf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/uYm0xtnLTZEf.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/uYm0xtnLTZEf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yi5Q-F_NvSZO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/yi5Q-F_NvSZO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: The uniform beam has a weight of 5000 lb. Determine the average tension in each of the two cables AB and AC if the beam is given an upward speed of 8 ft/s in 1.5 s starting from rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/yi5Q-F_NvSZO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748265495394.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/rPqWQ_1oCrIm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/rPqWQ_1oCrIm.jpg</video:thumbnail_loc>

            <video:title>Parallel vectors</video:title>

            <video:description><![CDATA[
Meaning and relations of parallel vectors; parallel and anti-parallel, like and unlike vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/rPqWQ_1oCrIm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KuLv179EIEpL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/KuLv179EIEpL.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the scalar product of two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/KuLv179EIEpL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FeAM_bXRrTEl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/837/FeAM_bXRrTEl.jpg</video:thumbnail_loc>

            <video:title>Relative atomic mass</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates calculating the Relative Atomic Mass for elements from isotopic data. We use the percentage abundance of each isotope to determine the weighted average atomic mass. Master this calculation for accurate use of the periodic table. Solved: (1) The element europium, \text{Eu}, exists in nature as two isotopes: {}^{151}\text{Eu} has a mass of 150.9196 \text{ amu}, and {}^{153}\text{Eu} has a mass of 152.9209 \text{ amu}. If the average atomic mass of europium is 151.96 \text{ amu}, calculate the relative abundance of the two europium isotopes.(2) Copper contains 2 isotopes:{}^{63}\text{Cu} atomic weight 62.9298 (69.09\%){}^{65}\text{Cu} atomic weight 64.9278 (30.91\%)What is the average atomic weight of Copper? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/837/FeAM_bXRrTEl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8JXoMqcoZWNA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/8JXoMqcoZWNA.jpg</video:thumbnail_loc>

            <video:title>Factorisation (3)</video:title>

            <video:description><![CDATA[
What if direct substitution gives 0/0 and both polynomials factorise? See how cancelling the common factor reveals the limit's actual value. Solved: Find \lim_{x \to 2} \frac{x^2 + x - 6}{x^2 - 5x + 6}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/8JXoMqcoZWNA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wP6gw5MIxVUt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/wP6gw5MIxVUt.jpg</video:thumbnail_loc>

            <video:title>Multiplication</video:title>

            <video:description><![CDATA[
Multiplication of a complex number by a scalar (real number) and by another complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/wP6gw5MIxVUt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i9D_ZvxARWMG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/193/i9D_ZvxARWMG.jpg</video:thumbnail_loc>

            <video:title>Curvilinear coordinates</video:title>

            <video:description><![CDATA[
Coordinate points, lines and surfaces on general curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/193/i9D_ZvxARWMG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n2f8rfwI3ord</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/76/n2f8rfwI3ord.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating continuity of real-valued two-variable functions. Solved: Is \begin {cases} 2xy, (x, y) \ne (1,2) \\ 0, (x,y) = (1,2) \end {cases} continuous at (1,2)?Determine whether f(x,y) = \begin{cases} x^2 +2y, (x, y) \ne (1,2) \\ 0, (x, y) = (1,2) \end {cases} continuous at (1,2). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/76/n2f8rfwI3ord.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zGWFuLEF5QF6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/zGWFuLEF5QF6.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Equations of motion and analysis procedure for a system of connected bodies in rectilinear motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/zGWFuLEF5QF6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f9K7itcriPbE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/f9K7itcriPbE.jpg</video:thumbnail_loc>

            <video:title>Rigid-body motion (3)</video:title>

            <video:description><![CDATA[
Overview of different kinds of rigid-body motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/f9K7itcriPbE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kwIqdtjtV_7w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/200/kwIqdtjtV_7w.jpg</video:thumbnail_loc>

            <video:title>Powers of i</video:title>

            <video:description><![CDATA[
Powers of i.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/200/kwIqdtjtV_7w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/h1mie8wsWPlj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/h1mie8wsWPlj.jpg</video:thumbnail_loc>

            <video:title>Mixed surds</video:title>

            <video:description><![CDATA[
Mixed surds consist of a rational coefficient multiplied by an irrational root. This lesson explains how to identify these structures and the process for converting an entire surd into a mixed surd to make further addition and subtraction possible.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/h1mie8wsWPlj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F-D58l2Z41ET</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/F-D58l2Z41ET.jpg</video:thumbnail_loc>

            <video:title>Magnitude and two points</video:title>

            <video:description><![CDATA[
How to obtain the components of a force in three dimensions using its magnitude and coordinates of any two distinct points along its line of action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/F-D58l2Z41ET.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3rYYHfLOFr8k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/198/3rYYHfLOFr8k.jpg</video:thumbnail_loc>

            <video:title>Cylindrical coordinates</video:title>

            <video:description><![CDATA[
Vector calculus properties in cylindrical coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/198/3rYYHfLOFr8k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RP0ipa8nDy2A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/200/RP0ipa8nDy2A.jpg</video:thumbnail_loc>

            <video:title>Complex numbers</video:title>

            <video:description><![CDATA[
Why are complex numbers necessary?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/200/RP0ipa8nDy2A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gncXQbGwxiAA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/gncXQbGwxiAA.jpg</video:thumbnail_loc>

            <video:title>Geometric meaning</video:title>

            <video:description><![CDATA[
Geometric meaning of the scalar triple product of three vectors as the volume of some parallelepiped.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/gncXQbGwxiAA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nbUOdG5c0sK7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/nbUOdG5c0sK7.jpg</video:thumbnail_loc>

            <video:title>Work of a weight</video:title>

            <video:description><![CDATA[
Calculating the work done by a weight.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/nbUOdG5c0sK7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0yY9znwPMWlr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/148/0yY9znwPMWlr.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for acceleration analysis of the motion of a rigid body undergoing general plane motion using the acceleration of a point relative to another point on the same rigid body.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/148/0yY9znwPMWlr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PelUfy5LtWGo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/PelUfy5LtWGo.jpg</video:thumbnail_loc>

            <video:title>Work of gravitational force</video:title>

            <video:description><![CDATA[
Calculating the work done by the gravitational force of attraction between any two bodies in the universe.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/PelUfy5LtWGo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I69Iv-zGzVNY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/I69Iv-zGzVNY.jpg</video:thumbnail_loc>

            <video:title>Properties of matrix inverses (1)</video:title>

            <video:description><![CDATA[
Properties of matrix inverses and their applications - uniqueness, inverses of products, transposes and scalar multiples.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/I69Iv-zGzVNY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TA-peLLQTI_o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/TA-peLLQTI_o.jpg</video:thumbnail_loc>

            <video:title>Properties of matrix inverses (2)</video:title>

            <video:description><![CDATA[
Properties of matrix inverses and their applications - elementary row operations on an invertible matrix to give the identity matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/TA-peLLQTI_o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Xc_qb_sJ0B3L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/Xc_qb_sJ0B3L.jpg</video:thumbnail_loc>

            <video:title>Condition</video:title>

            <video:description><![CDATA[
Condition for equilibrium of a particle in three dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/Xc_qb_sJ0B3L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2NqLPHAgJ808</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/2NqLPHAgJ808.jpg</video:thumbnail_loc>

            <video:title>Properties of matrix inverses (3)</video:title>

            <video:description><![CDATA[
Properties of matrix inverses and their applications - solutions of square systems of linear equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/2NqLPHAgJ808.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ne1bQVgIGqlA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/Ne1bQVgIGqlA.jpg</video:thumbnail_loc>

            <video:title>Fields</video:title>

            <video:description><![CDATA[
Meaning and examples of fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/Ne1bQVgIGqlA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3jBGjiB19Qfk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/222/3jBGjiB19Qfk.jpg</video:thumbnail_loc>

            <video:title>Formula</video:title>

            <video:description><![CDATA[
Simplifying the vector triple product using scalar coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/222/3jBGjiB19Qfk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sjPxV5-hkBaK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/sjPxV5-hkBaK.jpg</video:thumbnail_loc>

            <video:title>N-tuples</video:title>

            <video:description><![CDATA[
Examples of vector spaces - space of n-tuples and its operators.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/sjPxV5-hkBaK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LIkRUDlKTdYe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/LIkRUDlKTdYe.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions (3)</video:title>

            <video:description><![CDATA[
Piecewise functions can hide a trap at exact points. What if the rule changes precisely where you approach; does the limit follow the nearby path or the isolated value? Watch the exclusion case unfold. Solved: Evaluate \lim_{x \to 3} f(x) for the function: f(x) = \begin{cases} 2x + 5 & \text{if } x \neq 3 \\ 1 & \text{if } x = 3 \end{cases}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/LIkRUDlKTdYe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z2e1lGqfqFTb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/Z2e1lGqfqFTb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: Determine the velocity and acceleration of the plate at the instant \theta=30^\circ , if at this instant the circular cam is rotating about the fixed point O with an angular velocity \omega= 4rad/s and an angular acceleration \alpha=2rad/s^2 . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/Z2e1lGqfqFTb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744973152592.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/RPakbIYu6Alm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/RPakbIYu6Alm.jpg</video:thumbnail_loc>

            <video:title>Notations</video:title>

            <video:description><![CDATA[
An overview of common notations for derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/RPakbIYu6Alm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9-er1L4B_P6v</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/565/9-er1L4B_P6v.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of the empty relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/565/9-er1L4B_P6v.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/evMW4_LIplLL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/214/evMW4_LIplLL.jpg</video:thumbnail_loc>

            <video:title>Null space</video:title>

            <video:description><![CDATA[
Meaning and illustration of the null space of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/214/evMW4_LIplLL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5upHPPVw-W-a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/510/5upHPPVw-W-a.jpg</video:thumbnail_loc>

            <video:title>Kinematics of particles</video:title>

            <video:description><![CDATA[
Review of the fundamental concepts of kinematics of particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/510/5upHPPVw-W-a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Mqzp2Vep3WAM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/Mqzp2Vep3WAM.jpg</video:thumbnail_loc>

            <video:title>Rigid-body motion (1)</video:title>

            <video:description><![CDATA[
Overview of different kinds of rigid-body motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/Mqzp2Vep3WAM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f8xpzPQg71KE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/f8xpzPQg71KE.jpg</video:thumbnail_loc>

            <video:title>Matrices</video:title>

            <video:description><![CDATA[
Examples of vector spaces - space of matrices and its operators.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/f8xpzPQg71KE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t5oRvgg2NZqy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/193/t5oRvgg2NZqy.jpg</video:thumbnail_loc>

            <video:title>Orthogonal curvilinear coordinates</video:title>

            <video:description><![CDATA[
Coordinate points, lines and surfaces on orthogonal curvilinear coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/193/t5oRvgg2NZqy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gNQBf1cCaYQc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/gNQBf1cCaYQc.jpg</video:thumbnail_loc>

            <video:title>The squeeze theorem</video:title>

            <video:description><![CDATA[
Direct substitution hits a dead end. What if two known boundaries can quietly trap a stubborn function into revealing its exact limit? Watch how we corner the true value.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/gNQBf1cCaYQc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tOAzjGWltNTZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/337/tOAzjGWltNTZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of frictional forces on thrust bearings - pivot (end) and collar bearings, disks. Solved: Knowing that a couple of magnitude 15N\cdot m is required to start the vertical shaft rotating, determine the coefficient of static friction between the annular surface of contact. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/337/tOAzjGWltNTZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746868695369.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Sf4EKRAj4F85</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/566/Sf4EKRAj4F85.jpg</video:thumbnail_loc>

            <video:title>Equivalence class</video:title>

            <video:description><![CDATA[
Meaning of equivalence class for each element in the domain of a relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/566/Sf4EKRAj4F85.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6RXx-d7k7Wlm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/565/6RXx-d7k7Wlm.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Reflexivity, symmetry and transitivity of the empty relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/565/6RXx-d7k7Wlm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Aw_onn7bC8s9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/Aw_onn7bC8s9.jpg</video:thumbnail_loc>

            <video:title>Equations of motion</video:title>

            <video:description><![CDATA[
Equations of motion for force-acceleration analysis of rectilinear motion of particles in rectangular coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/Aw_onn7bC8s9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4XEP23nRN8l6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/4XEP23nRN8l6.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
A direct statement on the course's purpose. It establishes the critical role of set theory as the foundational language for all quantitative and logical disciplines.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/4XEP23nRN8l6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_R8HlYIBfmA1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/838/_R8HlYIBfmA1.jpg</video:thumbnail_loc>

            <video:title>Molar mass</video:title>

            <video:description><![CDATA[
This lesson formally defines molar mass for any substance and establishes its numerical equivalence with relative mass, providing the critical conversion factor between mass and moles. Solved: 1. Supposing there is 14.25\text{g} of nitric acid (\text{HNO}_3) in a beaker. How many moles of \text{HNO}_3 are there in the beaker?2. How many molecules are there in 3.46\text{g} of hydrogen chloride?3. How many atoms of nitrogen are present in 4.86\text{g} of \text{N}_2\text{O}_5? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/838/_R8HlYIBfmA1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j41ynr4gZenQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/887/j41ynr4gZenQ.jpg</video:thumbnail_loc>

            <video:title>The non-zero constraint</video:title>

            <video:description><![CDATA[
This lesson shows why the coefficient of the squared term cannot be zero. You will learn to calculate the specific value that makes an equation lose its quadratic nature. Solved: Given the equation (m + 6)x^2 - 8x + 10 = 0, determine the value of the constant m for which the equation ceases to be a quadratic equation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/887/j41ynr4gZenQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U_9ZpIJC8v0Q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/U_9ZpIJC8v0Q.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: A civil engineering's preliminary design for a freeway off-ramp is circular with radius R=60m. If she assumes that the coefficient of static friction between tires an road is at least u_s =0.4, what is the maximum speed at which vehicles can enter the ramp without losing traction? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/U_9ZpIJC8v0Q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745331961855.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/BZzesqo7mk6a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/BZzesqo7mk6a.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: A child twirls a small 50-g ball attached to the end of a 1-m string so that the ball traces a circle in a vertical plane as shown. What is the minimum speed which the ball must have when in position 1? If this speed is maintained throughout the circle, calculate the tension T in the string when the the ball is in position 2. Neglect any small motion of the child's hand. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/BZzesqo7mk6a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745925047562.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/4YOzjmDF_2XE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/4YOzjmDF_2XE.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course. This lesson presents the curriculum roadmap and explains how each chapter builds the logic needed to master arrangements and selections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/4YOzjmDF_2XE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dIWr5UTtynbo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/dIWr5UTtynbo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: A curve in a speed track has a radius of 1000 ft and a rated speed of 120 mi/h. Knowing that a racing car start skidding on the curve when travelling at a speed of 180 mi/h, determine (a) the banking angle \theta, (b) the coefficient of static friction between the tires and the track under the prevailing conditions, (c) the minimum speed at which the same car could negotiate the curve. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/dIWr5UTtynbo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745332380305.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/NAcq_Xp43FO0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/NAcq_Xp43FO0.jpg</video:thumbnail_loc>

            <video:title>Product rule</video:title>

            <video:description><![CDATA[
The product rule applies to sequential events where one task follows another. You find the total outcomes by multiplying the number of ways each individual step can be performed.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/NAcq_Xp43FO0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7DkgjtqTumYy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/7DkgjtqTumYy.jpg</video:thumbnail_loc>

            <video:title>Rod axial potential</video:title>

            <video:description><![CDATA[
A rod sits on the axis. How do you integrate variable distance from a point off the end? We solve the definite integral for axial potential. Solved: A thin non-conducting rod of length L = 25.0 \text{ cm} carries a total positive charge Q = 7.50 \text{ }\mu\text{C} distributed uniformly along its length. The rod is positioned on the x-axis such that it extends from x_1 = 25.0 \text{ cm} to x_2 = 50.0 \text{ cm}. Calculate the electric potential at the origin (x = 0). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/7DkgjtqTumYy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i1Cy_5psFZPC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/399/i1Cy_5psFZPC.jpg</video:thumbnail_loc>

            <video:title>Guide</video:title>

            <video:description><![CDATA[
What to focus on for this topic, for the current session.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/399/i1Cy_5psFZPC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M88siZI7jAyd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/200/M88siZI7jAyd.jpg</video:thumbnail_loc>

            <video:title>Number Systems</video:title>

            <video:description><![CDATA[
What are natural numbers, integers, rational numbers, irrational numbers and real numbers?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/200/M88siZI7jAyd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XX1ZGtYa9W0f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/398/XX1ZGtYa9W0f.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the MTH 201: Mathematical Methods I learning track.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/398/XX1ZGtYa9W0f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ldKB95XOsP64</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/ldKB95XOsP64.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 0.5-kg flyballs of a centrifugal governor revolve at a constant speed v in the horizontal circle of 150-mm radios shown. Neglecting the mass of links AB, BC,AD, and DE, and requiring that the links support only tensile forces, determine the range of the allowable values of v so that the magnitudes of the forces of the links do not exceed 75N. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/ldKB95XOsP64.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745926282194.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Qsk3FvWbVeuo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/Qsk3FvWbVeuo.jpg</video:thumbnail_loc>

            <video:title>Division</video:title>

            <video:description><![CDATA[
Division of a complex number by a constant (real number) and by another complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/Qsk3FvWbVeuo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aeetUgGpJp7I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/55/aeetUgGpJp7I.jpg</video:thumbnail_loc>

            <video:title>Rational functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of rational functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/55/aeetUgGpJp7I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5mQfrE8wFncZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/403/5mQfrE8wFncZ.jpg</video:thumbnail_loc>

            <video:title>Review (1)</video:title>

            <video:description><![CDATA[
Review of key concepts on convergence of infinite series.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/403/5mQfrE8wFncZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lqlPjTtvtZgM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/53/lqlPjTtvtZgM.jpg</video:thumbnail_loc>

            <video:title>Intervals</video:title>

            <video:description><![CDATA[
Meaning and examples of intervals on the real line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/53/lqlPjTtvtZgM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EdWJFYIheE1j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/55/EdWJFYIheE1j.jpg</video:thumbnail_loc>

            <video:title>Algebraic functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of algebraic functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/55/EdWJFYIheE1j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XENfW_FU6v_6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/XENfW_FU6v_6.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome and course overview.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/XENfW_FU6v_6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cKrejSYB3OLN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/cKrejSYB3OLN.jpg</video:thumbnail_loc>

            <video:title>Fundamental concepts (2)</video:title>

            <video:description><![CDATA[
The parallelogram law of addition of forces and the principle of transmissibility of forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/cKrejSYB3OLN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DDgNg00m-CuL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/74/DDgNg00m-CuL.jpg</video:thumbnail_loc>

            <video:title>Visualization</video:title>

            <video:description><![CDATA[
Graphing two-variable functions, in contrast to single-variable ones.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/74/DDgNg00m-CuL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7umshF18TKMv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Thumbnails/302/7umshF18TKMv.jpg</video:thumbnail_loc>

            <video:title>Guide</video:title>

            <video:description><![CDATA[
Understanding statics of particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Previews/302/7umshF18TKMv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fHbqi6htW_Z_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Thumbnails/301/fHbqi6htW_Z_.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to MEE 205.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Previews/301/fHbqi6htW_Z_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PCp2tsMXDsGo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/PCp2tsMXDsGo.jpg</video:thumbnail_loc>

            <video:title>Biquadratic equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of biquadratic equations by applying algebraic substitution to reduce fourth-degree expressions into solvable quadratic forms. You will master the mechanical back-substitution process to determine all valid real roots with absolute precision. Solved: 6. Solve the equation x^4 - 13x^2 + 36 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/PCp2tsMXDsGo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EmKMpgb699dG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/EmKMpgb699dG.jpg</video:thumbnail_loc>

            <video:title>Order of operations</video:title>

            <video:description><![CDATA[
Master the BODMAS/PEMDAS hierarchy to ensure mathematical precision when resolving multi-stage algebraic expressions. You will establish the rigorous sequence for processing brackets, orders, division, multiplication, addition, and subtraction to eliminate computational errors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/EmKMpgb699dG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NRIzLUlg1sF2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/NRIzLUlg1sF2.jpg</video:thumbnail_loc>

            <video:title>Particles and rigid bodies</video:title>

            <video:description><![CDATA[
Meaning of particles and rigid bodies in the context of engineering mechanics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/NRIzLUlg1sF2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3wKup-aICna_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/616/3wKup-aICna_.jpg</video:thumbnail_loc>

            <video:title>Hyperbolic functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of hyperbolic functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/616/3wKup-aICna_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_XLCWLifwlUR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/_XLCWLifwlUR.jpg</video:thumbnail_loc>

            <video:title>Rigid-body mechanics</video:title>

            <video:description><![CDATA[
Meaning of rigid-body mechanics and its branches - statics and dynamics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/_XLCWLifwlUR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/THGvEm_2u7eV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/616/THGvEm_2u7eV.jpg</video:thumbnail_loc>

            <video:title>Inverse hyperbolic functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of inverse hyperbolic functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/616/THGvEm_2u7eV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7R15cT2iTt30</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/666/7R15cT2iTt30.jpg</video:thumbnail_loc>

            <video:title>Installation</video:title>

            <video:description><![CDATA[
This is a practical lesson with a single objective: installing our code editor. We will download and run the Visual Studio Code installer, with specific, step-by-step instructions provided for Windows, macOS, and Linux Systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/666/7R15cT2iTt30.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hW0gIYU6tjIT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/74/hW0gIYU6tjIT.jpg</video:thumbnail_loc>

            <video:title>Multivariable functions</video:title>

            <video:description><![CDATA[
Meaning and examples of multivariable real-valued functions, in contrast to single-variable ones.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/74/hW0gIYU6tjIT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QyP9bicJ2G4T</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/838/QyP9bicJ2G4T.jpg</video:thumbnail_loc>

            <video:title>The mole</video:title>

            <video:description><![CDATA[
This lesson formally defines the mole, the SI unit of chemical quantity. We establish the mole as the indispensable counting unit that enables all quantitative chemical accounting. Solved: How many hydrogen ions are there in 1 mole of sulphuric acid, \text{H}_2\text{SO}_4 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/838/QyP9bicJ2G4T.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6koSVDEy_W2d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/6koSVDEy_W2d.jpg</video:thumbnail_loc>

            <video:title>Curved arrow notation (2)</video:title>

            <video:description><![CDATA[
Enolate attack on electrophiles requires precise arrow placement. Do your arrows show the right electron source and destination? This example corrects multi-step notation mistakes directly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/6koSVDEy_W2d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XhNgP-H8Xpl7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/74/XhNgP-H8Xpl7.jpg</video:thumbnail_loc>

            <video:title>Single-valued functions</video:title>

            <video:description><![CDATA[
Meaning and examples of single-valued multivariable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/74/XhNgP-H8Xpl7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LWpo-bJP_kGL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/LWpo-bJP_kGL.jpg</video:thumbnail_loc>

            <video:title>First partial derivatives</video:title>

            <video:description><![CDATA[
Meaning of the first partial derivatives of a function of two variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/LWpo-bJP_kGL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0ndU4HG8y2zq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/908/0ndU4HG8y2zq.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
A direct statement of the course's purpose and structure. This lesson outlines the path from fundamental quantities and vectors to the full analysis of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/908/0ndU4HG8y2zq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wUN73Ivm5ZA4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/74/wUN73Ivm5ZA4.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/74/wUN73Ivm5ZA4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-c5ipri2kN8Q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/567/-c5ipri2kN8Q.jpg</video:thumbnail_loc>

            <video:title>Residue classes</video:title>

            <video:description><![CDATA[
Meaning and evaluation of residue classes modulo m.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/567/-c5ipri2kN8Q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/beS5sjAcaaI_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/beS5sjAcaaI_.jpg</video:thumbnail_loc>

            <video:title>Rigid-body motion (5)</video:title>

            <video:description><![CDATA[
Overview of different kinds of rigid-body motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/beS5sjAcaaI_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EAc7iRm968Fw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/EAc7iRm968Fw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: Cylinder A has a mass of 3 kg and cylinder B has a mass of 8 kg. Determine the speed of A after it has moved 2 m starting from rest. Neglect the mass of the cord and pulleys. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/EAc7iRm968Fw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1746790343185.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/7qbotEaSPBhW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/7qbotEaSPBhW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: The pendulum shown is put in motion with a speed v_o when \theta = 0^\circ. Letting L = 2 ft, determine v_o if the pendulum first comes to a stop at \theta = 47^\circ. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/7qbotEaSPBhW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747071213738.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/S6t62cYkccvZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/S6t62cYkccvZ.jpg</video:thumbnail_loc>

            <video:title>Two bodies on a surface (1)</video:title>

            <video:description><![CDATA[
General approach for force-acceleration analysis of absolute and relative motion of bodies in contact, for two bodies on a surface.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/S6t62cYkccvZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Twijcl3Cjmqd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/569/Twijcl3Cjmqd.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and examples of a lattice.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/569/Twijcl3Cjmqd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QSn79aL9yonD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/567/QSn79aL9yonD.jpg</video:thumbnail_loc>

            <video:title>Congruence</video:title>

            <video:description><![CDATA[
Meaning of the congruence modulo m relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/567/QSn79aL9yonD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RGpGI0Tjy9-x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/567/RGpGI0Tjy9-x.jpg</video:thumbnail_loc>

            <video:title>Modular arithmetics</video:title>

            <video:description><![CDATA[
How to carry out modular arithmetic operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/567/RGpGI0Tjy9-x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cqnoZtTYtStB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/cqnoZtTYtStB.jpg</video:thumbnail_loc>

            <video:title>Worked examples II</video:title>

            <video:description><![CDATA[
Worked examples on classification of quadric surfaces by eigenvalue inspection and / or variable substitution. Solved: Classify 2xy+2\sqrt{2} x=1 and determine the angle of rotation required to align its axes with the x-y coordinates system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/cqnoZtTYtStB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-zxZHuI5fB-q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/-zxZHuI5fB-q.jpg</video:thumbnail_loc>

            <video:title>Rigid bodies</video:title>

            <video:description><![CDATA[
Meaning of rigid bodies, in contrast to particles; identifying rigid-body problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/-zxZHuI5fB-q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ab499L_VKZ09</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/788/Ab499L_VKZ09.jpg</video:thumbnail_loc>

            <video:title>Finalising content</video:title>

            <video:description><![CDATA[
This final lesson focuses on the professional habit of writing clear and compelling content. We will write the titles, short descriptions, and links for each of our portfolio projects.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/788/Ab499L_VKZ09.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yvXJ45xXD0wQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/yvXJ45xXD0wQ.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of a partially-ordered set (POSET).  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/yvXJ45xXD0wQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_9xTZDKcU_G0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/997/_9xTZDKcU_G0.jpg</video:thumbnail_loc>

            <video:title>Ordered pairs</video:title>

            <video:description><![CDATA[
Define an ordered pair as a collection of two objects where the sequence of elements determines the identity. You will learn to distinguish between sets and ordered pairs by applying the equality rule, which requires both corresponding elements to be identical. This is the basis for all mappings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/997/_9xTZDKcU_G0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FHt33gc0TJXI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/393/FHt33gc0TJXI.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/393/FHt33gc0TJXI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S1lUi4ZfGryT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/S1lUi4ZfGryT.jpg</video:thumbnail_loc>

            <video:title>Fundamental concepts (1)</video:title>

            <video:description><![CDATA[
Meaning of space, mass, time and force.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/S1lUi4ZfGryT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TRdjt9nz93ou</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/61/TRdjt9nz93ou.jpg</video:thumbnail_loc>

            <video:title>Slope of a line</video:title>

            <video:description><![CDATA[
A review of the meaning of the slope (gradient) of a straight line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/61/TRdjt9nz93ou.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iTAvIMJYebII</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/61/iTAvIMJYebII.jpg</video:thumbnail_loc>

            <video:title>Differentiability at a point</video:title>

            <video:description><![CDATA[
Differentiability of a function, and its derivative at a given point.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/61/iTAvIMJYebII.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d6r9onVJQWlY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/d6r9onVJQWlY.jpg</video:thumbnail_loc>

            <video:title>Rational inequality (2)</video:title>

            <video:description><![CDATA[
Follow this second walkthrough on rational inequalities to reinforce your use of critical values and sign tables. You will learn to correctly handle inequalities with terms on both sides by rearranging them into a single fraction before testing intervals and defining the final solution set. Solved: 8. Solve the inequality \frac{x-1}{x-2} > \frac{x-2}{x-3}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/d6r9onVJQWlY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RaBt5nIOIVYx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/616/RaBt5nIOIVYx.jpg</video:thumbnail_loc>

            <video:title>Inverse trigonometric functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of inverse trigonometric functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/616/RaBt5nIOIVYx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/otaZQ6AGYkLo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/400/otaZQ6AGYkLo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on continuity of real-valued single-variable functions - 2023/2024 mid-semester examination questions. Solved: What nature of discontinuity does the function f{[x]}=x^3 cos\frac{1}{x^2}, x\in \mathbb{R}, x\ne0 have at x=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/400/otaZQ6AGYkLo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hWjXxcgWkk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/hWjXxcgWkk.jpg</video:thumbnail_loc>

            <video:title>Solvent extraction</video:title>

            <video:description><![CDATA[
One big wash or two small ones? How does splitting the solvent volume change the mass of acid extracted from water? Watch to prove why batch extraction wins. Solved: Supposing the distribution coefficient of an organic acid between and organic solvent and water is 10. What mass of the solute will extracted into the organic solvent if 50 mL of water containing 1 g of the acid is mixed with:a. 50 mL of ether in a single extractionb. two equal volumes of ether in batch extraction 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/hWjXxcgWkk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8VodPQOKUHPl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/8VodPQOKUHPl.jpg</video:thumbnail_loc>

            <video:title>Exercises</video:title>

            <video:description><![CDATA[
Curly arrows track electron movement in organic mechanisms. Can you correctly identify the nucleophile and predict the product without guessing? These exercises test and fix your notation skills directly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/8VodPQOKUHPl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4ThP3GaIscWU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/887/4ThP3GaIscWU.jpg</video:thumbnail_loc>

            <video:title>Standard form</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to rearrange an equation into standard form by moving all terms to one side. You will learn to correctly identify the numerical values of a, b, and c after the rearrangement. Solved: Write the equation 5x - 14 = x^2 in the standard form ax^2 + bx + c = 0 and identify the specific values of a, b, and c. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/887/4ThP3GaIscWU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1SpuBi00oWzu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1008/1SpuBi00oWzu.jpg</video:thumbnail_loc>

            <video:title>Deductions from rules of indices</video:title>

            <video:description><![CDATA[
Master the logical derivation of zero, negative, and fractional indices from the fundamental laws of powers. You will execute the mechanical transformation of these special index forms into their reciprocal and radical equivalents to ensure computational accuracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1008/1SpuBi00oWzu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ch1wTz8RP7Lp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/ch1wTz8RP7Lp.jpg</video:thumbnail_loc>

            <video:title>Two-variable inequality (2)</video:title>

            <video:description><![CDATA[
Follow a second walkthrough on graphing two-variable inequalities to master shading feasible regions. You will rearrange the expression into slope-intercept form to identify the boundary line and use test points to confirm the valid half-plane. This skill is vital for solving systems of constraints. Solved: 12. Graph the solution region(s) for the system of inequalitiesy > x + 2 \text{ and } x + y \le 4 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/ch1wTz8RP7Lp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UUGD74jpvq9W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/UUGD74jpvq9W.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The small body has a speed v_A=5m/s at point A . Neglecting friction, determine its speed v_B at point B after it has risen 0.8m . Is knowledge of the shape of the track necessary? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/UUGD74jpvq9W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746783820485.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/oAwuFp2aSu8N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/oAwuFp2aSu8N.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating first partial derivatives from the first principles. Solved: If f(x,y)=x^2-2y^2, obtain \frac{\partial f} {\partial x} and \frac{\partial f} {\partial y} from first principles. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/oAwuFp2aSu8N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iuh4D8wx78vz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/iuh4D8wx78vz.jpg</video:thumbnail_loc>

            <video:title>Addition</video:title>

            <video:description><![CDATA[
Operation of addition (and subtraction) of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/iuh4D8wx78vz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5G2_VkSM1rH2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/5G2_VkSM1rH2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on algebra of matrices. Solved: Given that 3\left[\begin{array}{ccc}x & y\\ z & w\end{array}\right]=\left[\begin{array}{ccc} x & 6\\ -1 &2w\end{array}\right]+\left[\begin {array}{ccc} 4 & x+y \\z+w & 3\end{array}\right], find x, y, z and w. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/5G2_VkSM1rH2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pL4AVRzIMoyG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/66/pL4AVRzIMoyG.jpg</video:thumbnail_loc>

            <video:title>Kinds of sequences (2)</video:title>

            <video:description><![CDATA[
Monotone sequences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/66/pL4AVRzIMoyG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wHUFQ6-CJKpR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/wHUFQ6-CJKpR.jpg</video:thumbnail_loc>

            <video:title>Diagonalization of matrices</video:title>

            <video:description><![CDATA[
An overview of diagonal matrices and diagonalization of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/wHUFQ6-CJKpR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Mi3RChg-Sc69</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/Mi3RChg-Sc69.jpg</video:thumbnail_loc>

            <video:title>Degree of differential equations</video:title>

            <video:description><![CDATA[
Identifying the degree of differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/Mi3RChg-Sc69.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H0DrxkP0okKH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/212/H0DrxkP0okKH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on linear dependence and independence of vectors in a vector space. Solved: Determine whether or not the functions f,g,h are linearly independent(a) f(t)=e^t ,g(t)= \sin t ,h(t)=t(b) f(t)=e^t ,g(t)= e^{2t} ,h(t)=t(c) f(t)=\sin t ,g(t)= \cos t ,h(t)=2\sin t 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/212/H0DrxkP0okKH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YAgpDd1imHfI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/65/YAgpDd1imHfI.jpg</video:thumbnail_loc>

            <video:title>Arithmetic progressions</video:title>

            <video:description><![CDATA[
Meaning, examples, and descriptions of arithmetic progressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/65/YAgpDd1imHfI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AKJ0tiiDmsEl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/418/AKJ0tiiDmsEl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating line or double integrals using Green's theorem. Solved: Evaluate \oint_C \,[2x (x+y)dx, (x^2 + xy+y^2)dy] around the square shown below 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/418/AKJ0tiiDmsEl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747319929933.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/NWPn58ckFq5I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/NWPn58ckFq5I.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: LINK OA rotates with a counterclockwise angular velocity \omega=3rad/s . Determine the angular velocity of bar BC when \theta=20^\circ. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/NWPn58ckFq5I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744971231563.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/fYEbbXBX9JN6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/fYEbbXBX9JN6.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General analysis procedure for kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/fYEbbXBX9JN6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lPmY57sG1hR9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/142/lPmY57sG1hR9.jpg</video:thumbnail_loc>

            <video:title>Rigid-body motion (2)</video:title>

            <video:description><![CDATA[
Overview of different kinds of rigid-body motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/142/lPmY57sG1hR9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iOqcsfRXNehH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/66/iOqcsfRXNehH.jpg</video:thumbnail_loc>

            <video:title>Defining the terms of a sequence</video:title>

            <video:description><![CDATA[
Various ways of defining the terms of a sequence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/66/iOqcsfRXNehH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a9t_OUxC1mJB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/a9t_OUxC1mJB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on proof of linearity of maps. Solved: Suppose T:V\to{V} add, U_0\in{V} to every vector, such that T(V)=V+U_0(a) Is T linear? (b) what if U_0=0_V 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/a9t_OUxC1mJB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kf7pJqy3zFXj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/Kf7pJqy3zFXj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 2-kg collar is released from rest at A and slides down the inclined fixed rod on the vertical plane. The coefficient of kinetic friction is 0.40 . Calculate (a) the velocity v of the collar as it strikes the spring and (b) the maximum deflection x of the spring. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/Kf7pJqy3zFXj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746787047121.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vQdanPsRz6F4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/914/vQdanPsRz6F4.jpg</video:thumbnail_loc>

            <video:title>Summary and next steps</video:title>

            <video:description><![CDATA[
This lesson synthesises the mathematical framework of kinematics - spanning straight-line motion, projectile vectors, and variable acceleration calculus. You will consolidate these principles as a mandatory foundation for the upcoming study of Newtonian dynamics and the physical causes of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/914/vQdanPsRz6F4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/35TvIli2_QHD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/35TvIli2_QHD.jpg</video:thumbnail_loc>

            <video:title>Charges on a rim</video:title>

            <video:description><![CDATA[
Charges on a rim share equal distance from the centre. How do you find total potential without knowing the radius? We use superposition and algebraic sums to solve it. Solved: Four charged bolts are fixed onto the metallic rim of a car wheel. The charges on these bolts are q_1 = +0.40 \text{ }\mu\text{C}, q_2 = +1.60 \text{ }\mu\text{C}, q_3 = -1.20 \text{ }\mu\text{C}, and q_4 = -0.30 \text{ }\mu\text{C}. A mechanic measures that the electric potential at the exact centre of the wheel due to the q_1 bolt alone is 3.2 \times 10^4 \text{ V}. Calculate the total resultant electric potential at the centre of the wheel produced by all four bolts combined. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/35TvIli2_QHD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TjwJlOgf5y6C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/TjwJlOgf5y6C.jpg</video:thumbnail_loc>

            <video:title>Principle of transmissibility of forces</video:title>

            <video:description><![CDATA[
Statement, meaning and implications of the principle of transmissibility of forces on rigid bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/TjwJlOgf5y6C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_5zbxOnt65AL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/156/_5zbxOnt65AL.jpg</video:thumbnail_loc>

            <video:title>Forces and reactions (2)</video:title>

            <video:description><![CDATA[
Meaning and modelling of forces and reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/156/_5zbxOnt65AL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gGmV0m48nW7m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/915/gGmV0m48nW7m.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides an essential overview of the course structure and the transition from kinematics to dynamics. You will understand how we systematically build from Newton's first principles to complex multi-body systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/915/gGmV0m48nW7m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/isRc6WBPevmv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/isRc6WBPevmv.jpg</video:thumbnail_loc>

            <video:title>Theorems (2)</video:title>

            <video:description><![CDATA[
More theorems on the limits of real sequences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/isRc6WBPevmv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_VdN2E9Fj_ds</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/_VdN2E9Fj_ds.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
General properties of line integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/_VdN2E9Fj_ds.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iU1XGTgMJy7p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/915/iU1XGTgMJy7p.jpg</video:thumbnail_loc>

            <video:title>Forces</video:title>

            <video:description><![CDATA[
Formally defines force as a push or a pull that can cause an object to accelerate and classifies fundamental types into contact and non-contact forces. You will distinguish between interactions requiring physical touch and those acting at a distance through field effects.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/915/iU1XGTgMJy7p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OuLwZy8pPdIy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/OuLwZy8pPdIy.jpg</video:thumbnail_loc>

            <video:title>Factorisation</video:title>

            <video:description><![CDATA[
This lesson demonstrates solving a quadratic equation by splitting the middle term to create factors. You will learn to find the product and sum needed to factorise the expression and solve for the roots. Solved: Solve the equation 2x^2 - 7x - 4 = 0 by the method of factorisation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/OuLwZy8pPdIy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Hl_00I4Almjr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/Hl_00I4Almjr.jpg</video:thumbnail_loc>

            <video:title>Standard integrals</video:title>

            <video:description><![CDATA[
Overview of common functions and their integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/Hl_00I4Almjr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QWBtlvZPQDHY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/QWBtlvZPQDHY.jpg</video:thumbnail_loc>

            <video:title>Techniques of integration (1)</video:title>

            <video:description><![CDATA[
A review of the techniques of integration of single-variable real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/QWBtlvZPQDHY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dwCKFVoIiqKH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/dwCKFVoIiqKH.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of line integral, in contrast to a definite integral along the x-axis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/dwCKFVoIiqKH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MzO4aEOTJvdK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/MzO4aEOTJvdK.jpg</video:thumbnail_loc>

            <video:title>Forms of line integrals</video:title>

            <video:description><![CDATA[
Different forms of line integrals and how to evaluate  them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/MzO4aEOTJvdK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DqJZxZmGzVAo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/210/DqJZxZmGzVAo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on linear vector subspaces. Solved: Determine whether or not W is a vector subspace of \mathbf{R}^3 over \mathbf{R} where (a) W= [(a,b,c)\in R^3:ab=0](b) W= [(a,b,c)\in R^3:a+b+c=0](c) W= [(a,b,c)\in R^3:b=a^2] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/210/DqJZxZmGzVAo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2A0liktpu3g7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/213/2A0liktpu3g7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on basis and dimension of vector spaces. Solved: Find the dimension and basis of subspace W of P_3 [t] spanned by the vectorsu = t^3 + 2t^2 - 3t + 4,v = 2t^3 + 5t^2 -4t + 7,w = t^3 + 4t^2 + t + 2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/213/2A0liktpu3g7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/64cJJMySeCsn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/649/64cJJMySeCsn.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/649/64cJJMySeCsn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Thl_jJh9FfX5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/386/Thl_jJh9FfX5.jpg</video:thumbnail_loc>

            <video:title>Volume</video:title>

            <video:description><![CDATA[
Calculation of volume beneath a surface and above a region R in a plane by double integration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/386/Thl_jJh9FfX5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-N7jnA5klAb1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/-N7jnA5klAb1.jpg</video:thumbnail_loc>

            <video:title>Systems of units (1)</video:title>

            <video:description><![CDATA[
Units of measurement of mass, length, time, force, etc., in the S. I. and U. S. customary units.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/-N7jnA5klAb1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uFYgDP8zsSAY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/uFYgDP8zsSAY.jpg</video:thumbnail_loc>

            <video:title>General procedure</video:title>

            <video:description><![CDATA[
General procedure for solving engineering mechanics problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/uFYgDP8zsSAY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J-TZkcZxz9xx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/386/J-TZkcZxz9xx.jpg</video:thumbnail_loc>

            <video:title>Mass and centre of gravity</video:title>

            <video:description><![CDATA[
Calculation of total mass and centre of gravity by double integration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/386/J-TZkcZxz9xx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y1_TLM-Wp0Lf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/Y1_TLM-Wp0Lf.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Formal and informal definition of the convergence of a sequence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/Y1_TLM-Wp0Lf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HjONrFdk5BIa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/HjONrFdk5BIa.jpg</video:thumbnail_loc>

            <video:title>Absolute values</video:title>

            <video:description><![CDATA[
Define absolute value as the non-negative distance of a number from zero on the real line. You will learn to solve equations and inequalities involving absolute values by splitting them into their positive and negative cases. This foundation is essential for defining tolerance and error.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/HjONrFdk5BIa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QcYIwVkWlMNT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/QcYIwVkWlMNT.jpg</video:thumbnail_loc>

            <video:title>Inequality of means</video:title>

            <video:description><![CDATA[
Understand the fundamental relationship between arithmetic and geometric means for non-negative numbers. You will learn the proof that the arithmetic mean is always greater than or equal to the geometric mean, which is a vital tool for optimisation and proving advanced algebraic inequalities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/QcYIwVkWlMNT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cyQ572ZppxqB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/cyQ572ZppxqB.jpg</video:thumbnail_loc>

            <video:title>Triangle rule</video:title>

            <video:description><![CDATA[
Addition of force vectors using the triangle rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/cyQ572ZppxqB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3gNB17qdhA0a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/3gNB17qdhA0a.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on vector algebra and its geometric applications. Solved: ABCD is a plain quadrilateral. Show that the sum of vectors \vec{AB},\vec{CB}, \vec{CD} , and \vec{AD} is 4\vec{PQ} where P and Q are the midpoints of AC and BD respectively. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/3gNB17qdhA0a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eUmyBx25ucuB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/eUmyBx25ucuB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (15)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/eUmyBx25ucuB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8r4HB4UNYQFQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/8r4HB4UNYQFQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (16)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/8r4HB4UNYQFQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jRQzZcXynJN7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/jRQzZcXynJN7.jpg</video:thumbnail_loc>

            <video:title>Nested sets</video:title>

            <video:description><![CDATA[
Execute the systematic analysis of sets containing other sets as elements through rigorous calculation. You will master the mechanical identification of membership versus inclusion in complex nested structures to ensure absolute precision in hierarchical data categorisation. Solved: 1. Let A = { \emptyset, 1, {2, 3} }. (a) Determine the cardinality of A and that of its power set \mathcal{P}(A). (b) List all elements of \mathcal{P}(A). (c) Determine whether or not each ofthe following statements is true, false and explain why: (i) {2, 3} \subseteq A (ii) {2, 3} \in A (iii) \emptyset \subseteq A (iv) \emptyset \in A 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/jRQzZcXynJN7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qZfBSZWOU9Yi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Thumbnails/363/qZfBSZWOU9Yi.jpg</video:thumbnail_loc>

            <video:title>Adding Notes and editing sheet layout</video:title>

            <video:description><![CDATA[
This lesson is designed to equip students with skills to effectively communicate essential design details through notes and optimize the layout of engineering drawings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Previews/363/qZfBSZWOU9Yi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DRj0HCXZe5Yo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/DRj0HCXZe5Yo.jpg</video:thumbnail_loc>

            <video:title>Absorption laws</video:title>

            <video:description><![CDATA[
Define the absorption laws to understand how redundant set operations reduce to a simpler original set. You will learn to recognise specific structures where the union or intersection of sets cancels out nested operations, which is vital for simplifying complex boolean and symbolic logic.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/DRj0HCXZe5Yo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2JT_oEZDbKkJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/147/2JT_oEZDbKkJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of a rigid body undergoing general plane motion by locating an instantaneous centre of zero velocity. Solved: The drums have the angular velocities at the instant shown. Determine the angular velocity of the pulley C and the velocity of the load D. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/147/2JT_oEZDbKkJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744986864207.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/hxHSlUrckJpZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/hxHSlUrckJpZ.jpg</video:thumbnail_loc>

            <video:title>Theorems (1)</video:title>

            <video:description><![CDATA[
Some theorems on the limits of real sequences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/hxHSlUrckJpZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/psCAeaLksGLx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/psCAeaLksGLx.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of integration and its associated symbols.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/psCAeaLksGLx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4XXaVh10gt5_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/4XXaVh10gt5_.jpg</video:thumbnail_loc>

            <video:title>Parallelogram rule</video:title>

            <video:description><![CDATA[
Addition of force vectors using the parallelogram rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/4XXaVh10gt5_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q-Zgzqq8OnTv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/Q-Zgzqq8OnTv.jpg</video:thumbnail_loc>

            <video:title>Rollers</video:title>

            <video:description><![CDATA[
Reactions at rollers in a guide or on rough surfaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/Q-Zgzqq8OnTv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/G1ESphalcNqm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/G1ESphalcNqm.jpg</video:thumbnail_loc>

            <video:title>Change of base</video:title>

            <video:description><![CDATA[
This lesson explains the change of base formula used to rewrite logarithms in any required base. You will learn to convert non-standard bases into common or natural logarithms to allow for easier computation and solution of exponential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/G1ESphalcNqm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nJA1kyhWYrqO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/nJA1kyhWYrqO.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and overview of course content.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/nJA1kyhWYrqO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/amjE22B7H9Do</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Thumbnails/363/amjE22B7H9Do.jpg</video:thumbnail_loc>

            <video:title>Creating multiple detailed views</video:title>

            <video:description><![CDATA[
This lesson is designed to help students master the techniques for generating detailed views that highlight intricate areas of their designs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Previews/363/amjE22B7H9Do.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5O_xfwHqnwjN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Thumbnails/387/5O_xfwHqnwjN.jpg</video:thumbnail_loc>

            <video:title>Infimum and supremum (1)</video:title>

            <video:description><![CDATA[
Meaning of infimum and supremum of subsets of real numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Previews/387/5O_xfwHqnwjN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jLvSVzG06yEd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/407/jLvSVzG06yEd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on first-order ordinary differential equations - 2022/2023 final semester examination questions. Solved: Given the initial value problem \frac{dy}{dx}=ay{[x]}+b, y{[x_{0}}]=y_{0}, where a,b,x_{0},y_{0}\in\mathbb{R}, a \neq 0. Find a solution y{[x]}:\mathbb{R}\to\mathbb{R} of the problem when x_0=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/407/jLvSVzG06yEd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EjqaXgdOw-YX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/398/EjqaXgdOw-YX.jpg</video:thumbnail_loc>

            <video:title>Guide</video:title>

            <video:description><![CDATA[
Regular study vs examination preparation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/398/EjqaXgdOw-YX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lWYN0cIHOcqw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/296/lWYN0cIHOcqw.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
How to find the resultant of several concurrent forces by resolution of each force into rectangular components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/296/lWYN0cIHOcqw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AkywGxY9AzMS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/147/AkywGxY9AzMS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of a rigid body undergoing general plane motion by locating an instantaneous centre of zero velocity. Solved: The arm ABC rotates with an angular velocity of 4 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 8 rad/s counterclockwise, determine(a) the instantaneous centers of rotation of gears A and C,(b) the angular velocities of gears A and C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/147/AkywGxY9AzMS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744987124048.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/AF1skVjjxyVA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Thumbnails/363/AF1skVjjxyVA.jpg</video:thumbnail_loc>

            <video:title>Creating a Bill of Materials.</video:title>

            <video:description><![CDATA[
Students will understand how to generate and insert BOMs directly from assembly models, ensuring that part names, quantities, materials, and other relevant details are automatically listed and linked to model data.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Previews/363/AF1skVjjxyVA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vz1zPO8_5B4a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/Vz1zPO8_5B4a.jpg</video:thumbnail_loc>

            <video:title>Condition</video:title>

            <video:description><![CDATA[
Condition for equilibrium of a particle in two dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/Vz1zPO8_5B4a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j21M63LFHdQV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/j21M63LFHdQV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the collision of particles and their motion before and after collision.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/j21M63LFHdQV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ig2oljmlN0fV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Thumbnails/363/Ig2oljmlN0fV.jpg</video:thumbnail_loc>

            <video:title>Introduction to Annotation tools</video:title>

            <video:description><![CDATA[
The Annotation Tools in SolidWorks course introduces students to the wide array of annotation features that enhance the clarity and functionality of technical drawings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Previews/363/Ig2oljmlN0fV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9ODeRW8l3jiw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/9ODeRW8l3jiw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/9ODeRW8l3jiw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5Ha2ja4wvRyo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/5Ha2ja4wvRyo.jpg</video:thumbnail_loc>

            <video:title>Classifying numbers</video:title>

            <video:description><![CDATA[
Execute the systematic classification of numerical values into their most restrictive sets through a rigorous problem walkthrough. You will master the mechanical identification of rational, irrational, and integer elements to ensure precise domain definition. Solved: 1. Consider the following list of numbers: { -5, 0, \frac{2}{3}, \sqrt{7}, 4, \pi, \sqrt{-16} } Identify all the sets to which each number belongs from the following list: \mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{Q}', \mathbb{R}, \mathbb{C} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/5Ha2ja4wvRyo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Oj_6SsIuiVGX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/Oj_6SsIuiVGX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: Each of the two elastic rubber bands of the slingshot has an unstretched length of 200 mm. If they are pulled back to the position shown and released from rest, determine the speed of the 25-g pellet just after the rubber bands became unstretched. Neglect the mass of the rubber bands. Each rubber bands has a stiffness of k = 50 N/m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/Oj_6SsIuiVGX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747074396539.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/95xDkNDu5sOT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Thumbnails/364/95xDkNDu5sOT.jpg</video:thumbnail_loc>

            <video:title>Basic surface design tools</video:title>

            <video:description><![CDATA[
In this course, students will learn how to use fundamental surface design tools, including Extruded, Revolved, Lofted, and Swept Surfaces, to generate different surface types. Additionally, they will explore the Trim and Extend tools to refine surface edges, the Knit Surface tool to merge multiple surfaces into a single entity, and the Filter tool to create smooth transitions between surfaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Previews/364/95xDkNDu5sOT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ukITFd0U6ufp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/ukITFd0U6ufp.jpg</video:thumbnail_loc>

            <video:title>Magnitude and two angles</video:title>

            <video:description><![CDATA[
How to obtain the components of a force in three dimensions from its magnitude and two angles defining its orientation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/ukITFd0U6ufp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U-f7xjORd7Vr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/276/U-f7xjORd7Vr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on Taylor's theorem for a function of two variables. Solved: Expand xy-1 in powers of x-1 and y-1, neglecting terms of degree \ge2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/276/U-f7xjORd7Vr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sMlaUNAR_CWG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/sMlaUNAR_CWG.jpg</video:thumbnail_loc>

            <video:title>Projections</video:title>

            <video:description><![CDATA[
Review of the scalar or dot product of two vectors; how to obtain the projection (component) of a force to a given direction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/sMlaUNAR_CWG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oVohbI-HvJRp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/oVohbI-HvJRp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the scalar product of two vectors. Solved: 1.Complete the scalar product of vectors a=3i+2j+6k and b=2i+j+4k.2.Find the angles between vectors a=(2,-3,4) and b=(-3,4,6). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/oVohbI-HvJRp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qcuvAXrPo0pf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/276/qcuvAXrPo0pf.jpg</video:thumbnail_loc>

            <video:title>Theorem</video:title>

            <video:description><![CDATA[
Taylor's theorem for a function of two variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/276/qcuvAXrPo0pf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E5J47SZFeGFb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/E5J47SZFeGFb.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Equations and procedure for analysis of equilibrium of a particle in two dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/E5J47SZFeGFb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BvU_fIV_zs4d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/BvU_fIV_zs4d.jpg</video:thumbnail_loc>

            <video:title>Rectangular components</video:title>

            <video:description><![CDATA[
An illustration of the rectangular components of a force and its direction cosines in three dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/BvU_fIV_zs4d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zojYBtBXLYvh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/zojYBtBXLYvh.jpg</video:thumbnail_loc>

            <video:title>Completing the square</video:title>

            <video:description><![CDATA[
This lesson demonstrates the step-by-step process of solving an equation by completing the square. You will learn how to manipulate the expression to create a perfect square and express your final roots in surd form. Solved: Solve the equation x^2 - 8x + 4 = 0 by completing the square. Leave your answer in surd form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/zojYBtBXLYvh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M-yOJRSqMOnZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/M-yOJRSqMOnZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on general curvilinear motion concepts. Solved: A car travelling along the road has the velocities indicated in the figure when it arrives at points A, B, and C. If it takes 10s for it to go from A to B, and then 15s to go from B to C, determine the average acceleration between points A and B and between points B and C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/M-yOJRSqMOnZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742210540033.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/E46DB5HQf7Z6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/104/E46DB5HQf7Z6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on scalar and vector products using sign functions. Solved: Show that (\vec{a}\times\vec{b}).\vec{c}=\vec{a}.(\vec{b}\times\vec{c}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/104/E46DB5HQf7Z6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7d9krXbWH7hr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/7d9krXbWH7hr.jpg</video:thumbnail_loc>

            <video:title>Efficiency</video:title>

            <video:description><![CDATA[
Calculating the efficiency of a machine.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/7d9krXbWH7hr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5BJliQ9owFQT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/888/5BJliQ9owFQT.jpg</video:thumbnail_loc>

            <video:title>Equation with fractions</video:title>

            <video:description><![CDATA[
This lesson shows how to clear fractions from an equation by multiplying with the common denominator. You will learn to reduce the resulting expression into standard quadratic form to solve for the unknown variable. Solved: Solve the following fractional equation by first reducing it to a standard quadratic form: \frac{x}{x+2} + \frac{x+2}{x} = \frac{25}{12}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/888/5BJliQ9owFQT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C-DfHne8mscj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/406/C-DfHne8mscj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on numerical methods of solution of equations in one variable - 2022/2023 final semester examination questions. Solved: Find the approximate value \int_{3}^{7}x^2 In (x) dx using simpson's \frac{1}{3} rule with h=1 , correct to 6 decimal places. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/406/C-DfHne8mscj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1ZDrcwtCd42T</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/85/1ZDrcwtCd42T.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on integration by Simpson's 1/3 rule. Solved: Evaluate \int_{0}^{1}{\frac {dx} {1 + x}} using trapezoidal and simpson's rules with h = 0.125. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/85/1ZDrcwtCd42T.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/o2FKPzyaDDEi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/o2FKPzyaDDEi.jpg</video:thumbnail_loc>

            <video:title>Laws of algebra</video:title>

            <video:description><![CDATA[
Execute the systematic application of commutative, associative, and distributive laws through a rigorous problem walkthrough. You will master the mechanical simplification of algebraic expressions by correctly reordering and grouping terms to ensure computational precision. Solved: 2. Simplify 3(2x + 4) - 2(3x - 5) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/o2FKPzyaDDEi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gSCFAt0EkSTS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/141/gSCFAt0EkSTS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on manipulating matrices with MS-Excel (Google Sheets) - solution of a square system of linear equations. Solved: Using matrix inverse method, solve the system o equations: 3x_1-2x_2+2_3=10 x_1+2x_2-3x_3=-14x_1+x_2+2x_3=3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/141/gSCFAt0EkSTS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gbUQYhhcUXiI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/gbUQYhhcUXiI.jpg</video:thumbnail_loc>

            <video:title>Effect of concentration</video:title>

            <video:description><![CDATA[
Execute the systematic prediction of equilibrium shifts using Le Chateliers principle through a rigorous problem walkthrough. You will master the mechanical resolution of concentration imbalances to restore system stability with absolute precision. Solved: Worked Example on the effect of Change in Concentration on equilibrium position: For the equilibrium N_2O_4(g) \rightleftharpoons 2 NO_2(g) at a certain temperature, the equilibrium concentrations are: [N_2O_4] = 0.10 \text{ M}, [NO_2] = 0.40 \text{ M} Additional NO_2 is suddenly injected into the container so that the concentration of NO_2 immediately becomes 0.60 M, while the volume and temperature remain constant.Calculate the new equilibrium concentrations of N_2O_4 and NO_2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/gbUQYhhcUXiI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TUPotVqtHOOt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/299/TUPotVqtHOOt.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Procedure for summing force vectors in three dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/299/TUPotVqtHOOt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XXCZyQFnqRfa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/XXCZyQFnqRfa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: With what minimum horizontal velocity u can a boy throw a rock at A and have it just clear the obstruction at B? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/XXCZyQFnqRfa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746266695596.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/KoxcKDFdygxr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/KoxcKDFdygxr.jpg</video:thumbnail_loc>

            <video:title>Force to force-couple resolution</video:title>

            <video:description><![CDATA[
How to resolve a single force into an equivalent force-couple system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/KoxcKDFdygxr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PNvHT2DSvyFB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/PNvHT2DSvyFB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: The nozzle at A discharges cooling water with an initial velocity v_o at an angle of 6^\circ with the horizontal onto a grinding wheel 350 mm in diameter. Determine the range of values of the initial velocity for which the water will land on the grinding wheel between points B and C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/PNvHT2DSvyFB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742213949529.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WoGMGPOc3H7V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/WoGMGPOc3H7V.jpg</video:thumbnail_loc>

            <video:title>Overview</video:title>

            <video:description><![CDATA[
An overview of methods for calculating the moment of a force about a point or axis in two and three dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/WoGMGPOc3H7V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cUDE8VMoY7U3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/cUDE8VMoY7U3.jpg</video:thumbnail_loc>

            <video:title>Elementary calculation</video:title>

            <video:description><![CDATA[
Calculating moments using force times perpendicular distance.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/cUDE8VMoY7U3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BxeZlLbZkpWs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/BxeZlLbZkpWs.jpg</video:thumbnail_loc>

            <video:title>Vector formulation</video:title>

            <video:description><![CDATA[
Calculating moments using a vector product.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/BxeZlLbZkpWs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZNssDPOroAuI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/ZNssDPOroAuI.jpg</video:thumbnail_loc>

            <video:title>Exponentials and linear scaling</video:title>

            <video:description><![CDATA[
Exponential integrands with different bases require distinct scaling rules. How do you handle base e with linear coefficients versus arbitrary bases? We apply the correct factors to resolve this mix. Solved: Evaluate the indefinite integral \int (4e^{3x} + 5^{x}) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/ZNssDPOroAuI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A20aWZ4jmC0p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/A20aWZ4jmC0p.jpg</video:thumbnail_loc>

            <video:title>Evaluation (1)</video:title>

            <video:description><![CDATA[
Execute the systematic evaluation of polynomial functions through rigorous substitution of specified numerical values. You will master the mechanical calculation of outputs for linear and quadratic expressions to ensure precise functional analysis. Solved: 1. Given the polynomial P(x) = x^3 - 5x^2 + 2x - 8, evaluate P(-3). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/A20aWZ4jmC0p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ScoAk1m90E02</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/ScoAk1m90E02.jpg</video:thumbnail_loc>

            <video:title>Moment of a couple</video:title>

            <video:description><![CDATA[
Calculation and some properties of the moment of a couple.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/ScoAk1m90E02.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DmF4nt7L8FAi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/DmF4nt7L8FAi.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
What is the moment of a force about an axis? How is it calculated, and how is the direction determined?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/DmF4nt7L8FAi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DAVDjtyZU-4K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/DAVDjtyZU-4K.jpg</video:thumbnail_loc>

            <video:title>Reduction to a single force or couple</video:title>

            <video:description><![CDATA[
How and under what conditions does a system of forces on a rigid body reduce to a single force or couple?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/DAVDjtyZU-4K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GiJVNKemKpWu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/GiJVNKemKpWu.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General equations and procedure for analysis of the equilibrium of a rigid body under the action of co-planar forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/GiJVNKemKpWu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J2YQSiXtfta-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/J2YQSiXtfta-.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on solutions of general systems of linear equations. Solved: Solve the following system of equationsx_1-4x_2-3x_3+3x_4=1 -2x_1+7x_2+3x_3-6x_4=0-x_1+6x_2+6x_3+3x_4=1-2x_1+7x_2+5x_3-11x_4=-5 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/J2YQSiXtfta-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z4R_PSyPQ__l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/Z4R_PSyPQ__l.jpg</video:thumbnail_loc>

            <video:title>Constant acceleration (2)</video:title>

            <video:description><![CDATA[
This second example reinforces 1D constant acceleration problem-solving. We will again identify knowns, select the correct kinematic equation, and solve for the unknown. Master the application. Solved: A car starts from rest and moves with uniform acceleration of 10m/s^2 for 10s. It then maintains a constant speed for 20s. Find the total distance covered. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/Z4R_PSyPQ__l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i0pCHoIJ9HuT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/i0pCHoIJ9HuT.jpg</video:thumbnail_loc>

            <video:title>Defining work</video:title>

            <video:description><![CDATA[
Work is force acting through a displacement. You calculate it by multiplying constant force and displacement or by finding the area under a graph for variable forces. This lesson covers definitions, formulas, and graphical methods.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/i0pCHoIJ9HuT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tsCuiKlKFDC6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/tsCuiKlKFDC6.jpg</video:thumbnail_loc>

            <video:title>Equivalence and equipollence</video:title>

            <video:description><![CDATA[
Meaning of equivalent and equipollent force-couple systems, and how they are related for a system of forces on a rigid body.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/tsCuiKlKFDC6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KaRWV9MSfAUd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/394/KaRWV9MSfAUd.jpg</video:thumbnail_loc>

            <video:title>Cables, links, pulleys and springs</video:title>

            <video:description><![CDATA[
Modelling reactions at connections to cables, links or bars, pulleys and springs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/394/KaRWV9MSfAUd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ps6Rfkfytn6t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/ps6Rfkfytn6t.jpg</video:thumbnail_loc>

            <video:title>Kinetic energy</video:title>

            <video:description><![CDATA[
Kinetic energy is the energy an object has because it is moving. This lesson defines it as a scalar quantity and provides the standard formula to show how mass and speed determine the total energy of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/ps6Rfkfytn6t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z2QxihoWvAtd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/394/z2QxihoWvAtd.jpg</video:thumbnail_loc>

            <video:title>Pins and rough surfaces</video:title>

            <video:description><![CDATA[
Modelling reactions at pins and rough surfaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/394/z2QxihoWvAtd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rQyjZmN6Utx_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/rQyjZmN6Utx_.jpg</video:thumbnail_loc>

            <video:title>The work-energy theorem</video:title>

            <video:description><![CDATA[
The work-energy theorem states that the total work done on an object equals its change in kinetic energy. This lesson explains how to use this principle to find an object's final speed by calculating the energy transferred through force.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/rQyjZmN6Utx_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Fja3O9e32fx2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/Fja3O9e32fx2.jpg</video:thumbnail_loc>

            <video:title>Reduction to a wrench</video:title>

            <video:description><![CDATA[
How and under what conditions does a system of forces on a rigid body reduce to a wrench?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/Fja3O9e32fx2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rxTkevCZRLJ9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/rxTkevCZRLJ9.jpg</video:thumbnail_loc>

            <video:title>Reduction to force-couple system</video:title>

            <video:description><![CDATA[
How to reduce a system of forces on a rigid body to an equivalent force-couple system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/rxTkevCZRLJ9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5Xk2KRuDAjNq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/394/5Xk2KRuDAjNq.jpg</video:thumbnail_loc>

            <video:title>Rollers, rockers, etc.</video:title>

            <video:description><![CDATA[
Reactions at rollers, rockers, frictionless surfaces, tracks and bars.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/394/5Xk2KRuDAjNq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZmbhDBlnY6I4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/ZmbhDBlnY6I4.jpg</video:thumbnail_loc>

            <video:title>Two-force body</video:title>

            <video:description><![CDATA[
A simplified condition for the equilibrium of a rigid body under the action of only two co-planar forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/ZmbhDBlnY6I4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6cXSlhiSOwCO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/6cXSlhiSOwCO.jpg</video:thumbnail_loc>

            <video:title>Scalar triple products</video:title>

            <video:description><![CDATA[
Meaning and calculation of the scalar or mixed triple products of vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/6cXSlhiSOwCO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kRram2JdvfWK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/132/kRram2JdvfWK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on Taylor and Maclaurin series expansion of differentiable functions. Solved: Suppose y satisfies the equation (1-x^2)\frac{d^2y}{dx^2} -\frac{xdy}{dx} +m^2y=0show that 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/132/kRram2JdvfWK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K794GesNUKrl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/133/K794GesNUKrl.jpg</video:thumbnail_loc>

            <video:title>Worked examples II</video:title>

            <video:description><![CDATA[
More worked examples on direct classification of quadric surfaces. Solved: Classify 36x+16y^2-9z^2-72x+64y-36z=80 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/133/K794GesNUKrl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H2x8-kz0HGYD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/H2x8-kz0HGYD.jpg</video:thumbnail_loc>

            <video:title>Worked examples I</video:title>

            <video:description><![CDATA[
Worked examples on classification of quadric surfaces by variable substitution. Solved: Classify 2xy+2yz-y=1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/H2x8-kz0HGYD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XHCN31pN_LKJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/XHCN31pN_LKJ.jpg</video:thumbnail_loc>

            <video:title>Complex numbers</video:title>

            <video:description><![CDATA[
Define the complex number system by integrating the imaginary unit i to resolve square roots of negative values. You will master the standard form a + bi and establish the hierarchical relationship between real and non-real numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/XHCN31pN_LKJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LoV1YSvX47dC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/LoV1YSvX47dC.jpg</video:thumbnail_loc>

            <video:title>Mechanics</video:title>

            <video:description><![CDATA[
Review of the meaning of mechanics, engineering mechanics, mechanics of rigid bodies, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/LoV1YSvX47dC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0LKhqEAxzro4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/0LKhqEAxzro4.jpg</video:thumbnail_loc>

            <video:title>Rigid bodies</video:title>

            <video:description><![CDATA[
Meaning of rigid bodies as used in engineering mechanics, in contrast to particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/0LKhqEAxzro4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N6cf84iIWUKI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/N6cf84iIWUKI.jpg</video:thumbnail_loc>

            <video:title>Scalar products</video:title>

            <video:description><![CDATA[
Meaning and calculation of the scalar product of two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/N6cf84iIWUKI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GSIHJZs6YElL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/GSIHJZs6YElL.jpg</video:thumbnail_loc>

            <video:title>Rough surfaces and ball-and-socket joints</video:title>

            <video:description><![CDATA[
Reactions at rough surfaces and ball-and-socket joints  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/GSIHJZs6YElL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0inKsXM_i2dS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/0inKsXM_i2dS.jpg</video:thumbnail_loc>

            <video:title>Work of a spring</video:title>

            <video:description><![CDATA[
Calculate the work done by a spring force during compression or extension. This example uses the force constant and displacement to find the energy transferred by this variable force. Solved: A toy catapult spring has a stiffness constant k = 450 \, N/m. Calculate the work required to stretch the spring from an initial extension of 0.05 \, m to a final extension of 0.15 \, m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/0inKsXM_i2dS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CEAhYsMhtxhp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/135/CEAhYsMhtxhp.jpg</video:thumbnail_loc>

            <video:title>Worked examples II</video:title>

            <video:description><![CDATA[
More worked examples on the polar, cylindrical and spherical coordinates. Solved: Transform the equation x^2+y^2+2z^2-2x-3y-z=0 into the cylindrical coordinates 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/135/CEAhYsMhtxhp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l75o1lvXt3CL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/617/l75o1lvXt3CL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on the proof of limits of functions. Solved: Prove that \lim_{x\to 3}x^3=27 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/617/l75o1lvXt3CL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pa26qDci9yVl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/Pa26qDci9yVl.jpg</video:thumbnail_loc>

            <video:title>Vector products (1)</video:title>

            <video:description><![CDATA[
Review of the vector or cross product of vectors - magnitude and direction of vector products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/Pa26qDci9yVl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AwJgN59Vv6Gm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/AwJgN59Vv6Gm.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Some properties of vector products and scalar triple products of vectors, implied from some properties of matrix determinants.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/AwJgN59Vv6Gm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9YoGWcCB22sF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/9YoGWcCB22sF.jpg</video:thumbnail_loc>

            <video:title>The r vector</video:title>

            <video:description><![CDATA[
A closer look at the r vector for calculating the moments of a force about a given point or axis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/9YoGWcCB22sF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6vrRwz7VvXFv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/6vrRwz7VvXFv.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Review of the methods of calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/6vrRwz7VvXFv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lb6rJXPiHJyT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/lb6rJXPiHJyT.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
What exactly is the moment (or torque) of a force about a point or axis, where and how is it relevant?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/lb6rJXPiHJyT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wzRztCIXBVi9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/wzRztCIXBVi9.jpg</video:thumbnail_loc>

            <video:title>Zero moment</video:title>

            <video:description><![CDATA[
Making sense of when and how the moment of a force about a given point or axis is zero.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/wzRztCIXBVi9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_k5SP6mEafzU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/_k5SP6mEafzU.jpg</video:thumbnail_loc>

            <video:title>A sign convention</video:title>

            <video:description><![CDATA[
How to determine and specify directions (clockwise or counterclockwise) for moments about an axis perpendicular to a given plane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/_k5SP6mEafzU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bO6oOaK45ioA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/390/bO6oOaK45ioA.jpg</video:thumbnail_loc>

            <video:title>Varignon's theorem</video:title>

            <video:description><![CDATA[
How the moment of a force about a point or axis obtains from those of its components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/390/bO6oOaK45ioA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UUxx2twqh_AN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/UUxx2twqh_AN.jpg</video:thumbnail_loc>

            <video:title>Analysis of chromatography</video:title>

            <video:description><![CDATA[
Separation depends on phase affinity. Why do polar compounds stick to silica gel while non-polar ones race ahead? Watch to interpret Rf values and partition coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/UUxx2twqh_AN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/495_WkwOcJFW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/495_WkwOcJFW.jpg</video:thumbnail_loc>

            <video:title>Conservation of energy</video:title>

            <video:description><![CDATA[
The law of conservation of energy states that the total energy in a closed system remains constant as it only changes from one form to another. This principle allows you to equate initial and final energy states to solve complex mechanics problems without needing to calculate acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/495_WkwOcJFW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C2a7j_8VJU0A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/C2a7j_8VJU0A.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Review of the methods for calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/C2a7j_8VJU0A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AoviqJSg2Owl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/AoviqJSg2Owl.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Procedure for calculating the moment of a force about an arbitrary axis - using both scalar and vector approaches.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/AoviqJSg2Owl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qbzIDiQsWUnO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/qbzIDiQsWUnO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: An 80-lb sheet of plywood rests on two small wooden blocks as shown. It is allowed to lean 20^\circ from the vertical under the action of a force P which is perpendicular to the sheet. Friction at all surfaces of blocks A and B is sufficient to prevent slipping. Determine the magnitude P and the vertical reaction forces at A and B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/qbzIDiQsWUnO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738676407590.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/k72SKvgGn5gI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/k72SKvgGn5gI.jpg</video:thumbnail_loc>

            <video:title>Momentum and impulse</video:title>

            <video:description><![CDATA[
Linear momentum is the product of an object's mass and its velocity. Impulse is the change in this momentum caused by a force acting over a specific time interval. This lesson defines both vector quantities and establishes the dimensional link between them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/k72SKvgGn5gI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jKYQEZqlOm38</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/jKYQEZqlOm38.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: Bar EF has a square cross section and is field in space. The structure ABC has negligible weight and has a collar at C that has a square hole that slides freely on bar EF. The structure ABC supports a uniform rectangular sign with weight 1 KN (the two vertical edges of the sign align with points A and B). Determine the magnitude of the tension in cable AD and all of the reaction component at C referred to the x, y, and z directions provided. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/jKYQEZqlOm38.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738676994085.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ozEY2uMSXxWG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/ozEY2uMSXxWG.jpg</video:thumbnail_loc>

            <video:title>Tangency</video:title>

            <video:description><![CDATA[
This lesson explains tangency as the condition where a quadratic curve touches the x-axis at a single point. You will learn that this occurs when roots are equal and the discriminant is exactly zero.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/ozEY2uMSXxWG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GYY07c-PqQve</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/GYY07c-PqQve.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: The bent rod is supported at A, B, and C by journal bearings. Determine the components of reaction at the bearings if the rod is subjected to the 200-lb vertical force and the30-lb-ft couple moment. The bearings are in proper alignment and exert only force reaction on the rod. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/GYY07c-PqQve.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738572469223.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dDW64IDJdj2t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/dDW64IDJdj2t.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: The member is supported by a pin at A and cable BC. Determine the components of reaction at these supports if the cylinder has a mass of 40kg. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/dDW64IDJdj2t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738572654043.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/zghpx7rDiIbT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/zghpx7rDiIbT.jpg</video:thumbnail_loc>

            <video:title>Equivalent force systems</video:title>

            <video:description><![CDATA[
Meaning of equivalent force systems, and overview of operations for simplifying a given force system to an equivalent one.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/zghpx7rDiIbT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t9CcoBvQbzTi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/t9CcoBvQbzTi.jpg</video:thumbnail_loc>

            <video:title>Equivalent couples</video:title>

            <video:description><![CDATA[
Proof of equivalence of couples with equal moments - in the same or parallel planes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/t9CcoBvQbzTi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oIiwUfJSyyn4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/oIiwUfJSyyn4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: Determine the reaction at the ball supports B and C and the components of reaction at the ball-and-socket A (not shown) for the uniform loaded plate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/oIiwUfJSyyn4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738573134471.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/zAgREmHpsQR9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/620/zAgREmHpsQR9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluation of limits. Solved: \lim_{x \to 0} f(x) = \frac{x}{\sqrt{1-e^{-x^2}}} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/620/zAgREmHpsQR9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DOw3lFQGz9k3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Thumbnails/177/DOw3lFQGz9k3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on modelling of translational mechanical systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Previews/177/DOw3lFQGz9k3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UK7LxdJLhT4M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/UK7LxdJLhT4M.jpg</video:thumbnail_loc>

            <video:title>Addition of couples</video:title>

            <video:description><![CDATA[
How the moment of two couples derives from the sum of their individual moments.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/UK7LxdJLhT4M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_mA2GB2c_spn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/_mA2GB2c_spn.jpg</video:thumbnail_loc>

            <video:title>Conservation of linear momentum</video:title>

            <video:description><![CDATA[
The total momentum of a closed system remains constant if no external force acts on it. This principle allows you to equate momentum before and after an impact to find unknown velocities in collisions or explosions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/_mA2GB2c_spn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ok9CxkpQoenF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/ok9CxkpQoenF.jpg</video:thumbnail_loc>

            <video:title>Rational or irrational (1)</video:title>

            <video:description><![CDATA[
This lesson proves that roots are rational by showing the discriminant is a perfect square. You will learn to manipulate algebraic coefficients to verify this condition when coefficients are rational. Solved: Show that the roots of (p+r-q)x^2 - 2px + (p+q-r) = 0 are rational. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/ok9CxkpQoenF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-1GQLVj7OMG2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Thumbnails/177/-1GQLVj7OMG2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on modelling of translational mechanical systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Previews/177/-1GQLVj7OMG2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vCNOAn0atRqW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/vCNOAn0atRqW.jpg</video:thumbnail_loc>

            <video:title>Couple vectors</video:title>

            <video:description><![CDATA[
Representing moments of couples as vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/vCNOAn0atRqW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QIuVLF6FQZ0K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/QIuVLF6FQZ0K.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General analysis procedure for kinetics of particles by relating the linear momentum of the body with the impulse of the forces acting on it.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/QIuVLF6FQZ0K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ELH-9ge5_PTe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/ELH-9ge5_PTe.jpg</video:thumbnail_loc>

            <video:title>Nth roots of unity</video:title>

            <video:description><![CDATA[
Properties of the nth roots of unity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/ELH-9ge5_PTe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5oFloIf8iF4i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/5oFloIf8iF4i.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Formal and informal definitions of limits of functions of two variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/5oFloIf8iF4i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4-jLvzHTsnVn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/4-jLvzHTsnVn.jpg</video:thumbnail_loc>

            <video:title>Couple</video:title>

            <video:description><![CDATA[
Meaning of a couple (of forces) and their impact on the stability of a rigid body.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/4-jLvzHTsnVn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MerFQo6-T2hL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/MerFQo6-T2hL.jpg</video:thumbnail_loc>

            <video:title>Linear impulse and momentum</video:title>

            <video:description><![CDATA[
Definition and evaluation of linear impulse and momentum vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/MerFQo6-T2hL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kg9E8hl3IJmq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/393/Kg9E8hl3IJmq.jpg</video:thumbnail_loc>

            <video:title>Idealized models</video:title>

            <video:description><![CDATA[
Meaning and use of idealized models for the force analysis of rigid bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/393/Kg9E8hl3IJmq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/on70y8Hghhgb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/on70y8Hghhgb.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Introduction to force-couple systems and the necessity for an interplay of forces and couples.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/on70y8Hghhgb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xtF4H9FYMSLh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/393/xtF4H9FYMSLh.jpg</video:thumbnail_loc>

            <video:title>Internal and external forces</video:title>

            <video:description><![CDATA[
Internal and external forces on a rigid body - meaning and when each should be considered.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/393/xtF4H9FYMSLh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XXmx7Hfvy0nW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/XXmx7Hfvy0nW.jpg</video:thumbnail_loc>

            <video:title>Force-couple to force resultant</video:title>

            <video:description><![CDATA[
How to obtain the resultant (equivalent) single force from a force-couple system, where feasible.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/XXmx7Hfvy0nW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zI2bhpAiCxRz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/zI2bhpAiCxRz.jpg</video:thumbnail_loc>

            <video:title>Motion of the centre of mass</video:title>

            <video:description><![CDATA[
The centre of mass moves as if the total mass of the system were concentrated there and all external forces were applied at that point. This lesson explains how internal forces cancel out, allowing you to track complex systems using a single linear motion equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/zI2bhpAiCxRz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/siTyARqEioLy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/siTyARqEioLy.jpg</video:thumbnail_loc>

            <video:title>The centre of mass</video:title>

            <video:description><![CDATA[
The centre of mass is the average position of all mass in a system. It is the point where you treat a whole object as a single particle for motion calculations. This lesson shows how to find this balance point for groups of particles and solid objects.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/siTyARqEioLy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SWUeJdNpHuqY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/SWUeJdNpHuqY.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning and use of distributed loads.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/SWUeJdNpHuqY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/erK6nhdDA9wt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/200/erK6nhdDA9wt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on powers of i. Solved: Simplify i^{205}+i^{23}+i^{20}-i^{34} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/200/erK6nhdDA9wt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rZet3jmcVV1n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/rZet3jmcVV1n.jpg</video:thumbnail_loc>

            <video:title>Location</video:title>

            <video:description><![CDATA[
Determining the location of the resultant of distributed loads on a rigid body.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/rZet3jmcVV1n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OOovQ51tv9xB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/OOovQ51tv9xB.jpg</video:thumbnail_loc>

            <video:title>Magnitude</video:title>

            <video:description><![CDATA[
Determining the magnitude of the resultant of distributed loads on a rigid body.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/OOovQ51tv9xB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZiONgT_yQn0b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/ZiONgT_yQn0b.jpg</video:thumbnail_loc>

            <video:title>Tangency (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to find the constant value that makes a straight line tangent to a quadratic curve. You will learn to equate both equations and set the discriminant of the resulting quadratic to zero to ensure only one point of contact. Solved: Find the value of k for which y = 4x + k is a tangent to y = x^2 + 2x + 6. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/ZiONgT_yQn0b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qSJT1SIUA7QE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/qSJT1SIUA7QE.jpg</video:thumbnail_loc>

            <video:title>Velocity and acceleration</video:title>

            <video:description><![CDATA[
Velocity and acceleration of a point on a rigid body, measured relative to a frame in rotation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/qSJT1SIUA7QE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wsWAGsx5E2Sk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/394/wsWAGsx5E2Sk.jpg</video:thumbnail_loc>

            <video:title>Fixed supports</video:title>

            <video:description><![CDATA[
Modelling reactions at moment-resisting collars and fixed supports.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/394/wsWAGsx5E2Sk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6wKavZxKVzYV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/6wKavZxKVzYV.jpg</video:thumbnail_loc>

            <video:title>Rate of change of a vector</video:title>

            <video:description><![CDATA[
What is the rate of change of a vector defined in a rotating frame of reference, as observed from a fixed frame of reference?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/6wKavZxKVzYV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i83lWrVVDSWq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/82/i83lWrVVDSWq.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/82/i83lWrVVDSWq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SozclHdkzUpH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/SozclHdkzUpH.jpg</video:thumbnail_loc>

            <video:title>Energy loss</video:title>

            <video:description><![CDATA[
Determining energy loss for a given impact, and its relationship to the coefficient of restitution. Types of impact based on the value of the value of coefficient of restitution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/SozclHdkzUpH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/77Ps9N4PvX6S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/77Ps9N4PvX6S.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on rational powers and roots of complex numbers. Solved: 1.Solve completely the equationz^6+iz^3+i-1=02. Solve the equation z^6 - z^5 + 4z^4 - 6z^3 + 2z^2 - 8z + 8 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/77Ps9N4PvX6S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i3OLV7PDN72v</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/395/i3OLV7PDN72v.jpg</video:thumbnail_loc>

            <video:title>Complete constraints</video:title>

            <video:description><![CDATA[
When is a two-dimensional structure said to be completely-constrained?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/395/i3OLV7PDN72v.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JuXxpkY7UuIb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/JuXxpkY7UuIb.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General analysis procedure for collision of two bodies - direct and oblique central impacts, with and without motion constraints.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/JuXxpkY7UuIb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X2z_6WOvhni1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/X2z_6WOvhni1.jpg</video:thumbnail_loc>

            <video:title>Semicircular arc</video:title>

            <video:description><![CDATA[
A wire bends into a semicircle. How does constant distance from the centre simplify the potential integral? We sum the charge directly to find the answer. Solved: A thin, flexible plastic wire of length L = 22.0 \text{ cm} is used for a physics project. It is charged uniformly with a total negative charge Q = -6.60 \text{ }\mu\text{C} and bent into a perfect semicircle. Calculate the electric potential at the centre of curvature of this semicircle. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/X2z_6WOvhni1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gJv_GHAeJZhn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/278/gJv_GHAeJZhn.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
How to determine the stationary points of a two-variable function - and the nature of the stationary points. Solved: Correction: \Delta=f_{xy}^2-f_{xx}f_{yy}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/278/gJv_GHAeJZhn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GxjKO_KZ_no7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/393/GxjKO_KZ_no7.jpg</video:thumbnail_loc>

            <video:title>Free-body diagrams</video:title>

            <video:description><![CDATA[
Meaning, use and general procedure for producing free-body diagrams for the force analysis of rigid bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/393/GxjKO_KZ_no7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i2UW9ZB6jdpV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/393/i2UW9ZB6jdpV.jpg</video:thumbnail_loc>

            <video:title>Conditions of equilibrium</video:title>

            <video:description><![CDATA[
Meaning and conditions of equilibrium of rigid bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/393/i2UW9ZB6jdpV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GFh8wf2oRa3U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/395/GFh8wf2oRa3U.jpg</video:thumbnail_loc>

            <video:title>Improper constraints</video:title>

            <video:description><![CDATA[
When is a two-dimensional structure said to be completely-constrained?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/395/GFh8wf2oRa3U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/508iKsu0cPOn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/508iKsu0cPOn.jpg</video:thumbnail_loc>

            <video:title>Universal joints and fixed supports</video:title>

            <video:description><![CDATA[
Reactions at universal joints and fixed supports.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/508iKsu0cPOn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rqa4yS0XXcYq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/rqa4yS0XXcYq.jpg</video:thumbnail_loc>

            <video:title>Hinges</video:title>

            <video:description><![CDATA[
Reactions at single and double hinges.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/rqa4yS0XXcYq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6A56sk6uLFRe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/6A56sk6uLFRe.jpg</video:thumbnail_loc>

            <video:title>Bearings</video:title>

            <video:description><![CDATA[
Reactions at single and multiple journal and thrust bearings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/6A56sk6uLFRe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F5EXYnGMeim0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/395/F5EXYnGMeim0.jpg</video:thumbnail_loc>

            <video:title>Statical determinacy</video:title>

            <video:description><![CDATA[
When is a two-dimensional structure statically-determinate?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/395/F5EXYnGMeim0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gHOllPIq8pU0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/926/gHOllPIq8pU0.jpg</video:thumbnail_loc>

            <video:title>Summary and next steps</video:title>

            <video:description><![CDATA[
This final lesson summarises the work-energy theorem and the laws of conservation of energy and momentum to consolidate your problem-solving skills. It also explains how to extend these principles to study rotational motion in the next course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/926/gHOllPIq8pU0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AwPYjmOgCzHM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/397/AwPYjmOgCzHM.jpg</video:thumbnail_loc>

            <video:title>Constraints</video:title>

            <video:description><![CDATA[
When is a three-dimensional structure said to be completely, partially or improperly constrained?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/397/AwPYjmOgCzHM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nGE5tRPFIG8U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MuYvMAMRMj/Thumbnails/348/nGE5tRPFIG8U.jpg</video:thumbnail_loc>

            <video:title>Summary (1)</video:title>

            <video:description><![CDATA[
Summary of the fundamental concepts on moments of inertia.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MuYvMAMRMj/Previews/348/nGE5tRPFIG8U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qMEQnVEyeETY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/qMEQnVEyeETY.jpg</video:thumbnail_loc>

            <video:title>Jacobian Determinants</video:title>

            <video:description><![CDATA[
Definition and evaluation of Jacobian determinants.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/qMEQnVEyeETY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xUzmRCAL8_On</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/539/xUzmRCAL8_On.jpg</video:thumbnail_loc>

            <video:title>Examples of maps (3)</video:title>

            <video:description><![CDATA[
More examples of maps and their notations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/539/xUzmRCAL8_On.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BzfVli_9zkmH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/BzfVli_9zkmH.jpg</video:thumbnail_loc>

            <video:title>Two variables</video:title>

            <video:description><![CDATA[
Implicit differentiation of a function with one dependent variable and one independent variable using partial derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/BzfVli_9zkmH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vox8XU5TBTfG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/Vox8XU5TBTfG.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This video shows the course plan and how to use your knowledge of straight-line motion to study spinning objects. You will see why these rules are used to build engines and track planets. This is the starting point for the entire course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/Vox8XU5TBTfG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H3ixIboC-fVI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/617/H3ixIboC-fVI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the proof of limits of functions. Solved: 1)Prove that \lim_{x\to 2}x=2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/617/H3ixIboC-fVI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1jz0uhXY2Ye2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/1jz0uhXY2Ye2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: Boom OA is being elevated by the rope-and-pulley arrangement shown. If point B on the rope is given a constant velocity v_B=3.2m/s , determine the angular velocity \omega and angular acceleration \alpha of the boom for \theta=30^\circ . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/1jz0uhXY2Ye2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744971665994.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/em_ib1v9srF8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/194/em_ib1v9srF8.jpg</video:thumbnail_loc>

            <video:title>Volume element</video:title>

            <video:description><![CDATA[
Volume element (elemental volume) in orthogonal curvilinear coordinates and its relation to the Jacobian of transformation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/194/em_ib1v9srF8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8DD-5JFkiCgv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/8DD-5JFkiCgv.jpg</video:thumbnail_loc>

            <video:title>Several variables</video:title>

            <video:description><![CDATA[
General implicit differentiation of a function with several dependent and independent variables using Jacobian determinants.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/8DD-5JFkiCgv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AIME12Vhx7bO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/AIME12Vhx7bO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar product of two vectors. Solved: Give that u and v are unit vectors in the i and j plane making angles \theta and \phi respectively with the i-direction. (a)Express u and v in terms of i and j. (b) By defining u.v, deduce that \cos(\phi-\theta)=\cos \phi \cos \theta+\sin \phi \sin \theta.2.Simplify (a+2b).(a-3b). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/AIME12Vhx7bO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d10D0fgvDuP_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/d10D0fgvDuP_.jpg</video:thumbnail_loc>

            <video:title>Worked examples I</video:title>

            <video:description><![CDATA[
Worked examples on the equation of an ellipse. Solved: 1 Sketch the ellipse x^{2} +3y^{2} -4x+6y=-12 Sketch the ellipse\frac{x^2}{4} + \frac{y^2}{9} =1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/d10D0fgvDuP_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Fa8Q933gwGLZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/Fa8Q933gwGLZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (16)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The relay regulate voltage and current. Determine the force in the spring CD, which has a stiffness of K=120N/m, so that it will allow the armature to make contact at A in figure (a) with a vertical force of 0.4N. Also, determine the force in the spring when the coil is energized and attracts the armature to E, figure (b), thereby breaking contact at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/Fa8Q933gwGLZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736865949660.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/OhJbERhAwl--</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/527/OhJbERhAwl--.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/527/OhJbERhAwl--.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mevznw1YXiHp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/mevznw1YXiHp.jpg</video:thumbnail_loc>

            <video:title>Effect of pressure</video:title>

            <video:description><![CDATA[
Execute the systematic prediction of gaseous equilibrium shifts resulting from pressure and volume changes through a rigorous problem walkthrough. You will master the mechanical comparison of stoichiometric mole counts to determine directional response with absolute precision. Solved: 1. Consider the equilibrium: 2 SO_2(g) + O_2(g) \rightleftharpoons 2 SO_3(g) Answer the following questions. In each case, assume the temperature remains constant. a. If the partial pressure of SO_3 is increased, what happens to the partial pressure of SO_2? b. If the partial pressure of SO_2 is decreased, what happens to the partial pressure of SO_3? c. If the concentration of SO_2 is increased, what happens to the equilibrium constant for the reaction? d. If the concentration of O_2 is decreased, what happens to the concentration of SO_3? 2. The gas-phase equilibrium PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) is established in a rigid 3.0 L vessel at 520 K. At equilibrium, the partial pressures are: P_{PCl_5} = 0.90 \text{ bar}, P_{PCl_3} = 0.60 \text{ bar}, P_{Cl_2} = 0.60 \text{ bar} Chlorine gas is then injected into the vessel until its partial pressure immediately after addition is 1.20 bar, while the temperature remains constant. Calculate the new equilibrium partial pressure of each gas. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/mevznw1YXiHp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Em5n5HHosep7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/Em5n5HHosep7.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the divergence of a vector field.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/Em5n5HHosep7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PzZ0593ZwP7B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/PzZ0593ZwP7B.jpg</video:thumbnail_loc>

            <video:title>Initial-value and boundary-value problems</video:title>

            <video:description><![CDATA[
Meaning of initial-value problems and boundary-value problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/PzZ0593ZwP7B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MKOPPLroYi00</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/192/MKOPPLroYi00.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on the use of sign conventions for gradient, divergence, curl and Laplacian. Solved: Prove the following identities for arbitrary vector function \vec{A}(x,y,z) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/192/MKOPPLroYi00.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DHSbK98dGkOM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/192/DHSbK98dGkOM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the use of sign conventions for gradient, divergence, curl and Laplacian. Solved: Given r=\sqrt{x^2+y^2+z^2} =\|{r}\|, 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/192/DHSbK98dGkOM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KR_mK85kmU0P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/KR_mK85kmU0P.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions (2)</video:title>

            <video:description><![CDATA[
Dense piecewise functions fail direct substitution at interval boundaries. How do you test limit existence when the approach point sits exactly on a rule boundary? Watch the one-sided evaluation deliver the answer. Solved: Determine if \lim_{x \to \frac{1}{2}} f(x) exists for the function f(x) = \begin{cases} 2x + 1 & \text{if } x < 0 \\ x^2 + 1 & \text{if } 0 \le x < \frac{1}{4} \\ 4x + \frac{1}{2} & \text{if } \frac{1}{4} \le x < \frac{1}{2} \\ \frac{5}{2} & \text{if } \frac{1}{2} \le x < \frac{3}{4} \\ 5x - 1 & \text{if } x \ge \frac{3}{4} \end{cases}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/KR_mK85kmU0P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eDNfx-JGQR1f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/eDNfx-JGQR1f.jpg</video:thumbnail_loc>

            <video:title>Parabola</video:title>

            <video:description><![CDATA[
Equation of a parabola.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/eDNfx-JGQR1f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0959syTqwilF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/0959syTqwilF.jpg</video:thumbnail_loc>

            <video:title>Rational or irrational (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to determine if roots are rational or irrational using the discriminant. You will learn to identify that a non-perfect square discriminant results in irrational roots within the context of a practical measurement problem. Solved: Determine if the roots of x^2 + 9x + 9 = 0 are rational or irrational. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/0959syTqwilF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-3ZlCcfZ_324</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/59/-3ZlCcfZ_324.jpg</video:thumbnail_loc>

            <video:title>Continuity at an endpoint</video:title>

            <video:description><![CDATA[
Continuity at an endpoint of the domain of a function.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/59/-3ZlCcfZ_324.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v5W_Ww5yqvL5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Thumbnails/363/v5W_Ww5yqvL5.jpg</video:thumbnail_loc>

            <video:title>Setting up sheet format and creating 2D representations.</video:title>

            <video:description><![CDATA[
This lesson teaches students how to create and customize sheet formats for engineering drawings and accurately represent 3D models in 2D layouts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qyBmnY26Zm/Previews/363/v5W_Ww5yqvL5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XNASRiKmKf4-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/XNASRiKmKf4-.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the vector product of two vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/XNASRiKmKf4-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gjG4IgboAWGp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/gjG4IgboAWGp.jpg</video:thumbnail_loc>

            <video:title>Order of operations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of complex numerical expressions using the BODMAS/PEMDAS hierarchy through a rigorous problem walkthrough. You will master the mechanical sequence required to process brackets and exponents before arithmetic operations to ensure absolute computational accuracy. Solved: 3. Evaluate 24 \div 4 \times 2 - (3 + 5^2). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/gjG4IgboAWGp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i7qvBy2qjgnk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/196/i7qvBy2qjgnk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the divergence and curl of a vector field in orthogonal curvilinear coordinates. Solved: Calculate the divergence of \vec{v}=r\cos\theta\mathbf{\hat{e}}_r +r\sin\theta\mathbf{\hat{e}}_\theta+z\mathbf{\hat{e}}_z 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/196/i7qvBy2qjgnk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/r6jxYrkuA-uu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/196/r6jxYrkuA-uu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on the divergence and curl of a vector field in orthogonal curvilinear coordinates. Solved: Calculate the curl of \theta\mathbf{\hat{e}}_r 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/196/r6jxYrkuA-uu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KN4VirQnfvKx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/135/KN4VirQnfvKx.jpg</video:thumbnail_loc>

            <video:title>Cylindrical coordinates</video:title>

            <video:description><![CDATA[
An overview of the cylindrical coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/135/KN4VirQnfvKx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2xz8W_j-aiwp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/197/2xz8W_j-aiwp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the Laplacian of scalar and vector fields in orthogonal curvilinear coordinates. Solved: Calculate the Laplacian of \mathbf{\hat{e}}_\theta 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/197/2xz8W_j-aiwp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/o_eQPmSMc2UB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/o_eQPmSMc2UB.jpg</video:thumbnail_loc>

            <video:title>Long division</video:title>

            <video:description><![CDATA[
Execute polynomial long division through a systematic walkthrough of the divide, multiply, and subtract algorithm. You will master the mechanical process of reducing high-degree expressions to determine quotients and remainders precisely. Solved: 4. Divide x^3 - 7x + 6 by x - 2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/o_eQPmSMc2UB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uP-5unnPIV2v</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/uP-5unnPIV2v.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
An introduction to first-order differential equations and their solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/uP-5unnPIV2v.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Rwq9Xw-iZLFi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/Rwq9Xw-iZLFi.jpg</video:thumbnail_loc>

            <video:title>Space, time and mass</video:title>

            <video:description><![CDATA[
Meaning and measurement of space, time and mass.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/Rwq9Xw-iZLFi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e5IZtCobPzy7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1188/e5IZtCobPzy7.jpg</video:thumbnail_loc>

            <video:title>Value and location</video:title>

            <video:description><![CDATA[
This lesson determines the maximum or minimum value and the x-coordinate where it occurs. You will learn to correctly identify the location of the turning point and the corresponding extreme value of the quadratic function.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1188/e5IZtCobPzy7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UTwA9MOjYJJy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/615/UTwA9MOjYJJy.jpg</video:thumbnail_loc>

            <video:title>Sums and products</video:title>

            <video:description><![CDATA[
Derivatives of sums and products of functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/615/UTwA9MOjYJJy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WWG7Vb_WBk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1070/WWG7Vb_WBk.jpg</video:thumbnail_loc>

            <video:title>Lassaigne test (2)</video:title>

            <video:description><![CDATA[
How do you spot sulfur with nitroprusside, halogens with silver nitrate, and both nitrogen and sulfur with iron(III) chloride? Watch to interpret the colours.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1070/WWG7Vb_WBk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dGC0jGdxsyEJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/11/dGC0jGdxsyEJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector projections. Solved: Find the magnitude of the component of \vec{a} = 4 \underline{i }-3\underline{j}+\underline{k} in the direction of \vec{b}=\underline{i}-2\underline{j}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/11/dGC0jGdxsyEJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hfNzYreNSfHY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/hfNzYreNSfHY.jpg</video:thumbnail_loc>

            <video:title>Standardisation</video:title>

            <video:description><![CDATA[
This lesson demonstrates the procedure for determining the exact molarity of a sodium hydroxide solution using a primary standard of potassium hydrogen phthalate. You will calculate the concentration by resolving the stoichiometric relationship between the mass of KHP and the volume of titrant. Solved: Example:Sodium hydroxide solution is usually standardized by titrating a pure sample of potassium hydrogen phthalate KHC_8H_4O_4 (KHP), an acid with one acidic hydrogen and a molar mass of 204.22\text{ gmol}^{-1}. It takes 34.67mL of sodium hydroxide solution to titrate a 0.1082g sample of KHP. What is the molarity of the sodium hydroxide? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/hfNzYreNSfHY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XVmE7BfmEYSh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/XVmE7BfmEYSh.jpg</video:thumbnail_loc>

            <video:title>Disk axial potential</video:title>

            <video:description><![CDATA[
A disk holds surface charge. How do you integrate rings to find axial potential and prove the far-field limit? We derive the formula and verify point charge behaviour. Solved: A circular plastic lid of radius R = 15.0 \text{ cm} is uniformly charged on its top surface with a surface charge density \sigma = +4.50 \text{ nC/m}^2. Calculate the electric potential at a point P located x = 20.0 \text{ cm} along the central axis of the lid. Furthermore, show mathematically that at very large distances, this lid behaves like a simple point charge. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/XVmE7BfmEYSh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UDj3wV5xdS4B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/UDj3wV5xdS4B.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Formal definition of the scalar triple product and its definition in terms of Cartesian components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/UDj3wV5xdS4B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hPYHyQitB_gW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/hPYHyQitB_gW.jpg</video:thumbnail_loc>

            <video:title>Special limits</video:title>

            <video:description><![CDATA[
Evaluation of limits at infinity using a special limit.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/hPYHyQitB_gW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pa23luNKMOXW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/pa23luNKMOXW.jpg</video:thumbnail_loc>

            <video:title>Three-force body</video:title>

            <video:description><![CDATA[
A simplified condition for the equilibrium of a rigid body under the action of only three co-planar forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/pa23luNKMOXW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Oe3BBsEgT2gr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/Oe3BBsEgT2gr.jpg</video:thumbnail_loc>

            <video:title>Indeterminate forms (1)</video:title>

            <video:description><![CDATA[
Indeterminate form ???-???.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/Oe3BBsEgT2gr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tq4PQx3w_Xsg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/11/tq4PQx3w_Xsg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on vector projections. Solved: Find the projectile of a vector \underline{i}+\underline{j}+\underline{k} on the plane x+z=5 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/11/tq4PQx3w_Xsg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T0LKeGEzYvxr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/207/T0LKeGEzYvxr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on manipulating hyperbolic functions using complex numbers in exponential and polar forms. Solved: 1.Show that cosh^2 \theta-sinh^2\theta=12. Verify the following relations:(a) \sinh(x+y) = \sinh x \cosh y + \cosh x \sinh y (b) \cosh(x+y) = \cosh x \cosh y + \sinh x \sinh y 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/207/T0LKeGEzYvxr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rxkOdDI8OIGT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/66/rxkOdDI8OIGT.jpg</video:thumbnail_loc>

            <video:title>Worked examples</video:title>

            <video:description><![CDATA[
Worked examples on identifying different kinds of sequences. Solved: Describe the following sequences:(i) {{1-\frac{1}{n}}} (ii){ {n^3}}(iii){ {(-1)^n}}- alternating sequence (iv) {\frac{1}{n^2}}(v){ \frac{1}{\sqrt{n}}} (vi) {\frac{n}{n^2+1} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/66/rxkOdDI8OIGT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P7-5uU54hFvv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/P7-5uU54hFvv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on vector equations with unknown vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/P7-5uU54hFvv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fHKR_9I6_5N1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/fHKR_9I6_5N1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on vector equations with unknown vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/fHKR_9I6_5N1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jcRPTwUndAeR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/202/jcRPTwUndAeR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the modulus and argument of a complex number. Solved: 1. Prove that |z_1|-|z_2|\le|z_1+z_2|\le|z_1|+|z_2| 2. Solve the equation|z| - 2z = 3 - 4i 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/202/jcRPTwUndAeR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L3nz4s-38veg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/L3nz4s-38veg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on vector equations with unknown vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/L3nz4s-38veg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZxcqbAYd_B3e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/ZxcqbAYd_B3e.jpg</video:thumbnail_loc>

            <video:title>Cubic equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of cubic equations by applying the Factor Theorem and synthetic division to reduce third-degree expressions into solvable quadratic factors. You will master the mechanical identification of roots to ensure absolute algebraic precision. Solved: 5. Solve x^3 - 2x^2 - 5x + 6 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/ZxcqbAYd_B3e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gxXAFJdSegh7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/219/gxXAFJdSegh7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on images of linear maps. Solved: For T:M22\to M22 defined by T(A)=kA,k\in IR,k\ne 0, determine ker (T), range (T) and find a basis of each. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/219/gxXAFJdSegh7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t4SIkB6LaMyo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/t4SIkB6LaMyo.jpg</video:thumbnail_loc>

            <video:title>Techniques of integration (3)</video:title>

            <video:description><![CDATA[
A review of the techniques of integration of single-variable real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/t4SIkB6LaMyo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_F8_rlg2_ROl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1188/_F8_rlg2_ROl.jpg</video:thumbnail_loc>

            <video:title>Maximum value</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to determine the maximum value of a quadratic expression by completing the square. You will learn to identify the vertex when the x-squared coefficient is negative and calculate the highest possible value for the function. Solved: Identify the maximum value of the expression 7 + 10x - x^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1188/_F8_rlg2_ROl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VhqlAuarDLuw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/65/VhqlAuarDLuw.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and types of progressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/65/VhqlAuarDLuw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T2WoVMEO3ZjO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/T2WoVMEO3ZjO.jpg</video:thumbnail_loc>

            <video:title>Special trigonometric limits (4)</video:title>

            <video:description><![CDATA[
Mixed algebraic and trigonometric terms under a root block direct substitution. How do you isolate the lowest power of the variable to trigger the standard sine limit safely? Watch the variable extraction clear the indeterminate form. Solved: Evaluate \lim_{x \to 0} \frac{8x}{\sqrt{6x^3 + 4\sin^2x}}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/T2WoVMEO3ZjO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FWG_171S9xpv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/FWG_171S9xpv.jpg</video:thumbnail_loc>

            <video:title>Properties of integrals</video:title>

            <video:description><![CDATA[
Properties of integrals of real-valued single-variable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/FWG_171S9xpv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tVG-LNyLvyqc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Thumbnails/387/tVG-LNyLvyqc.jpg</video:thumbnail_loc>

            <video:title>Infimum and supremum (2)</video:title>

            <video:description><![CDATA[
Properties of infimum and supremum of subsets of real numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Previews/387/tVG-LNyLvyqc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R94BbR5DkLlQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/222/R94BbR5DkLlQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on vector triple products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/222/R94BbR5DkLlQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MX6ScczFToWz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/222/MX6ScczFToWz.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on vector triple products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/222/MX6ScczFToWz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5b9SSI8BnzQh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/5b9SSI8BnzQh.jpg</video:thumbnail_loc>

            <video:title>Rational numbers</video:title>

            <video:description><![CDATA[
Define rational numbers as values expressible as the ratio of two integers with a non-zero denominator. You will master the identification of terminating and recurring decimals, establishing the distinction between rational and irrational sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/5b9SSI8BnzQh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B0gEC62NxbIx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/B0gEC62NxbIx.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on linear combinations of vectors in a vector space. Solved: Express V=(1,-2,5) \in IR^3 as a linear combination of the vectors u_1=(1,1,1),u_2=(1,2,3) and u_3=(2,-1,1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/B0gEC62NxbIx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YHNBjUomZHdi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/YHNBjUomZHdi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on linear spans of vector spaces. Solved: Show that the vectors u_1=(1,1,1),u_2=(1,2,3) and u_3=(1,5,8) span IR^3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/YHNBjUomZHdi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RwFdt7sPtoHK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/RwFdt7sPtoHK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on linear spans of vector spaces. Solved: Show that (1,1),(3,-2) span IR^3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/RwFdt7sPtoHK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LwyTGUSA7bNo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/LwyTGUSA7bNo.jpg</video:thumbnail_loc>

            <video:title>Linear span</video:title>

            <video:description><![CDATA[
Definition of a linear span or spanning set of a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/LwyTGUSA7bNo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PDIrJOOOGWKk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1188/PDIrJOOOGWKk.jpg</video:thumbnail_loc>

            <video:title>Boundary limit</video:title>

            <video:description><![CDATA[
This lesson proves a maximum boundary by completing the square to find the highest value of a quadratic expression. You will learn to use the vertex form to demonstrate why an expression cannot exceed a specific numerical limit. Solved: Prove that the expression 8x - 5 - 4x^2 can never be greater than -1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1188/PDIrJOOOGWKk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8gWuUegk5c58</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/8gWuUegk5c58.jpg</video:thumbnail_loc>

            <video:title>Several concurrent forces</video:title>

            <video:description><![CDATA[
Addition of several concurrent forces by successive applications of the parallelogram / triangle rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/8gWuUegk5c58.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oUaSMdeoebIY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/oUaSMdeoebIY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar triple product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/oUaSMdeoebIY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_JxkzBDBqIK1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/_JxkzBDBqIK1.jpg</video:thumbnail_loc>

            <video:title>Compound linear inequality</video:title>

            <video:description><![CDATA[
Solve compound inequalities by isolating the variable in all parts of the expression simultaneously. This walkthrough demonstrates how to determine the intersection of multiple constraints and express the final solution set using interval notation and a number line. Solved: 2. Solve the inequality -2 \le \frac{x}{4} + 1 \le 3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/_JxkzBDBqIK1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kMj9Wf80_IgV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/kMj9Wf80_IgV.jpg</video:thumbnail_loc>

            <video:title>Irrational numbers</video:title>

            <video:description><![CDATA[
Define irrational numbers as real values that cannot be expressed as a ratio of integers and possess non-terminating, non-recurring decimal expansions. You will examine the properties of surds and transcendental constants like pi, mastering their position on the real number line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/kMj9Wf80_IgV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/32ak1Bwu7oiK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/218/32ak1Bwu7oiK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on kernels of linear maps. Solved: Given T: P_2 \to P_2 defined by T(a + bx + cx^2) = (ax - c), determine ker(T) and find a basis for it. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/218/32ak1Bwu7oiK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GLXIizHL0kN7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/218/GLXIizHL0kN7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on kernels of linear maps. Solved: Find ker(T), where T: \mathbb{R}^3 \to \mathbb{R}^2 is defined by T(x_1, x_2, x_3) = (x_1 + x_2, x_2 - x_3). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/218/GLXIizHL0kN7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZU0VMaM12j0b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/ZU0VMaM12j0b.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar triple product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/ZU0VMaM12j0b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4nML19P830p_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/4nML19P830p_.jpg</video:thumbnail_loc>

            <video:title>The squeeze theorem (3)</video:title>

            <video:description><![CDATA[
Arbitrary functions bounded by known expressions resist direct evaluation. How do you force the unknown limit to match its bounding functions? Watch the squeeze theorem isolate the exact value. Solved: Determine the value of \lim_{x \to 0} f(x), given that \sqrt{5 - 2x^2} \leq f(x) \leq \sqrt{5 - x^2} for all x in the interval [-1, 1]. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/4nML19P830p_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SPsuroht0LBL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1189/SPsuroht0LBL.jpg</video:thumbnail_loc>

            <video:title>Quadratic inequalities</video:title>

            <video:description><![CDATA[
This lesson explains how to solve quadratic inequalities using the sign of the x-squared coefficient and the turning point. You will learn to determine if the solution lies between or outside the roots by identifying whether the graph is a hill or a valley.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1189/SPsuroht0LBL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OcfVI64PFfkC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/OcfVI64PFfkC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Define T:M_mxn\to{M_nxm} by T(A)=A^T. Show that T is a linear transformation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/OcfVI64PFfkC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sfD2X7sHkH7F</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/sfD2X7sHkH7F.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let a = (1, 3, 4) and let T: \mathbb{R}^3 \to \mathbb{R} be defined by T(v) = a.v. Is T linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/sfD2X7sHkH7F.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rGKc6ftn1OWB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/rGKc6ftn1OWB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let S:F[a,b]\to\mathbb{R} be the integral operator defined by S(f)=\int^b_a f(x)dx. Show that S is a linear transformation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/rGKc6ftn1OWB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A8Oe9ZFX-feP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/A8Oe9ZFX-feP.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Show that the zero transformation T: V \to W defined by T(v) = 0_w for all v \epsilon V is linear. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/A8Oe9ZFX-feP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/txBz5r3lmQGH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/txBz5r3lmQGH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let T: P_2 \to P_2, where P_2 is the space of the polynomials of degree not exceeding 2, with real coefficients. If T(a + bx + cx^2) = ax + bx^2, is T linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/txBz5r3lmQGH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4txZ3H89gIGf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/4txZ3H89gIGf.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let T: P_2 \to P_2, where P_2 is the space of the polynomials of degree not exceeding 2, with real coefficients. If T(a + bx + cx^2) = 2, is T linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/4txZ3H89gIGf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fR71H-ndGAUM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/fR71H-ndGAUM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let T: \mathbb{R}^n \to \mathbb{R} be defined by T(v) = ||v||. Is T linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/fR71H-ndGAUM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gfGDndk32iEO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/gfGDndk32iEO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (15)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let T: \mathbb{R}^3 \to \mathbb{R}^3 be defined by T(x_1, x_2, x_3) = (x_1, x_1 - x_2, x_2 + x_3). Is T linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/gfGDndk32iEO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T-xD7ALhb8Ar</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/T-xD7ALhb8Ar.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/T-xD7ALhb8Ar.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZjZlmA3ihljb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/81/ZjZlmA3ihljb.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of homogeneous functions - identifying the order of homogeneous functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/81/ZjZlmA3ihljb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8jzAzEJUeiwi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/210/8jzAzEJUeiwi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on linear vector subspaces. Solved: Let V=IR^3 be a linear vector space over IR. Show that W=\{(a,b,c)\in IR^3:a=2b=3c\} is a subspace of V. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/210/8jzAzEJUeiwi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NtHFrq26jw_1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/81/NtHFrq26jw_1.jpg</video:thumbnail_loc>

            <video:title>Euler's theorem</video:title>

            <video:description><![CDATA[
Euler's theorem for homogeneous functions. Solved: Evaluate x\frac{\partial f}{\partial x}+y\frac{\partial f}{\partial y} for each of the following:(a) f(x,y)=x^2+y^2(b) f(x,y)=\frac{x^2+y^2}{4xy}+\frac{y}{x}sin(\frac{x}{y}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/81/NtHFrq26jw_1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b8ifKCyv81O7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/220/b8ifKCyv81O7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on matrix representations of linear maps. Solved: For T:IR^2\to IR^3 defined by T(x,y)=(x,x+y,3x-y), obtain the matrix representation with respect to the standard bases. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/220/b8ifKCyv81O7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UOQE3bNiJCgG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/221/UOQE3bNiJCgG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the transition matrix between two bases of a vector space. Solved: Given that S_1=[(0,1),(1,4)] and S_2=[(1,0),(0,1)] are bases of IR^2, find the transition matrix from S_2 to S_1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/221/UOQE3bNiJCgG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DixiVZH5R_C_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/931/DixiVZH5R_C_.jpg</video:thumbnail_loc>

            <video:title>Summary and next steps</video:title>

            <video:description><![CDATA[
Review the main laws for torque, inertia, and angular momentum to finish this course. These rules are the foundation for studying planets and orbits in the next gravitation course. Finalise your work and see how these principles apply to universal gravity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/931/DixiVZH5R_C_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/orWvnMQ1n45p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/orWvnMQ1n45p.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector components in two and three dimensions. Solved: If \vec{p}=am +b\underline{n} and \vec{q}=c\underline{m}+d\underline{n} , find 2\vec{p}+\vec{q} in terms of the components vectors \underline{m}\space and\space \underline {n} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/orWvnMQ1n45p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/er-c4MafB0G4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/10/er-c4MafB0G4.jpg</video:thumbnail_loc>

            <video:title>External division</video:title>

            <video:description><![CDATA[
External division of a line in a given ratio by a point.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/10/er-c4MafB0G4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GLq_idiAM5Sz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/GLq_idiAM5Sz.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on vector components in two and three dimensions. Solved: Find the angle between vectors 2\underline{i}+3\underline{j}-5\underline{k}\space and\space\underline{j} . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/GLq_idiAM5Sz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BP5QELBnOi-k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/BP5QELBnOi-k.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on vector components in two and three dimensions. Solved: Is there \Lambda\in IR\space such \space that\space3\underline{i}-\underline{j}+2\underline{k}=-\underline{i}+\underline{j}-2\underline{k}-\Lambda(6\underline{i}-3\underline{j}+6\underline{k}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/BP5QELBnOi-k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MrjqhI7dY7Jp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/MrjqhI7dY7Jp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector algebra and its geometric applications. Solved: Find the sum of the vectors \vec{AB},\vec{-CB}, \vec{CD}, \vec{DE} and \vec{EF} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/MrjqhI7dY7Jp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oqw77_bAADJ5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7qZafmufII/Thumbnails/641/oqw77_bAADJ5.jpg</video:thumbnail_loc>

            <video:title>Independent variable absent</video:title>

            <video:description><![CDATA[
Solving higher-order ODEs by reduction to lower-order ones when the independent variable is absent.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7qZafmufII/Previews/641/oqw77_bAADJ5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SHpzVUpxT2fu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/SHpzVUpxT2fu.jpg</video:thumbnail_loc>

            <video:title>Two points</video:title>

            <video:description><![CDATA[
Vector equation of a straight line through two given points.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/SHpzVUpxT2fu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zh8N9CNIJHzX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/Zh8N9CNIJHzX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on vector components in two and three dimensions. Solved: Find angle OAB, given that \vec{OA}=-5\underline{i}+3\underline{k}\space and\space\vec{OB}=\underline{i}+7\underline{j}+2\underline{k}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/Zh8N9CNIJHzX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K53P6cZkejhb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qR6MmrqeFq/Thumbnails/651/K53P6cZkejhb.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qR6MmrqeFq/Previews/651/K53P6cZkejhb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n1FOPDu2Pz-G</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/n1FOPDu2Pz-G.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on vector algebra and its geometric applications. Solved: ABCD is a quadrilateral. P and Q are the midpoints of AD and DC respectively. Show that \vec{PQ}=\vec{AP} +\vec{QC}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/n1FOPDu2Pz-G.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9o43Id_ernAr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/9o43Id_ernAr.jpg</video:thumbnail_loc>

            <video:title>Practice questions</video:title>

            <video:description><![CDATA[
This lesson provides comprehensive practice questions covering the entire chapter on acids, bases, and salts. You will apply equilibrium principles to solve diverse problems involving pH calculations, salt hydrolysis, and buffer capacity. Master these examples to ensure exam readiness.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/9o43Id_ernAr.mp4</video:content_loc>

          <video:duration>61</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cuk2sdwn6bOk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/278/cuk2sdwn6bOk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on stationary points of a function of two variables. Solved: Find the nature of the stationary points of the function f(x,y)=x^4+4x^2y^2-2x^2+2y^2-1.Correction: \Delta=f_{xy}^2-f_{xx}f_{yy}. The expression used in the video is wrong, because the square was erroneously omitted. Fortunately, that did not affect our overall result, because f_{xy}=0 here. Please take note of this correction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/278/cuk2sdwn6bOk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N62tEBmEc1Lo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AnjynvnQEI/Thumbnails/654/N62tEBmEc1Lo.jpg</video:thumbnail_loc>

            <video:title>Introduction to Physics</video:title>

            <video:description><![CDATA[
This chapter covers everything you will be learning in High School physics  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AnjynvnQEI/Previews/654/N62tEBmEc1Lo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PLGv5VyMV345</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/PLGv5VyMV345.jpg</video:thumbnail_loc>

            <video:title>Notations</video:title>

            <video:description><![CDATA[
Notations for first and higher-order partial derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/PLGv5VyMV345.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fZlIm_TBwS9y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/276/fZlIm_TBwS9y.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on Taylor's theorem for a function of two variables. Solved: Expand the function sin(xy) about the point (1, \pi/3), neglecting terms of degree \ge 3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/276/fZlIm_TBwS9y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LwG3gU2H1pMk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/LwG3gU2H1pMk.jpg</video:thumbnail_loc>

            <video:title>Higher-order partial derivatives</video:title>

            <video:description><![CDATA[
Meaning of higher-order partial derivatives of multivariable functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/LwG3gU2H1pMk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yH6PaTLDU6UO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/413/yH6PaTLDU6UO.jpg</video:thumbnail_loc>

            <video:title>The implicit function theorem</video:title>

            <video:description><![CDATA[
The implicit function for a system of implicit functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/413/yH6PaTLDU6UO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QmI-52uB-zUm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/413/QmI-52uB-zUm.jpg</video:thumbnail_loc>

            <video:title>Existence of solutions</video:title>

            <video:description><![CDATA[
Examining the existence of solutions of a linear system of equations and its relation to the Jacobian determinant.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/413/QmI-52uB-zUm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CbsxSdGZHSRe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/873/CbsxSdGZHSRe.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Learn why certain atomic nuclei are unstable and how they break down naturally to reach a stable state. This lesson defines radioactive disintegration and provides the essential foundation for understanding nuclear decay and radiation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/873/CbsxSdGZHSRe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9g4lG20UvGwa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/413/9g4lG20UvGwa.jpg</video:thumbnail_loc>

            <video:title>Other theorems</video:title>

            <video:description><![CDATA[
Other theorems on the Jacobian determinant.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/413/9g4lG20UvGwa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gy24It_ikbLr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/982/gy24It_ikbLr.jpg</video:thumbnail_loc>

            <video:title>Acidic medium (2)</video:title>

            <video:description><![CDATA[
This lesson builds on the half-reaction method by providing additional complex examples of balancing redox equations in acidic media. We will focus on reactions involving polyatomic ions and multiple electron transfers to solidify your procedural fluency. Completing this ensures you can confidently apply the acidic medium balancing rules to any undergraduate problem. Solved: Balance the reaction below in acid medium:AS2???O3(s)???+NO-3(aq) ?????? H3???AsO4(aq)???+NO(g)??? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/982/gy24It_ikbLr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KUW68bKMAVKD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/KUW68bKMAVKD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on implicit differentiation of functions of several variables using partial derivatives and Jacobian determinants. Solved: Find the gradient of the conic f(x, y) = ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0, where a, b, c, g, f and h are constants. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/KUW68bKMAVKD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9pIYrB64ouBw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/410/9pIYrB64ouBw.jpg</video:thumbnail_loc>

            <video:title>Directional derivative</video:title>

            <video:description><![CDATA[
Definition of the directional derivative of a function of several variables, its maximum value and what direction it occurs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/410/9pIYrB64ouBw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QzLR4lchAX2G</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/278/QzLR4lchAX2G.jpg</video:thumbnail_loc>

            <video:title>Maxima and minima</video:title>

            <video:description><![CDATA[
How to find the stationary points of a function of two variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/278/QzLR4lchAX2G.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wawAFxlc1Ax4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/wawAFxlc1Ax4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on implicit differentiation of functions of several variables using partial derivatives and Jacobian determinants. Solved: Let F(x, y, z) = x^2 + y^2 + z^2 = 0, G(x, y, z) = x^2 - y^2 + 2z^2 = 0, where y(x), z(x). Obtain \frac {dy} {dx} and \frac {dz} {dx}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/wawAFxlc1Ax4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L_zS1pm_Hsv9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1034/L_zS1pm_Hsv9.jpg</video:thumbnail_loc>

            <video:title>Arrangements with identical items (2)</video:title>

            <video:description><![CDATA[
This lesson provides further worked examples involving multiple sets of identical items. You will learn to handle more complex scenarios where several different groups of objects are repeated within a single arrangement. Solved: 2. In how many different ways can the letters of the word MATHEMATICS be arranged? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1034/L_zS1pm_Hsv9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/adkNgbZ4mxL7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/adkNgbZ4mxL7.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for evaluating limits of functions of several variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/adkNgbZ4mxL7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qhwEoJK7L7Uj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/qhwEoJK7L7Uj.jpg</video:thumbnail_loc>

            <video:title>Tangent plane and normal line to a surface</video:title>

            <video:description><![CDATA[
Equations of the tangent plane and normal line to a surface.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/qhwEoJK7L7Uj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KBMvbfR-3_vv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/410/KBMvbfR-3_vv.jpg</video:thumbnail_loc>

            <video:title>The gradient vector</video:title>

            <video:description><![CDATA[
Definition of the gradient vector for a function of several variables.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/410/KBMvbfR-3_vv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YYoit0rEYpz0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/YYoit0rEYpz0.jpg</video:thumbnail_loc>

            <video:title>Chemical formulae (4)</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates the complete combustion analysis method, converting the mass of gaseous products into the mole ratio needed to determine the compound's empirical formula. Solved: further illustration:A compound contains only C, H, N, and O. Combustion of a 0.157g sample of the compound gave 0.213g of CO2 and 0.0310g of H2O. In another experiment, a 0.103g sample of the compound gave 0.0230g of NH3. Determine the empirical formula of the compound. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/YYoit0rEYpz0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VOe8LZ3lhxQT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/VOe8LZ3lhxQT.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar product of two vectors. Solved: 1.If a=3i+5j+2k and b=2i+2j-8k, show that a and b are perpendicular.2.Let m=3i-2j+k and n=i+3j-pk. Find the value of p such that m.n=-4. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/VOe8LZ3lhxQT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9XzXZ6JJe0lH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/9XzXZ6JJe0lH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar product of two vectors. Solved: 1.A parallelogram has its adjacent sides determined by a=3i+4j and b=-2i+j. Find the angle between the diagonals of the parallelogram.2.Given that |a| and |b| denote the magnitude of vectors, a and b, respectively, what is the scalar product of the vectors (|b|a+|a|b) and (|b|a-|a|b)? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/9XzXZ6JJe0lH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qJCHoA3OXQKj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/qJCHoA3OXQKj.jpg</video:thumbnail_loc>

            <video:title>Equation of a surface</video:title>

            <video:description><![CDATA[
Equation of a surface, in contrast to a plane; the direction of the gradient vector of a surface at a given point.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/qJCHoA3OXQKj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Lrwh2ehBAqFa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/Lrwh2ehBAqFa.jpg</video:thumbnail_loc>

            <video:title>Equation of a curve</video:title>

            <video:description><![CDATA[
Derivation and visualization of the parametric equations of curves in three dimensions and how they are related to those of straight lines; direction of the derivative of the parametric equation of a curve.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/Lrwh2ehBAqFa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y3G7eSodUwfT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/y3G7eSodUwfT.jpg</video:thumbnail_loc>

            <video:title>Tangent line and normal plane to a curve</video:title>

            <video:description><![CDATA[
Equations of the tangent line and normal plane to a curve.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/y3G7eSodUwfT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Em7zQ906ajgF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/395/Em7zQ906ajgF.jpg</video:thumbnail_loc>

            <video:title>Partial constraints</video:title>

            <video:description><![CDATA[
When is a two-dimensional structure said to be partially-constrained?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/395/Em7zQ906ajgF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1IM-Ko8R4SDF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/1IM-Ko8R4SDF.jpg</video:thumbnail_loc>

            <video:title>Intersection of surfaces</video:title>

            <video:description><![CDATA[
Lines formed by intersection of surfaces and their tangent vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/1IM-Ko8R4SDF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c7hyIDFXp7aI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/c7hyIDFXp7aI.jpg</video:thumbnail_loc>

            <video:title>Time taken</video:title>

            <video:description><![CDATA[
Calculate the time needed to deposit a specific mass during electrolysis using Faraday's first law. Relate current and charge to find the exact duration of the reaction. This worked example demonstrates the step-by-step computation for time-dependent problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/c7hyIDFXp7aI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xQD8fvB8CZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/xQD8fvB8CZ.jpg</video:thumbnail_loc>

            <video:title>Resultant point potential</video:title>

            <video:description><![CDATA[
Square charge arrangements test the superposition principle. How do you sum scalar potentials when signs differ? We calculate the resultant potential for symmetric and asymmetric cases. Solved: Four point charges are positioned at the corners of a square. If the electric potential at the centre of the square contributed by a single positive charge is +32.0 \text{ V}, calculate the total resultant potential at the centre when: (i) all four corners hold a charge of +q, (ii) three corners hold a charge of +q and one corner holds a charge of -q. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/xQD8fvB8CZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Hrm13sIrGiZh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/Hrm13sIrGiZh.jpg</video:thumbnail_loc>

            <video:title>Faraday's first law</video:title>

            <video:description><![CDATA[
Faraday’s first law states that the mass of substance released at an electrode is proportional to the quantity of electricity passed. This lesson explains the relationship between electrical charge and chemical change. It provides the theoretical basis for all quantitative calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/Hrm13sIrGiZh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Srj4ub6amL8i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/Srj4ub6amL8i.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of trusses by the method of joints.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/Srj4ub6amL8i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3L7zs9gKIF_5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/109/3L7zs9gKIF_5.jpg</video:thumbnail_loc>

            <video:title>Some special matrices (3)</video:title>

            <video:description><![CDATA[
Upper and lower triangular matrices, banded matrices, tridiagonal matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/109/3L7zs9gKIF_5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4X_fhPS2siy2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/4X_fhPS2siy2.jpg</video:thumbnail_loc>

            <video:title>Scalar multiplication</video:title>

            <video:description><![CDATA[
How to multiply a matrix by a number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/4X_fhPS2siy2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/anWZR-Jv1Nlz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/109/anWZR-Jv1Nlz.jpg</video:thumbnail_loc>

            <video:title>Some special matrices (4)</video:title>

            <video:description><![CDATA[
Sparse and dense matrices, diagonally-dominant matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/109/anWZR-Jv1Nlz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0Lg36hNYJsnS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/0Lg36hNYJsnS.jpg</video:thumbnail_loc>

            <video:title>Properties of matrix multiplication</video:title>

            <video:description><![CDATA[
Non-commutativity, associativity, distributivity over addition, identity and inverse elements for the operation of multiplication of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/0Lg36hNYJsnS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uJEuaU603_it</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/pHznHJ5kB7/Thumbnails/935/uJEuaU603_it.jpg</video:thumbnail_loc>

            <video:title>Summary of gravitation</video:title>

            <video:description><![CDATA[
A concise review of Newton's law of gravitation and Kepler's laws. This lesson ensures the foundational principles of celestial mechanics are consolidated.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/pHznHJ5kB7/Previews/935/uJEuaU603_it.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fIRoLL0Cc5tv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/fIRoLL0Cc5tv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: If y = 100 mm, \frac {dy} {dt} = 600 mm/s and \frac {d^2{y}} {dt^2} = -200 mm/s^2, what horizontal force force is exerted on the 0.4-kg slider A by the smooth circular slot? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/fIRoLL0Cc5tv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744394224535.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sq2Q6Lk_s1FV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/sq2Q6Lk_s1FV.jpg</video:thumbnail_loc>

            <video:title>Electrolytic process</video:title>

            <video:description><![CDATA[
Learn how electricity causes chemical changes in electrolytic cells. This lesson explains how electrodes work during electroplating and industrial metal extraction. It covers the basic theory of using external power to force chemical reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/sq2Q6Lk_s1FV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Rv2JcptOHZXB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/843/Rv2JcptOHZXB.jpg</video:thumbnail_loc>

            <video:title>Algebra</video:title>

            <video:description><![CDATA[
This lesson presents the algebraic method for balancing complex chemical equations unsuitable for simple inspection. You will learn to assign unknown coefficients, form a system of simultaneous equations based on elemental conservation, and solve for the minimum integer coefficients. This technique guarantees balance for challenging reactions. Solved: \text{Cu}_{(s)} + \text{HNO}_{3(aq)} \rightarrow \text{Cu(NO}_3)_{2aq} + \text{NO}_{(g)} + \text{H}_2\text{O}_{(l)}(i) Assign coefficient to each of the species involved (both reactants and products)(ii) Account for each of the atoms using the stoichiometric coefficients(iii) Assume one of the co-efficients is equal to 1. Usually (a)(iv) Put all the coefficient back into the original equation(v) Multiply through by the HCF of the denominators (3) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/843/Rv2JcptOHZXB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bd8q9ZgajOrc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/982/bd8q9ZgajOrc.jpg</video:thumbnail_loc>

            <video:title>Electron transfer</video:title>

            <video:description><![CDATA[
This lesson introduces the half-reaction method, the universal technique for balancing complex redox reactions in aqueous solution. You will learn to separate the overall reaction into oxidation and reduction half-reactions, balance mass and charge independently in each half, and then combine them to yield the final balanced equation. This method is crucial for quantitative electrochemistry. Solved: \text{Balancing Redox Reactions using Electron-Transfer Method}\text{Fe}^{3+}_{(aq)} + \text{Zn}_{(s)} \rightarrow \text{Fe}^{2+}_{(aq)} + \text{Zn}^{2+}_{(aq)} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/982/bd8q9ZgajOrc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fZ8DF0X7j-mM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/109/fZ8DF0X7j-mM.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/109/fZ8DF0X7j-mM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5JkeXqyPcqsS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/109/5JkeXqyPcqsS.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of a matrix; order, row, column and field of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/109/5JkeXqyPcqsS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xsBHZq149iHM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/109/xsBHZq149iHM.jpg</video:thumbnail_loc>

            <video:title>Some special matrices (2)</video:title>

            <video:description><![CDATA[
Square, diagonal, scalar and identity (unit) matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/109/xsBHZq149iHM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gzqjiZRQ1a8j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/gzqjiZRQ1a8j.jpg</video:thumbnail_loc>

            <video:title>Algebraic operations and laws</video:title>

            <video:description><![CDATA[
Master the fundamental laws of algebra by defining the commutative, associative, and distributive properties. You will establish the mechanical rules for term manipulation and grouping to ensure absolute precision during the simplification of complex algebraic expressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/gzqjiZRQ1a8j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tXxYowsE39G6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/tXxYowsE39G6.jpg</video:thumbnail_loc>

            <video:title>Natural numbers and integers</video:title>

            <video:description><![CDATA[
Define natural numbers as the counting set and integers as the extension including zero and negative values. You will master their discrete properties and fundamental operations, establishing the numerical base required for rational and irrational number classification.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/tXxYowsE39G6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TZGl9egAtkqa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/TZGl9egAtkqa.jpg</video:thumbnail_loc>

            <video:title>Variation of parameters</video:title>

            <video:description><![CDATA[
More worked examples on the method of undetermined coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/TZGl9egAtkqa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BlSKEV-Yac35</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/318/BlSKEV-Yac35.jpg</video:thumbnail_loc>

            <video:title>Trusses, frames and machines</video:title>

            <video:description><![CDATA[
Meaning, similarities and differences between trusses, frames and machines.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/318/BlSKEV-Yac35.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HyBLuf5LGEXU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/109/HyBLuf5LGEXU.jpg</video:thumbnail_loc>

            <video:title>Some special matrices (1)</video:title>

            <video:description><![CDATA[
Row, column and null matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/109/HyBLuf5LGEXU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8hb6bEohuimt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/318/8hb6bEohuimt.jpg</video:thumbnail_loc>

            <video:title>Internal and external forces</video:title>

            <video:description><![CDATA[
Meaning and use of internal and external forces in the analysis of a structure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/318/8hb6bEohuimt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fN70qRAfP1Fo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/8YS8I7xzGW/Thumbnails/937/fN70qRAfP1Fo.jpg</video:thumbnail_loc>

            <video:title>What is chemistry?</video:title>

            <video:description><![CDATA[
Formally defines chemistry as the scientific study of the properties and behaviour of matter. It establishes the scope of the subject from atoms to complex materials.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/8YS8I7xzGW/Previews/937/fN70qRAfP1Fo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c2zZ8gViiYuL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/319/c2zZ8gViiYuL.jpg</video:thumbnail_loc>

            <video:title>Modelling trusses</video:title>

            <video:description><![CDATA[
Simplifying joint connections and load conditions of trusses for analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/319/c2zZ8gViiYuL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8gBFBARm9GC-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/8gBFBARm9GC-.jpg</video:thumbnail_loc>

            <video:title>Zero-force members</video:title>

            <video:description><![CDATA[
Identifying members of a truss that bear no load, by the method of joints.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/8gBFBARm9GC-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lk0mYVE6vlDb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/lk0mYVE6vlDb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: The 2-kg truck is travelling at 15 m/s when the brakes on all its wheels are applied, causing it to skid for a distance of 10 m before coming to rest. Determine the constant horizontal force developed in the coupling C, and the frictional force developed between the tires of the truck and the road during this time. The total mass of the boat and the trailer is 1 Mg. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/lk0mYVE6vlDb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742308802100.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ig1rpuwKAThF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/ig1rpuwKAThF.jpg</video:thumbnail_loc>

            <video:title>Factors affecting discharge</video:title>

            <video:description><![CDATA[
Understand how ions compete for discharge at electrodes during electrolysis. This lesson explains why the position of an ion in the electrochemical series, its concentration, and the nature of the electrode determine which substance forms at the cathode and anode.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/ig1rpuwKAThF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7VZRiLvfvmE6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/7VZRiLvfvmE6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the method of undetermined coefficients. Solved: Solve the following:1 \frac {d^2y} {dx^2} + 3\frac {dy} {dx} +2y = e^{2x}2 \frac {d^3y} {dx^3} - 2\frac {d^2y} {dx^2} -\frac {dy} {dx} +2y = 6x + sin x 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/7VZRiLvfvmE6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NHWTKyA6u79p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/321/NHWTKyA6u79p.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of planar trusses using the method of sections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/321/NHWTKyA6u79p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/27s_fqLiygQh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/27s_fqLiygQh.jpg</video:thumbnail_loc>

            <video:title>Simplifying logarithms (3)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for simplifying complex logarithmic expressions and proving algebraic identities. You will learn to manipulate terms involving multiple variables and use the laws of logarithms to demonstrate that two seemingly different expressions are mathematically equal. Solved: 3. Show that \log_a(a+b)^2 = 2 + \log_a(1 + \frac{2b}{a} + \frac{b^2}{a^2}). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/27s_fqLiygQh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vd1UGu0oInFs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/Vd1UGu0oInFs.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: A light train made up of two cars is travelling at 90 km/h when the brakes are applied to both cars. Knowing that car A has a mass of 25 Mg and car B has a mass of 20 Mg, and that the braking force is 30 kN on each car, determine(a) The distance travelled by the train before it comes to a stop,(b) the force in the coupling between the cars while the train is slowing down. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/Vd1UGu0oInFs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742308352019.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Hor1gjQvf9nE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/Hor1gjQvf9nE.jpg</video:thumbnail_loc>

            <video:title>Method of joints</video:title>

            <video:description><![CDATA[
The principle of analysis of trusses using the method of joints.  
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          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/Hor1gjQvf9nE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-lBS8nKJZUEB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/-lBS8nKJZUEB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: Determine the steady-state angle \alpha if the constant force P is applied to the cart of mass M. The pendulum bob has mass m and the rigid bar of length L has negligible mass. Ignore all friction. Evaluate your expression for P = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/-lBS8nKJZUEB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742307541024.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/famDtOaEJ4iU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/famDtOaEJ4iU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: The 50-kg block A is released from rest. Determine the velocity of the 15-kg block B in 2 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/famDtOaEJ4iU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742306207773.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gv3BbKKFH1tZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/gv3BbKKFH1tZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: The 40-kg block shown in Fig. 2(b) is moving up initially with a speed of 3.5 m/s. What constant value of P will result in an upward speed of 6 m/s in 10 s? Assume that the weightless pulleys are frictionless and that the coefficient of friction between the blocks and the plane is 0.10. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/gv3BbKKFH1tZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742305089326.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/kA2SjVG4nVWg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/kA2SjVG4nVWg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: Collar A has a ramp that is welded to it and a force P = 5 lb applied as shown. Collar A and the ramp weigh 3 lb, block B weighs 0.8 lb. Neglecting friction, determine the tension in the cable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/kA2SjVG4nVWg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742304425581.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/qPhKSFLMN-n7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/415/qPhKSFLMN-n7.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of space trusses - by methods of joints and sections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/415/qPhKSFLMN-n7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_9VE0875Rxi4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/_9VE0875Rxi4.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions (1)</video:title>

            <video:description><![CDATA[
Piecewise functions split their rules across separate intervals. How do you isolate the correct expression when the approach point sits safely inside one section? Watch the interval check confirm the right formula. Solved: Evaluate \lim_{x \to \frac{2}{5}} f(x) for the function f(x) = \begin{cases} x & \text{if } x \le 0 \\ x^2 & \text{if } 0 < x < 1 \\ 2 - x & \text{if } x \ge 1 \end{cases}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/_9VE0875Rxi4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jhfeel3HcDHO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/jhfeel3HcDHO.jpg</video:thumbnail_loc>

            <video:title>Rational or irrational</video:title>

            <video:description><![CDATA[
This lesson explains how the discriminant identifies if real roots are rational or irrational. You will learn that perfect square discriminants result in rational roots, while other positive values produce irrational solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/jhfeel3HcDHO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qzweqwap6dpC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/817/qzweqwap6dpC.jpg</video:thumbnail_loc>

            <video:title>Physical and chemical processes</video:title>

            <video:description><![CDATA[
This lesson further establishes the critical distinction between physical and chemical changes with worked examples. Solved: 1. Consider the following separations of materials. State whether a physical process or a chemical reaction is involved in each separation.a. Sodium chloride is obtained from seawater by evaporation of the water.b. Mercury is obtained by heating the substance mercury(II) oxide; oxygen is also obtained.c. Pure water is obtained from ocean water by evaporating the water, then condensing it.e. Iron is produced from an iron ore that contains the substance iron(III) oxide.d. Gold is obtained from river sand by panning (allowing the heavy metal to settle in flowing water) [Question 1.51, General Chemistry by Ebbing and Gammon]2. Sodium metal reacts vigorously with water. A piece of sodium weighing 19.70 g was added to a beaker containing 126.22 g of water. During reaction, hydrogen gas was produced and bubbled from the solution. The solution, containing sodium hydroxide, weighed 145.06 g. How many grams of hydrogen gas were produced? [Question 1.93, General Chemistry by Ebbing and Gammon] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/817/qzweqwap6dpC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O2AKpXOk4K6W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/978/O2AKpXOk4K6W.jpg</video:thumbnail_loc>

            <video:title>Wavelengths and energy</video:title>

            <video:description><![CDATA[
This worked example applies the Rydberg formula to calculate emission wavelengths for electron transitions in the hydrogen atom. We will then use these results to determine the photon energy and classify the type of electromagnetic radiation emitted. Solved: 1. Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition?a. n = 4 \rightarrow n = 3b. n = 5 \rightarrow n = 4c. n = 5 \rightarrow n = 32. Calculate the corresponding energy of the light emitted for the transition in 1 (a) above 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/978/O2AKpXOk4K6W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zo3e6S1zEF4B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/Zo3e6S1zEF4B.jpg</video:thumbnail_loc>

            <video:title>Matrix addition</video:title>

            <video:description><![CDATA[
How to add or subtract two or more matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/Zo3e6S1zEF4B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tsIDMBQfeq3-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/tsIDMBQfeq3-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/tsIDMBQfeq3-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738679956417.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vkSRn5uzsIAw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/vkSRn5uzsIAw.jpg</video:thumbnail_loc>

            <video:title>Non-uniform density</video:title>

            <video:description><![CDATA[
Charge density varies along the rod. How do you integrate when lambda is a function of position? We keep the variable inside the integral to solve it. Solved: A thin non-conducting tube of length L = 15.0 \text{ cm} carries a non-uniform linear charge density \lambda = kx, where k = 40.0 \text{ }\mu\text{C/m}^2 and x is the distance measured from the left end of the tube (x = 0). Calculate the electric potential at a point P on the central axis of the tube, located at a distance d = 5.00 \text{ cm} to the left of the x = 0 end. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/vkSRn5uzsIAw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZjYvpo5PzHlm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/ZjYvpo5PzHlm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: A 200-N force is applied as shown to the bracket ABC. Determine the moment of the force about A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/ZjYvpo5PzHlm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738680126503.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vZYEvVSyhCBY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/vZYEvVSyhCBY.jpg</video:thumbnail_loc>

            <video:title>Equality of matrices</video:title>

            <video:description><![CDATA[
When are two matrices said to be equal?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/vZYEvVSyhCBY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iQypE9cDH5DB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/iQypE9cDH5DB.jpg</video:thumbnail_loc>

            <video:title>Properties of scalar multiplication</video:title>

            <video:description><![CDATA[
Properties of scalar multiplication of matrices - distributivity, associativity, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/iQypE9cDH5DB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2kZtSlVTwgNq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/979/2kZtSlVTwgNq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
This lesson applies de Broglie???s equation to calculate the wavelength of moving electrons. It demonstrates how particle speed and mass determine measurable wave behaviour. Solved: Questions for illustration1. Neutron diffraction is used in determining the structures of molecules.a. Calculate the de Broglie wavelength of a neutron moving at 1.00% of the speed of light.b. Calculate the velocity of a neutron with a wavelength of 75 pm (1 \text{ pm} = 10^{-12} \text{ m}).2. An atom of a particular element is traveling at 1% of the speed of light. The de Broglie wavelength is found to be 3.31 \times 10^{-3} \text{ pm}. Which element is this?These questions were copied from Chemical Principles by Steven R. Zumdahl and Donald J. DeCoste Chapter 12, Questions 35 and 37. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/979/2kZtSlVTwgNq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/btXL0oo0pi_g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/btXL0oo0pi_g.jpg</video:thumbnail_loc>

            <video:title>Distinct, identical or imaginary</video:title>

            <video:description><![CDATA[
This lesson details how the discriminant determines if roots are distinct, identical, or non-real. You will learn to categorise these solutions based on whether the discriminant is greater than, equal to, or less than zero.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/btXL0oo0pi_g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NHxl4zi1YaMm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/NHxl4zi1YaMm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: Determine the coordinate direction angles of the force F applied at the end of the pipe such that the moment of F about the point A is zero. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/NHxl4zi1YaMm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738691207420.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/o6ij1Rthholl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/318/o6ij1Rthholl.jpg</video:thumbnail_loc>

            <video:title>Equilibrium conditions</video:title>

            <video:description><![CDATA[
Review of the conditions of equilibrium for a rigid body, in two and three dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/318/o6ij1Rthholl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dUzEbA2R0YIW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/319/dUzEbA2R0YIW.jpg</video:thumbnail_loc>

            <video:title>Simple trusses</video:title>

            <video:description><![CDATA[
Basic make-up of simple trusses - from triangular to bigger ones.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/319/dUzEbA2R0YIW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CjFsqFxyspaJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/319/CjFsqFxyspaJ.jpg</video:thumbnail_loc>

            <video:title>Tensile and compressive forces</video:title>

            <video:description><![CDATA[
Identifying if a member is under tensile or compressive load.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/319/CjFsqFxyspaJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7M04cBSS15me</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/7M04cBSS15me.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: A rectangular piece of sheet metal is clamped along edge A B in a machine called a brake. The sheet is to be bent along line A B by applying a y direction force F. Determine the moment of this force about the line A B if F = 200 lb. Use both vector and scalar approaches. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/7M04cBSS15me.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738693396674.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/oh2nC2Od30GF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/oh2nC2Od30GF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: Determine the value of a that minimizes the perpendicular distance from point C to a section of pipeline that passes through points A and B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/oh2nC2Od30GF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738691540291.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/kj2X2ZFZuaHc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/kj2X2ZFZuaHc.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and notations for the transpose of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/kj2X2ZFZuaHc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hd0VlQZQbv4d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/hd0VlQZQbv4d.jpg</video:thumbnail_loc>

            <video:title>Operations on sets (1)</video:title>

            <video:description><![CDATA[
Execute a technical walkthrough of set operations using Venn diagrams to map unions, intersections, and complements. You will resolve complex shaded regions for multi-set expressions, establishing the spatial verification required for formal algebraic identities. Solved: 1. In a lecture hall at University of Benin containing 60 students, a survey was conducted regarding the use of two chat platforms: WhatsApp (W) and Telegram (T).45 students use WhatsApp.25 students use Telegram.15 students use both platforms.Determine the following:(a). How many students use only WhatsApp?(b). How many students use only Telegram?(c). How many students use neither of the two platforms? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/hd0VlQZQbv4d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kBkXpD_GKhSn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/871/kBkXpD_GKhSn.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
Recap the mechanics of galvanic and electrolytic cells, energy conversion, and Faraday's laws. This summary confirms your mastery of redox reactions and cell potential calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/871/kBkXpD_GKhSn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hXqClDkQxpy_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MuYvMAMRMj/Thumbnails/348/hXqClDkQxpy_.jpg</video:thumbnail_loc>

            <video:title>Summary (2)</video:title>

            <video:description><![CDATA[
Summary of the fundamental concepts on moments of inertia.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MuYvMAMRMj/Previews/348/hXqClDkQxpy_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oWrXq-euvMF7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/oWrXq-euvMF7.jpg</video:thumbnail_loc>

            <video:title>Properties (2)</video:title>

            <video:description><![CDATA[
More properties of linear maps.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/oWrXq-euvMF7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DSY-teTzES9A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FRMRVFZnzv/Thumbnails/656/DSY-teTzES9A.jpg</video:thumbnail_loc>

            <video:title>Significant figures and Decimal places</video:title>

            <video:description><![CDATA[
In this lesson, we will be discussing how to round numbers  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FRMRVFZnzv/Previews/656/DSY-teTzES9A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZkIXE9bEvilv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/ZkIXE9bEvilv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: A force P of magnitude 520 lb acts on the frame shown at point E. Determine the moment of P about a line joining points O and D. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/ZkIXE9bEvilv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738694718922.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5S93nhpVFVuq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/5S93nhpVFVuq.jpg</video:thumbnail_loc>

            <video:title>More special matrices (3)</video:title>

            <video:description><![CDATA[
Hermitian and skew-Hermitian (anti-Hermitian) matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/5S93nhpVFVuq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wBjHtCotyFIl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/wBjHtCotyFIl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: Determine the resultant moment of the two forces about the Oa axis. Express the result as a cartesian vector. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/wBjHtCotyFIl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738694929571.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/EAyNN82GhQDu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/EAyNN82GhQDu.jpg</video:thumbnail_loc>

            <video:title>More special matrices (1)</video:title>

            <video:description><![CDATA[
Symmetric and skew-symmetric matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/EAyNN82GhQDu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v6BtyrvMLjac</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/v6BtyrvMLjac.jpg</video:thumbnail_loc>

            <video:title>Properties of determinants (3)</video:title>

            <video:description><![CDATA[
Properties of determinants involving elementary row (or column) operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/v6BtyrvMLjac.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z0Y8nBbpiVkt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/Z0Y8nBbpiVkt.jpg</video:thumbnail_loc>

            <video:title>Differentiating a position vector (2)</video:title>

            <video:description><![CDATA[
This second example reinforces vector differentiation. We differentiate the position vector to find velocity, and then differentiate velocity to find acceleration. Master the application of the calculus rules. Solved: 6. A particle's position is described by \vec{r}(t) = (2.0t^3 - 5.0t)\underline{i} + (6.0t^2)\underline{j} \text{ m}. Find(a) the velocity, and(b) the speedof the particle at t = 2.0s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/Z0Y8nBbpiVkt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S0eX3PivDoe5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/415/S0eX3PivDoe5.jpg</video:thumbnail_loc>

            <video:title>Modelling</video:title>

            <video:description><![CDATA[
Space trusses and simplifying assumptions on load transmission and joint connections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/415/S0eX3PivDoe5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MHyj5QZ3hqjl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/MHyj5QZ3hqjl.jpg</video:thumbnail_loc>

            <video:title>Properties of the transpose</video:title>

            <video:description><![CDATA[
Properties of matrix transposes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/MHyj5QZ3hqjl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-23yGImEHPYm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/133/-23yGImEHPYm.jpg</video:thumbnail_loc>

            <video:title>Worked examples I</video:title>

            <video:description><![CDATA[
Worked examples on direct classification of quadric surfaces. Solved: Classify 4x^2-9y^2+z^2+36=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/133/-23yGImEHPYm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l99rtWwyIKi4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/322/l99rtWwyIKi4.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for the analysis of frames.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/322/l99rtWwyIKi4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3KwP95rV_Xei</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/3KwP95rV_Xei.jpg</video:thumbnail_loc>

            <video:title>Solving logarithmic equations (2)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving systems of logarithmic equations and equations with nested logs. You will learn to use base conversion and substitution to resolve simultaneous systems and isolate unknown variables across different logarithmic bases. Solved: 5. Solve the equations \log_e x = 4 \log_e y\log_3 x = 2 + 2 \log_3 y. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/3KwP95rV_Xei.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BSrr89XHJ7oU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/BSrr89XHJ7oU.jpg</video:thumbnail_loc>

            <video:title>Real or imaginary (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to find the range of an unknown coefficient when roots must be real. You will learn to set the discriminant to be greater than or equal to zero and solve the resulting inequality to find the required values. Solved: Find the range of values of m for which mx^2 + 6x + (m - 8) = 0 has real roots. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/BSrr89XHJ7oU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6tOE47GJi6oA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1146/6tOE47GJi6oA.jpg</video:thumbnail_loc>

            <video:title>Far-field approximation</video:title>

            <video:description><![CDATA[
Dipole potential decays faster than a point charge. Why does the field drop as one over r squared at large distances? We derive the angular formula for this far-field limit.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1146/6tOE47GJi6oA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qqr4LKWNwZ7e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/qqr4LKWNwZ7e.jpg</video:thumbnail_loc>

            <video:title>Solving logarithmic equations (3)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving advanced logarithmic equations where the unknown variable is the base. You will learn to use the definition of a logarithm to convert these equations into power forms and apply algebraic techniques to solve for the base. Solved: 6. Solve the equations \log_x (2y) = 3\log_x (4y) = 2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/qqr4LKWNwZ7e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/69hKe4QdLLEs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/69hKe4QdLLEs.jpg</video:thumbnail_loc>

            <video:title>Theorems (1)</video:title>

            <video:description><![CDATA[
Some theorems on elementary transformations - row and column operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/69hKe4QdLLEs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DT9EhSF6pj9C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/DT9EhSF6pj9C.jpg</video:thumbnail_loc>

            <video:title>Equivalent matrices</video:title>

            <video:description><![CDATA[
Meaning of equivalence, row equivalence and column equivalence of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/DT9EhSF6pj9C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YZ8Unk9bjFmV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/YZ8Unk9bjFmV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: The tension in each of the two supporting cables AB and AC is 10 lb. Determine the resultant force acting at A due to the two cables. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/YZ8Unk9bjFmV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739464196129.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xyn2jOEKkOqh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/xyn2jOEKkOqh.jpg</video:thumbnail_loc>

            <video:title>Energy changes for a reaction</video:title>

            <video:description><![CDATA[
Reactions involve energy changes as bonds break and form. This lesson explains how to measure these shifts by comparing reactant and product energy. You will learn why these processes either release or absorb heat from the surroundings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/xyn2jOEKkOqh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZQtji8F5sJif</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/ZQtji8F5sJif.jpg</video:thumbnail_loc>

            <video:title>Tangency (2)</video:title>

            <video:description><![CDATA[
This lesson shows how to find gradients of tangent lines passing through the origin. You will learn to equate the linear and quadratic equations and solve for the unknown gradient by setting the discriminant to zero. Solved: Find the gradients m of the lines through the origin which are tangents to y = x^2 + 4x + 9. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/ZQtji8F5sJif.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DM5_swO6lyqy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/DM5_swO6lyqy.jpg</video:thumbnail_loc>

            <video:title>Integrating an acceleration vector (2)</video:title>

            <video:description><![CDATA[
This second example reinforces vector integration. We integrate acceleration to find velocity, and then velocity to find position. Master the correct use of initial conditions as constants of integration. Solved: 8. A particle has an acceleration \vec{a}(t) = (3.0t^2)\underline{i} \text{ m/s}^2. At t = 1.0\text{s}, its position is \vec{r} = (6.0\underline{i} + 2.0\underline{j}) \text{ m} and its velocity is \vec{v} = (4.0\underline{i} - 3.0\underline{j}) \text{ m/s}. Find its position vector \vec{r} at t = 3.0\text{s}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/DM5_swO6lyqy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gy6ELE9HDbhu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/688/Gy6ELE9HDbhu.jpg</video:thumbnail_loc>

            <video:title>Decimal system (Denary)</video:title>

            <video:description><![CDATA[
We will dissect the decimal system (Base 10) in this lesson. You'll learn its structure and the value of digits based on their position. This is the foundation for understanding all other number bases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/688/Gy6ELE9HDbhu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EoHzd3KgZx99</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/977/EoHzd3KgZx99.jpg</video:thumbnail_loc>

            <video:title>Relative velocity (3)</video:title>

            <video:description><![CDATA[
This advanced worked example determines the necessary heading for a plane to maintain a due North course against a crosswind. You will apply vector components and trigonometric functions to calculate the correct steering angle. Precision in this two-dimensional analysis is vital for aviation navigation. Solved: 3. A plane wants to fly due North from city A to city B. The airspeed of the plane is 200\text{ km/hr}. The wind blows from the West (towards the East) at 100\text{ km/hr}. In what direction should the pilot head? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/977/EoHzd3KgZx99.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uPNbcILLB_7i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/uPNbcILLB_7i.jpg</video:thumbnail_loc>

            <video:title>Distinct, identical or imaginary (2)</video:title>

            <video:description><![CDATA[
This lesson shows how to solve for an unknown constant when an equation has equal roots. You will learn to set the discriminant to zero and solve the resulting expression to find the values required for this specific root condition. Solved: Find the values of p for which (p + 3)x^2 - 2(p - 1)x + (p + 3) = 0 has equal roots. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/uPNbcILLB_7i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ualfWON_rvkY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/ualfWON_rvkY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: A steel tank is to be positioned in an excavation. Determine by trigonometry(a) the magnitude and direction for the smallest force P for which the resultant R of the two forces applied at A is vertical,(b) the corresponding magnitude of R. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/ualfWON_rvkY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739465261153.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/p4gKcqqbWFZ6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/p4gKcqqbWFZ6.jpg</video:thumbnail_loc>

            <video:title>Equations involving surds</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving a quadratic equation where the coefficients are surds. You will learn to apply the quadratic formula to find exact roots and use the method for finding the square root of a compound surd to simplify your final answer. Solved: 9. Find the roots of the equation z^2 - 2\sqrt{2}z + \sqrt{3} = 0 in the form \sqrt{a} \pm \sqrt{b}, where a and b are rational numbers. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/p4gKcqqbWFZ6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/o91U5kU6Jif3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/692/o91U5kU6Jif3.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video provides a step-by-step worked example for converting binary numbers to base 10. You will learn the core method that applies to all conversions, ensuring a clear understanding.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/692/o91U5kU6Jif3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xFOtVl43lHQF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/692/xFOtVl43lHQF.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson demonstrates converting hexadecimal numbers with fractional parts to base 10. We will use a complete worked example to show how the same principles apply, solidifying your ability to convert any number base, regardless of complexity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/692/xFOtVl43lHQF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1zk-g-zXG5Df</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/1zk-g-zXG5Df.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: Determine the magnitude and direction of the resultant F_R = F_1 + F_2 + F_3 of the three forces by first finding the resultant F' = F_2 + F_3 and then finding F_R = F' + F_1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/1zk-g-zXG5Df.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739466810831.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ifXiOBVQRMwF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/ifXiOBVQRMwF.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of the curvilinear motion of a particle by angular impulse and momentum principles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/ifXiOBVQRMwF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TD3q3JlcDhgA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/TD3q3JlcDhgA.jpg</video:thumbnail_loc>

            <video:title>Theorems (2)</video:title>

            <video:description><![CDATA[
Some theorems on elementary matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/TD3q3JlcDhgA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ekIKaJYSNs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/ekIKaJYSNs.jpg</video:thumbnail_loc>

            <video:title>Reciprocal ratios</video:title>

            <video:description><![CDATA[
Understand cosecant, secant, and cotangent as the multiplicative inverses of sine, cosine, and tangent. These ratios are essential for simplifying complex trigonometric expressions and solving advanced calculus problems. Master their relationship to primary ratios to build a complete mathematical toolkit.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/ekIKaJYSNs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TMLekbnkpC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/TMLekbnkpC.jpg</video:thumbnail_loc>

            <video:title>Primary ratios</video:title>

            <video:description><![CDATA[
Apply the sine ratio to calculate the vertical height of a wall using a ladder's length and its angle of inclination. This walkthrough demonstrates how to translate a physical problem into a right-angled triangle for a quick solution. Master this process to solve basic engineering problems. Solved: A 7 \text{ m} ladder leans against a vertical wall. If the ladder makes an angle of 74^{\circ} with the horizontal ground, calculate the height of the wall reached by the ladder. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/TMLekbnkpC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B5Pxj0_s7x3X</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/693/B5Pxj0_s7x3X.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson provides another example of converting a denary number with a decimal point to another base. We'll use the multiplication method to handle the fractional part, solidifying your ability to handle any base conversion problem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/693/B5Pxj0_s7x3X.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/q0kF0a_hJ6Nt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1025/q0kF0a_hJ6Nt.jpg</video:thumbnail_loc>

            <video:title>Proving series (3)</video:title>

            <video:description><![CDATA[
This walkthrough proves a quadratic series formula using mathematical induction. You will learn to manipulate the algebraic sum to match the inductive goal for n equals k plus one. Solved: 3. Prove that 1^2 + 2^2 + 3^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6} for all natural numbers n \ge 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1025/q0kF0a_hJ6Nt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0fZEVWl2AwBp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/0fZEVWl2AwBp.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on elementary row operations. Solved: Reduce the matrix A =\begin{pmatrix}1&2&-4\\-1&-1&5\\2&7&-3\end{pmatrix} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/0fZEVWl2AwBp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y2_tAbIOqcFZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/y2_tAbIOqcFZ.jpg</video:thumbnail_loc>

            <video:title>Theorems (3)</video:title>

            <video:description><![CDATA[
Some theorems on equivalent matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/y2_tAbIOqcFZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cRSHIlNLXliU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/cRSHIlNLXliU.jpg</video:thumbnail_loc>

            <video:title>Reduced row echelon form (1)</video:title>

            <video:description><![CDATA[
Meaning of the reduced row echelon form of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/cRSHIlNLXliU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zrr69n-EidJ4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/Zrr69n-EidJ4.jpg</video:thumbnail_loc>

            <video:title>Determinants of orders 1 and 2</video:title>

            <video:description><![CDATA[
Computing determinants of orders 1 and 2.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/Zrr69n-EidJ4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FKXKhhdHSi_G</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/FKXKhhdHSi_G.jpg</video:thumbnail_loc>

            <video:title>Determinants of any order</video:title>

            <video:description><![CDATA[
Formal definition (Laplace expansion formula) of determinants, and how to evaluate determinants of any order.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/FKXKhhdHSi_G.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZHim_JsaOT7o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/ZHim_JsaOT7o.jpg</video:thumbnail_loc>

            <video:title>Reduced row echelon form (2)</video:title>

            <video:description><![CDATA[
Reduction of a matrix to its reduced row echelon form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/ZHim_JsaOT7o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3aZt5AUyDB70</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/3aZt5AUyDB70.jpg</video:thumbnail_loc>

            <video:title>Signs, minors and cofactors</video:title>

            <video:description><![CDATA[
Meaning of sign factor, minor and cofactor of an element in a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/3aZt5AUyDB70.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DXmG_q2Zdl4_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/DXmG_q2Zdl4_.jpg</video:thumbnail_loc>

            <video:title>Properties of determinants (2)</video:title>

            <video:description><![CDATA[
Properties of determinants involving zero or identical rows (or columns), triangular and diagonal matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/DXmG_q2Zdl4_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s7w5qGUyX-0O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/s7w5qGUyX-0O.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning and notations of determinants, singular and non-singular matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/s7w5qGUyX-0O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P6C32u9JlSUl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/P6C32u9JlSUl.jpg</video:thumbnail_loc>

            <video:title>Properties of determinants (1)</video:title>

            <video:description><![CDATA[
Determinants of matrix transposes and products, similar matrices, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/P6C32u9JlSUl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5l2fpB6G-I-t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/5l2fpB6G-I-t.jpg</video:thumbnail_loc>

            <video:title>Row echelon form (2)</video:title>

            <video:description><![CDATA[
Reduction of a matrix to a row echelon form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/5l2fpB6G-I-t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U03CWR4W242a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/U03CWR4W242a.jpg</video:thumbnail_loc>

            <video:title>Properties of determinants (4)</video:title>

            <video:description><![CDATA[
Properties of determinants involving sums, derivatives and integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/U03CWR4W242a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hYYZWmbAVKnK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/695/hYYZWmbAVKnK.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson provides a second worked example on adding and subtracting number bases. This will solidify your understanding and reinforce the core principles, preparing you for more complex problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/695/hYYZWmbAVKnK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fXBFk5XrAPbY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/688/fXBFk5XrAPbY.jpg</video:thumbnail_loc>

            <video:title>Duodecimal and Hexadecimal System.</video:title>

            <video:description><![CDATA[
This lesson covers higher-order number systems: the duodecimal (base 12) and hexadecimal (base 16) systems. We'll examine their structure, unique digits, and practical use cases. This knowledge is key for advanced computer science and data representation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/688/fXBFk5XrAPbY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CFF3seMqjut7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/CFF3seMqjut7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the components of a force. Solved: To insert the small cylindrical part into a close-fitting hole, the robot arm must exert a 90-N force on the part parallel to the axis of the hole as shown. Determine the components of the force which the part exerts on the robot along axes (a) parallel and perpendicular to the arm AB, and (b) parallel and perpendicular to the arm BC. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/CFF3seMqjut7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739468788457.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/be_R1pbgI8hk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/296/be_R1pbgI8hk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components. Solved: Determine the magnitude of the resultant force acting on the gusset plate and its direction, measured counterclockwise from the positive x axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/296/be_R1pbgI8hk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739469234290.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Jl0iB0JsieJa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/Jl0iB0JsieJa.jpg</video:thumbnail_loc>

            <video:title>More special matrices</video:title>

            <video:description><![CDATA[
Orthogonal, singular, non-singular, invertible and non-invertible matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/Jl0iB0JsieJa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BD-20TR4-Ltq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/BD-20TR4-Ltq.jpg</video:thumbnail_loc>

            <video:title>Matrix inverse</video:title>

            <video:description><![CDATA[
Definition of the inverse element and the inverse of a matrix.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/BD-20TR4-Ltq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iOAiAkQcbLS1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/iOAiAkQcbLS1.jpg</video:thumbnail_loc>

            <video:title>Similar matrices</video:title>

            <video:description><![CDATA[
When are two matrices said to be similar?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/iOAiAkQcbLS1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ii6I9_x1735k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/693/Ii6I9_x1735k.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video demonstrates how to convert a denary number to a binary number. You will learn the division method, a core skill for converting from base 10 to any other number base.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/693/Ii6I9_x1735k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XYBmQh5dN7nq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/695/XYBmQh5dN7nq.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This lesson provides a worked example for adding and subtracting numbers in different bases. You'll learn the core principles and apply them to solve a problem. This is the first step in mastering number base arithmetic.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/695/XYBmQh5dN7nq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sd_CXEwUgMtI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/698/Sd_CXEwUgMtI.jpg</video:thumbnail_loc>

            <video:title>Problems</video:title>

            <video:description><![CDATA[
This lesson brings everything together. You will solve a series of varied problems that require you to combine conversion and arithmetic skills. This is your final practice before facing real exam questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/698/Sd_CXEwUgMtI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gcc-qOsty4WL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/gcc-qOsty4WL.jpg</video:thumbnail_loc>

            <video:title>Properties of matrix inverses (4)</video:title>

            <video:description><![CDATA[
Properties of matrix inverses and their applications - implications on rank, determinant, homogeneous square systems of linear equations, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/gcc-qOsty4WL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lO0xYP_1tajh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/lO0xYP_1tajh.jpg</video:thumbnail_loc>

            <video:title>Cramer's rule</video:title>

            <video:description><![CDATA[
How to solve a square system of linear equations using determinants - Cramer's rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/lO0xYP_1tajh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/igrjDSLFx1dg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/igrjDSLFx1dg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the divergence of vector fields and some Laplacian. Solved: Given that the vector field\vec{A}=3x^2yz^3\mathbf{i}-4xy^3z^2\mathbf{j}+e^{xyz}\mathbf{k} ,find div \vec{A} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/igrjDSLFx1dg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gk5T85NKnyuT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/gk5T85NKnyuT.jpg</video:thumbnail_loc>

            <video:title>Diagonalizability</video:title>

            <video:description><![CDATA[
When are matrices diagonalizable?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/gk5T85NKnyuT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m1jR-EFn4MOz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/m1jR-EFn4MOz.jpg</video:thumbnail_loc>

            <video:title>Multiplicity of eigenvalues</video:title>

            <video:description><![CDATA[
Meaning of algebraic and geometric multiplicities of eigenvalues - with worked examples.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/m1jR-EFn4MOz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YRvLUanA_rEg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1029/YRvLUanA_rEg.jpg</video:thumbnail_loc>

            <video:title>Proving general formulas (2)</video:title>

            <video:description><![CDATA[
This walkthrough solves a complex induction proof for a non-linear recurrence relation. You will learn to use the inductive hypothesis to substitute terms and algebraically simplify the expression to verify the explicit formula for n equals k plus one. Solved: 2. A sequence is defined by a_1 = 1, a_{n+1} = 3a_n + 2 for all n \ge 1. Prove that its general formula is a_n = 2 \cdot 3^{n-1} - 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1029/YRvLUanA_rEg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M3CNn0O9S-xy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/M3CNn0O9S-xy.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on resolution of a force in three dimensions into its components. Solved: Determine the magnitude of the x, y, z components of the force F. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/M3CNn0O9S-xy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739786155988.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/GmJSNa5z_eZd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/GmJSNa5z_eZd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: The cable at the end of the beam exerts a force of 450 lb on the beam. Express F as a Cartesian vector. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/GmJSNa5z_eZd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739786290338.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ttsWGlJG46vA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1029/ttsWGlJG46vA.jpg</video:thumbnail_loc>

            <video:title>Proving general formulas (3)</video:title>

            <video:description><![CDATA[
Prove the general formula for a second-order recursive sequence using strong induction. This walkthrough verifies base cases and applies the recurrence relation to link successive terms. Solved: 3. A sequence is defined by a_1 = 3, a_2 = 5, a_n = 3a_{n-1} - 2a_{n-2} for n > 2. Prove that the general formula is a_n = 2^n + 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1029/ttsWGlJG46vA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FUxL912jFN6D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/FUxL912jFN6D.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: A force acts at the origin of a coordinate system in a direction defined by the angles \theta_x=70.9^\circ and \theta_y=144.9^\circ. Knowing that the z component of the force is -52.0 lb, determine (a) the angle \theta_v (b) the other components and the magnitude of the force. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/FUxL912jFN6D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O-CLyB16AhYI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/528/O-CLyB16AhYI.jpg</video:thumbnail_loc>

            <video:title>Spaces</video:title>

            <video:description><![CDATA[
Meaning, representations and examples of sets and spaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/528/O-CLyB16AhYI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EB8toVIl_NsZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/8YS8I7xzGW/Thumbnails/937/EB8toVIl_NsZ.jpg</video:thumbnail_loc>

            <video:title>Branches</video:title>

            <video:description><![CDATA[
Chemistry is not a monolithic subject. This lesson defines its principal branches - organic, inorganic, physical, analytical, and biochemistry - to provide a clear map of the discipline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/8YS8I7xzGW/Previews/937/EB8toVIl_NsZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HfTSMIV-WxaX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/HfTSMIV-WxaX.jpg</video:thumbnail_loc>

            <video:title>Population growth</video:title>

            <video:description><![CDATA[
Modelling population growth with first-order ordinary differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/HfTSMIV-WxaX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eLwHsbLVTR4K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/eLwHsbLVTR4K.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on vector algebra and its geometric applications. Solved: Show that the lines joining the points of adjacent sides of any quadrilateral form a parallelogram. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/eLwHsbLVTR4K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wj_H4Ka_23Xu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/528/Wj_H4Ka_23Xu.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/528/Wj_H4Ka_23Xu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jVZbqW3yf0Dw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/jVZbqW3yf0Dw.jpg</video:thumbnail_loc>

            <video:title>Product rule</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to apply the product rule to real-world counting problems. You will learn to multiply outcomes for multi-step tasks to find the total number of possible results efficiently. Solved: 1. A doctor needs to travel from Lagos to Ibadan, and then from Ibadan to Ilorin. There are 4 different bus companies operating the Lagos to Ibadan route, and 3 different bus companies operating the Ibadan to Ilorin route. In how many ways can the doctor complete the journey from Lagos to Ilorin. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/jVZbqW3yf0Dw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VupqJ8QRYOZX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/VupqJ8QRYOZX.jpg</video:thumbnail_loc>

            <video:title>Equivalent systems</video:title>

            <video:description><![CDATA[
When are two systems of linear equations equivalent? What is the impact of elementary row operations on the systems of equations?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/VupqJ8QRYOZX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1RZf1OL63SkZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/1RZf1OL63SkZ.jpg</video:thumbnail_loc>

            <video:title>Rate of chemical reactions</video:title>

            <video:description><![CDATA[
Modelling rate of chemical reactions with first-order ordinary differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/1RZf1OL63SkZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7X0LMkbKf7Wp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/7X0LMkbKf7Wp.jpg</video:thumbnail_loc>

            <video:title>Homogeneous systems</video:title>

            <video:description><![CDATA[
Conditions for existence of different forms of solutions for homogeneous systems of linear equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/7X0LMkbKf7Wp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DcAVD8CBvA2H</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/DcAVD8CBvA2H.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: The cord passing over two small pegs A and B on the board is subjected to a tension of 10 lb. Determine the minimum tension P and the orientation \theta of the cord passing over pegs C and D, so that the resultant couple produced by both cords is 20 lb . in. clockwise. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/DcAVD8CBvA2H.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738864318807.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/OLjj7XbAqola</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/OLjj7XbAqola.jpg</video:thumbnail_loc>

            <video:title>Subtraction rule</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to solve complex counting problems by subtracting unwanted cases from the total possibilities. You will learn to use this indirect method to quickly calculate outcomes for "at least" or "at most" conditions. Solved: 3. A security code has 4 digits, where each digit can be from the numbers 0 to 9. If repetition of digits is allowed, how many different codes contain at least one digit 7? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/OLjj7XbAqola.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v1Gi1iu-u17K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/v1Gi1iu-u17K.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: (i) Determine (a) the x, y and z components of the 500-N force, (b) the angles \Theta_x , \Theta_y and \Theta_z that the force forms with the coordinate axes.(ii)Determine (a) the x, y and z components of the 800-N force, (b) the angles \Theta_x, \Theta_y and \Theta_z that the force forms with the coordinate axes. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/v1Gi1iu-u17K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746865956271.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/RnL1QJvNuI5u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/RnL1QJvNuI5u.jpg</video:thumbnail_loc>

            <video:title>The eigenvalue problem</video:title>

            <video:description><![CDATA[
Formal definition of eigenvalues and eigenvectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/RnL1QJvNuI5u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-sc3PrqnM-fZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/-sc3PrqnM-fZ.jpg</video:thumbnail_loc>

            <video:title>Characteristic polynomial of degree n</video:title>

            <video:description><![CDATA[
General expression for the characteristic polynomial of a given square matrix of order n, in terms of its principal minors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/-sc3PrqnM-fZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0ACq9ps2IS4f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/0ACq9ps2IS4f.jpg</video:thumbnail_loc>

            <video:title>Characteristic polynomials</video:title>

            <video:description><![CDATA[
Meaning of characteristic polynomials of matrices and how to calculate them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/0ACq9ps2IS4f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qiuLF7QN-EBA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/386/qiuLF7QN-EBA.jpg</video:thumbnail_loc>

            <video:title>Mass moments of inertia</video:title>

            <video:description><![CDATA[
Meaning and calculation of mass moments of inertia by double integration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/386/qiuLF7QN-EBA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9HSEImKv7E0W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/9HSEImKv7E0W.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: The angle between the guy wire AB and the mast is 20^{\circ}. Knowing that the tension in AB is 300 lb, determine (a) the x, y, and z components of the force exerted on the boat at B, (b) the angles \Theta_x,\Theta_y and \Theta_z defining the direction of the force exerted at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/9HSEImKv7E0W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739794216339.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/K0z7u0OSg8Xh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/K0z7u0OSg8Xh.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: Four pegs of the same diameter are attached to a board as shown. Two strings are passed around the pegs and pulled with the forces indicated. Determine the diameter of the pegs knowing that the resultant couple applied to the board is 1132.5 lb.in. counterclockwise. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/K0z7u0OSg8Xh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738864662953.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Z-8A-SZP_Uyu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/334/Z-8A-SZP_Uyu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of frictional forces on wedges. Solved: A 15^\circ wedge is force under a 50-kg pipe as shown. Knowing that the coefficient of static friction at both surfaces of the wedge is 0.20, determine the largest coefficient of static friction between the pipe and the vertical wall for which slipping will occur at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/334/Z-8A-SZP_Uyu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741109918354.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/I26xqArQZRGg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/977/I26xqArQZRGg.jpg</video:thumbnail_loc>

            <video:title>Relative velocity (1)</video:title>

            <video:description><![CDATA[
This worked example calculates the resultant velocity of a passenger on a moving walkway relative to the ground. You will apply the one-dimensional relative velocity formula to solve cases for motion in both the same and opposite directions. Mastery of these vector additions is foundational. Solved: 1. A passenger walks at 2.0 \text{ m/s} relative to a moving walkway. The walkway moves at 3.0 \text{ m/s} relative to the ground. Find the passenger's speed relative to the ground if they walk(a) in the same direction, and(b) in the opposite direction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/977/I26xqArQZRGg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PjG_k1iorQ1L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/PjG_k1iorQ1L.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on algebra of complex numbers. Solved: 1. Given z_1=2+i, z_2=3-2i, z_3=-1+4i, calculate(a) z_1+z_2(b) z_1-z_2(c) \frac{z_1}{z_2}(d) z_1z_22. Simplify (a) \frac{5+5i}{3-4i} + \frac{20}{4+3i}(b) \left(\frac{2+i}{1-i}\right) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/PjG_k1iorQ1L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WBq5ylZSjo2D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/WBq5ylZSjo2D.jpg</video:thumbnail_loc>

            <video:title>Finite and infinite sets</video:title>

            <video:description><![CDATA[
A finite set contains a countable number of elements, whereas an infinite set does not. This lesson defines both types of sets, illustrates them with examples, and explains the significance of distinguishing between the two. It also introduces the concept of cardinality and discusses how it applies to both finite and infinite sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/WBq5ylZSjo2D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qJwHYHfFO6G-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/qJwHYHfFO6G-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion. Solved: The position of a particle is defined by r = \{4(t - sint)i + (2t^2 -3)j\} m, where t is in seconds and the argument for the sine is in radians. Determine the speed of the particle and the normal and tangential components of acceleration when t = 1 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/qJwHYHfFO6G-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rjZZXSFUeunv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/rjZZXSFUeunv.jpg</video:thumbnail_loc>

            <video:title>Components</video:title>

            <video:description><![CDATA[
Meaning of components of a force, in general.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/rjZZXSFUeunv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c4vcTLXoKqo1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/c4vcTLXoKqo1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (16)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Determine the components of F that act along rod AC and perpendicular to it. Point B is located 3m along the rod from end C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/c4vcTLXoKqo1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739872104277.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/9vzHENBymnP3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/9vzHENBymnP3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (15)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: The cable AB exerts a 32-lb force T on the collar at A. Express T in terms of components. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/9vzHENBymnP3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739796146187.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dyu6L1J8LLcw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/dyu6L1J8LLcw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: Determine the moment about point B of each force acting on the beam. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/dyu6L1J8LLcw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738687910238.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0FSWbvdUQbVl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/0FSWbvdUQbVl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: The 30-N force P is applied perpendicular to the portion BC of the bent bar. Determine the moments of P about point B and about point A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/0FSWbvdUQbVl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688122669.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/oxx4I4SVWKQw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/oxx4I4SVWKQw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: The small crane is mounted along the side of a pickup bed and facilitates the handling of heavy loads. When the boom elevation angle is \theta = 40^{\circ} , the force in the hydraulic cylinder BC is 4.5 kN , and this force applied at point C is in the direction from B to C (the cylinder is in compression). Determine the moment of this 4.5 kN force about the boom pivot point O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/oxx4I4SVWKQw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688174558.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/3MitAwVDUAe8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/3MitAwVDUAe8.jpg</video:thumbnail_loc>

            <video:title>Conservation of linear momentum</video:title>

            <video:description><![CDATA[
Determining the direction of conservation of linear momentum for the system of bodies in collision.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/3MitAwVDUAe8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CsgP3_ivdtMJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/CsgP3_ivdtMJ.jpg</video:thumbnail_loc>

            <video:title>Parametric curves</video:title>

            <video:description><![CDATA[
Parametric forms of equations of straight and curved lines.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/CsgP3_ivdtMJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bWGGv6P41M1l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/bWGGv6P41M1l.jpg</video:thumbnail_loc>

            <video:title>Quadratic inequality (1)</video:title>

            <video:description><![CDATA[
Solve a quadratic inequality by factorising the expression to find critical values and testing the resulting intervals. This walkthrough shows how to identify the valid solution set using a sign table or number line analysis. Mastering this technique is essential for non-linear constraints. Solved: 5. Solve the inequality 2x^2 - 3x - 5 > 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/bWGGv6P41M1l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/88zwsZb9i37t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/88zwsZb9i37t.jpg</video:thumbnail_loc>

            <video:title>Differentials</video:title>

            <video:description><![CDATA[
Scalar and vector differentials used in line integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/88zwsZb9i37t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/csNfUf9Ji4Ls</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/418/csNfUf9Ji4Ls.jpg</video:thumbnail_loc>

            <video:title>Theorem</video:title>

            <video:description><![CDATA[
Statement of Green's theorem in a plane and its use in evaluating line integrals by double integrals, and vice-versa.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/418/csNfUf9Ji4Ls.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FJZm_8Esa27C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/FJZm_8Esa27C.jpg</video:thumbnail_loc>

            <video:title>Identity and inverse elements</video:title>

            <video:description><![CDATA[
Identify the additive and multiplicative identities and their corresponding inverse elements within the real number system. You will master the mechanical application of these properties to isolate variables and maintain equality during algebraic manipulation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/FJZm_8Esa27C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vEK4RS3NVhHa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/vEK4RS3NVhHa.jpg</video:thumbnail_loc>

            <video:title>Passive charge sharing</video:title>

            <video:description><![CDATA[
Disconnected capacitors share charge until voltages match. How does the initial charge split between two different sizes? We calculate the final distribution using conservation of charge. Solved: A 2.00\text{-}\mu\text{F} capacitor is charged by being connected across a 12.0\text{-V} battery. It is then disconnected from the battery and connected in parallel with an uncharged 4.00\text{-}\mu\text{F} capacitor. Determine the magnitude of the resulting charge on each capacitor. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/vEK4RS3NVhHa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kUhXZDxV9IhS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/kUhXZDxV9IhS.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
More examples on applications of first-order ordinary differential equations. Solved: A sewing machine is said to depreciate in value at any given time, at a rate proportional to the square of its value. Adam bought a sewing machine for#12, and found out it depreciated in value by#4 in two years. What will this machine be worth in another 10 years. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/kUhXZDxV9IhS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aGR4VXvQAo62</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/386/aGR4VXvQAo62.jpg</video:thumbnail_loc>

            <video:title>Area moments of inertia</video:title>

            <video:description><![CDATA[
Calculating area moments of inertia of a region R in a plane by double integration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/386/aGR4VXvQAo62.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XB-fqC4RSaYp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/XB-fqC4RSaYp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on algebra of complex numbers. Solved: 1. Prove that z_1\cdot\overline{z}_2+\overline{z}_1\cdot z_2 is a real number for any z_1,z_2\in\mathbb{c} .2. Solve the equations:(a) z + (-5 + 7i) = (2 - i)(b) \frac{z}{-1 + 3i} = 3 + 2i(c) z(2 + 3i) = 4 + 5i 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/XB-fqC4RSaYp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3FLn1tYBb675</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/3FLn1tYBb675.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: An experimental device imparts a force of magnitude F = 47 lb to the front edge of the rim at A to simulate the effect of a slam dunk. Determine the moments of the force F about point O and about point B. Finally, locate, from the base O, a point C on the ground about which the force imparts zero moment. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/3FLn1tYBb675.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688391260.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/e_ruNbfWPFzn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/e_ruNbfWPFzn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Two force F_1 and F_2 are applied to the hook, as shown. Express F_1 in Cartesian vector notation. Note the orientation of the axes. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/e_ruNbfWPFzn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739788023067.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/iGeH3YtmUnPX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/iGeH3YtmUnPX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on gradients, directional derivatives and normals to surfaces. Solved: Find the equations of (a)tangent line (b)normal line to the surface at 2x^2+y^2+2z=3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/iGeH3YtmUnPX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RUMjywvcaRXp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/RUMjywvcaRXp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/RUMjywvcaRXp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YvRlwqTW7DaU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/YvRlwqTW7DaU.jpg</video:thumbnail_loc>

            <video:title>Conservative vector fields</video:title>

            <video:description><![CDATA[
Meaning and properties of line integrals of conservative vector fields - path independence of their line integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/YvRlwqTW7DaU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ir9vwZKQhXoq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/100/ir9vwZKQhXoq.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning and symbols for double integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/100/ir9vwZKQhXoq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8xfMUx6OKM84</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/418/8xfMUx6OKM84.jpg</video:thumbnail_loc>

            <video:title>Proof</video:title>

            <video:description><![CDATA[
Proof of Green's theorem in a plane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/418/8xfMUx6OKM84.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/u9QySwP94xj2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/201/u9QySwP94xj2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on algebra of complex numbers. Solved: 1. Solve the equations:(a) z^2 + z + 1 = 0,(b) z^3 + 1 = 02. Find real numbers x and y for which the following relations hold:(a) (1 - 2i)x + (1 + 2i)y = 1 + i(b) \frac{x - 3}{3 + i} + \frac{y - 3}{3 - i} = i(c) (4 - 3i)x^2 + (3 + 2i)xy = 4y^2 - \frac{1}{2}x^2 + (3xy - 2y^2)i 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/201/u9QySwP94xj2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bc7v6UDzwL_s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/331/bc7v6UDzwL_s.jpg</video:thumbnail_loc>

            <video:title>Types of friction</video:title>

            <video:description><![CDATA[
Meaning of dry friction and fluid friction; meaning and use of lubrications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/331/bc7v6UDzwL_s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fsPuJf_jV8nj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/140/fsPuJf_jV8nj.jpg</video:thumbnail_loc>

            <video:title>Transformation to canonical forms</video:title>

            <video:description><![CDATA[
Algorithm for transformation of quadratic forms to canonical forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/140/fsPuJf_jV8nj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IcC1QNNQXDbn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/IcC1QNNQXDbn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: Determine the angle \theta at which the 500-N force must act at A so that the moment of this force about point B is equal to zero. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/IcC1QNNQXDbn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688468534.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/LQT5xpNZ5mc7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/6/LQT5xpNZ5mc7.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/6/LQT5xpNZ5mc7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LQHm0zQvNKKL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/332/LQHm0zQvNKKL.jpg</video:thumbnail_loc>

            <video:title>Static and kinetic friction coefficients</video:title>

            <video:description><![CDATA[
Meaning and use of coefficients of static and kinetic friction between surfaces in dry friction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/332/LQHm0zQvNKKL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3O7L2wt6nt1k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/332/3O7L2wt6nt1k.jpg</video:thumbnail_loc>

            <video:title>States of rest or relative motion</video:title>

            <video:description><![CDATA[
Different states of rest or relative motion between surfaces in contact, and the conditions for each state.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/332/3O7L2wt6nt1k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L0GEGpH-Bmj_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/333/L0GEGpH-Bmj_.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of problems involving dry friction - for particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/333/L0GEGpH-Bmj_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CiwZ5x5Bg7ul</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/332/CiwZ5x5Bg7ul.jpg</video:thumbnail_loc>

            <video:title>Angles of friction</video:title>

            <video:description><![CDATA[
Meaning and use of angles of static and kinetic friction, and angle of repose.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/332/CiwZ5x5Bg7ul.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a5myGBIPGJLc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/332/a5myGBIPGJLc.jpg</video:thumbnail_loc>

            <video:title>Static and kinetic friction forces</video:title>

            <video:description><![CDATA[
Meaning of static and kinetic friction forces and when they are applicable in dry friction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/332/a5myGBIPGJLc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LM6Kgj9L2f_q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/889/LM6Kgj9L2f_q.jpg</video:thumbnail_loc>

            <video:title>Real or imaginary (2)</video:title>

            <video:description><![CDATA[
This lesson explains how to find the range of an unknown coefficient when an equation has no real roots. You will learn to set the discriminant to be less than zero and solve the resulting inequality to identify the valid values for an unknown. Solved: Find the range of values of q for which x^2 + qx + 16 = 0 has no real roots. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/889/LM6Kgj9L2f_q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AdZ495IE27uH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/202/AdZ495IE27uH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the modulus and argument of a complex number. Solved: 1. Obtain the modulus and argument of each of the following (a) \frac{(1+i)(2+i)}{3-i}(b) \frac{(3+i)(2-i)}{2+3i}(c) -6(d) 3i2. Find all complex numbers z such that4z^2 + 8|z|^2 = 8. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/202/AdZ495IE27uH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OkNABA9G7d1L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/1022/OkNABA9G7d1L.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson defines solubility equilibrium and the solubility product constant, Ksp. You will learn to write equilibrium expressions for sparingly soluble ionic compounds and understand why some solids do not fully dissolve in water.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/1022/OkNABA9G7d1L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qK3KorPbhml2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/qK3KorPbhml2.jpg</video:thumbnail_loc>

            <video:title>Staging and committing</video:title>

            <video:description><![CDATA[
Saving work in Git is a deliberate, two-stage process. First, you use the **staging area** (`git add`) to select specific changes, then you **commit** (`git commit`) them as a permanent snapshot in your project's history. Mastering this core workflow is essential.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/qK3KorPbhml2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tIW5VYir73k9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/tIW5VYir73k9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on vector algebra and its geometric applications. Solved: D,E,F are the midpoints of the sides BC,CA,AB respectively of a triangle ABC.(a) Show that \vec{AD}= \frac{1}{2}(\vec{AB}+\vec{AC})(b) Hence, deduce that \vec{AD}+\vec{BE}=\vec{FC} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/tIW5VYir73k9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jBHuv-NZiNnM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/97/jBHuv-NZiNnM.jpg</video:thumbnail_loc>

            <video:title>Overview</video:title>

            <video:description><![CDATA[
An overview of equations of various quadric surfaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/97/jBHuv-NZiNnM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v-arXoE-Ly5M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/331/v-arXoE-Ly5M.jpg</video:thumbnail_loc>

            <video:title>Friction</video:title>

            <video:description><![CDATA[
Meaning of friction and how to identify problems involving friction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/331/v-arXoE-Ly5M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hQebcojMQCop</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/421/hQebcojMQCop.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of problems involving dry friction - for rigid bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/421/hQebcojMQCop.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hplWf3MJJh3V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/331/hplWf3MJJh3V.jpg</video:thumbnail_loc>

            <video:title>Equilibrium</video:title>

            <video:description><![CDATA[
Review of the conditions and equations of equilibrium of particles and rigid bodies in two dimensions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/331/hplWf3MJJh3V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sWvG2Z4KZViU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/334/sWvG2Z4KZViU.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Principles and procedure for analysis of frictional forces on wedges.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/334/sWvG2Z4KZViU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3aESwiR4s_JY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/3aESwiR4s_JY.jpg</video:thumbnail_loc>

            <video:title>Solving logarithmic equations (1)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving logarithmic equations where the variable appears as an argument or within the exponent. You will learn to use base-matching techniques and the definition of a logarithm to isolate and solve for unknown values in complex algebraic structures. Solved: 4. Solve for x in \log_2 x^{\log_2 x} = 4 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/3aESwiR4s_JY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GjhLbdpDskeo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/GjhLbdpDskeo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on rational powers and roots of complex numbers. Solved: 1.Given z=-2(1+i\sqrt{3)}, evaluate z^\frac{2}{3}2. Evaluate (-2)^{0.45333...} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/GjhLbdpDskeo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z59hhR9BxFTk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/Z59hhR9BxFTk.jpg</video:thumbnail_loc>

            <video:title>Force</video:title>

            <video:description><![CDATA[
Meaning and measurement of force.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/Z59hhR9BxFTk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lr1MZDjikvNG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/149/lr1MZDjikvNG.jpg</video:thumbnail_loc>

            <video:title>Newtonian mechanics</video:title>

            <video:description><![CDATA[
Meaning, history, applications and limitations of Newtonian mechanics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/149/lr1MZDjikvNG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_AompTz_eVy7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/963/_AompTz_eVy7.jpg</video:thumbnail_loc>

            <video:title>CSS reset</video:title>

            <video:description><![CDATA[
Learn to organize your stylesheet for simplicity and apply a robust CSS reset, providing a clean, predictable design canvas across all browsers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/963/_AompTz_eVy7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vukXY4fswMb4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/vukXY4fswMb4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: If the tension developed in each cable cannot exceed 300lb, determine the largest weight of the crate that can be supported. Also, what is the force developed along strut AD 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/vukXY4fswMb4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739877576835.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/eHE0UbALBNOP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/eHE0UbALBNOP.jpg</video:thumbnail_loc>

            <video:title>Battery-connected squeeze</video:title>

            <video:description><![CDATA[
Squeezing a capacitor changes its storage capacity. How does the battery respond when plate separation drops while connected? We calculate the extra charge pumped into the circuit. Solved: Two parallel-plate capacitors, each with a capacitance of 4.00 \text{ }\mu\text{F}, are connected in parallel to a 20.0 \text{ V} battery. While the battery remains connected, one of the capacitors is squeezed so that its plate separation is reduced to 25.0\% of its initial value. Determine (a) the magnitude of the additional charge that the battery pumps into the circuit and (b) the final total charge stored by the network. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/eHE0UbALBNOP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w0FBMQUGH7jd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/w0FBMQUGH7jd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: In trying to move across a slippery icy surface, a 175-lb man uses two ropes, AB and AC. Knowing that the force exerted on the man by the icy surface is perpendicular to that surface, determine the tension in each rope. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/w0FBMQUGH7jd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740069444369.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xIryJwAUGeZA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/xIryJwAUGeZA.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates. Solved: The roller coaster travels down the helical path at constant speed such that the parametric equations that define its position are x = c sin kt, y = c cos kt, z = h-bt, where c, h, and b are constants. Determine the magnitudes of its velocity and acceleration. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/xIryJwAUGeZA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742211765696.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/bKc-2AWG0Ljc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Thumbnails/340/bKc-2AWG0Ljc.jpg</video:thumbnail_loc>

            <video:title>Common areas and lines (1)</video:title>

            <video:description><![CDATA[
Areas of common areas, lengths of common lines, and their centroids.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Previews/340/bKc-2AWG0Ljc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kq3SR8X_YpIO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Thumbnails/340/kq3SR8X_YpIO.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
Summary of important concepts on centroids and centres of gravity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Previews/340/kq3SR8X_YpIO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wcBmm63PmJAX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Thumbnails/340/wcBmm63PmJAX.jpg</video:thumbnail_loc>

            <video:title>Common areas and lines (2)</video:title>

            <video:description><![CDATA[
Areas of common areas, lengths of common lines, and their centroids.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Previews/340/wcBmm63PmJAX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/o3sFpQ3LK_uQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/205/o3sFpQ3LK_uQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on representation, multiplication, division and powers of complex numbers in exponential form. Solved: 1.Given the following complex numbers:z_1=6+6i\sqrt{3}, z_2=1+i(a)Express z_1 z_2 in Euler form(b)Obtain z_1z_2 and \frac{z_1}{z_2}2. Express z = (1 - i)^{10}(\sqrt{3} + i)^5 in Euler form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/205/o3sFpQ3LK_uQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LdBWCR-Xvy0l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/LdBWCR-Xvy0l.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: Rod AB is fixed in space. Spring CD has stiffness 1.5 N/mm and an unstretched length of 400 mm. If there is no friction between the collar and the rod, determine the weight of the collar W that produces the equilibrium configuration shown, and the reaction between the collar and the rod AB. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/LdBWCR-Xvy0l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740069716423.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/wobsPwFPIQOU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/wobsPwFPIQOU.jpg</video:thumbnail_loc>

            <video:title>Pivots and free variables</video:title>

            <video:description><![CDATA[
How to determine what variables to parameterize in reporting infinitely many solutions for linear systems of equations. Solved: Solve the following system3x+2y+7z=0 4x-3y-2z=05x+9y+23z=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/wobsPwFPIQOU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cESRC2HIkhkG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/cESRC2HIkhkG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: Determine the moment associated with the pair of 400-N forces applied to the T-shaped structure. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/cESRC2HIkhkG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738864880706.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/rwJTN7m0baSN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/rwJTN7m0baSN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: Collars A and B are connected by a 525-mm-long wire and can slide freely on frictionless rods. If a force P = (341 N)j is applied to collar A, determine(a) the tension in the wire when y = 155 mm,(b) the magnitude of the force Q required to maintain the equilibrium of the system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/rwJTN7m0baSN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740073725734.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JrvXMLU1DSUF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/JrvXMLU1DSUF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: A team of engineering students is designing a catapult launch a small ball at A so that it lands in the box. If it is known that the initial velocity vector makes a 30^\circ angle with the horizontal, determine the range of launch speeds v_0 for which the ball will land inside the box. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/JrvXMLU1DSUF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746267825723.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/kJQX311UihQH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/kJQX311UihQH.jpg</video:thumbnail_loc>

            <video:title>Simplifying set expressions (1)</video:title>

            <video:description><![CDATA[
Execute the systematic reduction of complex set expressions through the rigorous application of algebraic laws. You will master the mechanical use of distributive, idempotent, and identity laws to simplify nested operations into their most concise logical forms. Solved: 1. Simplify (A \cup B) \cap (A \cup B'). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/kJQX311UihQH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tpGM7JIx89Hi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/tpGM7JIx89Hi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: To test the strength of 625 x 500-mm suitcase, forces are applied as shown. If P = 88 N, (a) determine the resultant of the applied forces,(b) locate the two points where the line of action of the resultant intersects the edge of the suitcase. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/tpGM7JIx89Hi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740077704365.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/s7ycIzg2nA4_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/s7ycIzg2nA4_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating limits of two-variable real-valued functions. Solved: Evaluate \lim_{(x,y)\to(0, 0)} (x^3 + y^3) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/s7ycIzg2nA4_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mAbBNK7uIImL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/mAbBNK7uIImL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: Replace the loading on the frame by a single resultant force. Specify where its line of action intersects member CD, measured from point C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/mAbBNK7uIImL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740077889882.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0xgJjrkM75y5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/0xgJjrkM75y5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: Determine whether the force-and-couple system shown can be reduced to a single equivalent force R. If it can, determine R and the point where the line of action of R intersects the yz plane. If it cannot be reduced, replaced the given system with an equivalent wrench and determine its resultant, its pitch, and the point where its axis intersects the yz plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/0xgJjrkM75y5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740298530114.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Jt_zjFRvRcEu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/206/Jt_zjFRvRcEu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on manipulating Sines and Cosines using complex numbers. Solved: 1.For any real numbers m, p, show that e^{2mi\cot^-1p}(\frac{1+ip}{-1+ip})^m=1 , where i=\sqrt{-1} .2. Show that \sum_{k=1}^{n} \cos (2k-1) \theta = \frac{\sin n\theta \cos n\theta}{\sin \theta} and \sum_{k=1}^{n} \sin (2k-1) \theta = \frac{\sin^2 n\theta}{\sin \theta}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/206/Jt_zjFRvRcEu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Njd67wy1jcGY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/Njd67wy1jcGY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: A flagpole is guyed by three cables. If the tensions in the cables have the same magnitude P, replace the forces exerted on the pole with an equivalent wrench and determine (a) the resultant force R, (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the xz plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/Njd67wy1jcGY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740299547930.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/w6UDLVRojuqj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/w6UDLVRojuqj.jpg</video:thumbnail_loc>

            <video:title>The work-energy theorem (1)</video:title>

            <video:description><![CDATA[
Apply the work-energy theorem to find the stopping distance of a skidding motorcycle. This walkthrough shows how to equate the change in kinetic energy to the work done by friction to calculate the total displacement. Solved: A 180 \, kg motorcycle travelling at 25 \, m/s skids to a halt on a level road. If the coefficient of kinetic friction between the tyres and the road is 0.75, calculate the distance the motorcycle skids before coming to a complete stop. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/w6UDLVRojuqj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pSE_Cdz8di_K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1023/pSE_Cdz8di_K.jpg</video:thumbnail_loc>

            <video:title>Limiting reagents (1)</video:title>

            <video:description><![CDATA[
This walkthrough explains how to identify the limiting reagent when barium hydroxide reacts with chloric acid. You will learn to compare molar ratios to determine which reactant finishes first and use that result to calculate the exact amount of water molecules produced. Solved: Example: For the reaction: \text{Ba(OH)}_2 + 2\text{HClO}_3 \rightarrow \text{Ba(ClO}_3)_2 + 2\text{H}_2\text{O}. Calculate the respective number of moles and molecules of water formed when 0.100 mol \text{Ba(OH)}_2 is treated with 0.250 mol \text{HClO}_3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1023/pSE_Cdz8di_K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HsOuSdHHKppR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/HsOuSdHHKppR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The 450-kg uniform I-beam supports the load shown. Determine the reactions at the supports. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/HsOuSdHHKppR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736623512186.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/hjdtFd8gHcKU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/hjdtFd8gHcKU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Determine the reaction at fixed support A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/hjdtFd8gHcKU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736822987501.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gZ--icrF8Jcl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/337/gZ--icrF8Jcl.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General principles and procedure for analysis of frictional forces on thrust bearings - pivot (end) and collar bearings, disks.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/337/gZ--icrF8Jcl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cOmVBq8067h-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/336/cOmVBq8067h-.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General principles and procedure for analysis of frictional forces on flat belts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/336/cOmVBq8067h-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FBhMbXsOSLGE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/FBhMbXsOSLGE.jpg</video:thumbnail_loc>

            <video:title>Polar reversal</video:title>

            <video:description><![CDATA[
Reversing polarity causes charge cancellation. How do you calculate the final state when positive meets negative? We resolve the net charge and new distribution. Solved: Capacitors C_1 = 15.0 \text{ }\mu\text{F} and C_2 = 5.00 \text{ }\mu\text{F} are connected in parallel and charged by a 100\text{-V} source. The capacitors are then disconnected from the source and from each other. They are subsequently reconnected to each other such that the positive plate of one is joined to the negative plate of the other. Determine the magnitude of the final charge on each capacitor. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/FBhMbXsOSLGE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RhRgT5yo_wag</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/335/RhRgT5yo_wag.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General principles and procedure for analysis of frictional forces on square-threaded screws.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/335/RhRgT5yo_wag.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c7C4vhJ-81w7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/339/c7C4vhJ-81w7.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General principles and procedure for analysis of frictional forces (rolling resistance) on wheels.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/339/c7C4vhJ-81w7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UsFwnHRBx-Dm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/335/UsFwnHRBx-Dm.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of square-threaded screws.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/335/UsFwnHRBx-Dm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KrxLJvT5hckO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/338/KrxLJvT5hckO.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General principles and procedure for analysis of frictional forces on journal bearings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/338/KrxLJvT5hckO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ntyjxMOCfk23</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/ntyjxMOCfk23.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Determine the reactions at the supports. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/ntyjxMOCfk23.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736823034619.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/SJWTYGbn7bjb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/526/SJWTYGbn7bjb.jpg</video:thumbnail_loc>

            <video:title>Special matrices</video:title>

            <video:description><![CDATA[
Review of symmetric, orthogonal and orthonormal matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/526/SJWTYGbn7bjb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EqdK9AIZFSQ8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1188/EqdK9AIZFSQ8.jpg</video:thumbnail_loc>

            <video:title>Minimum value</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to find the minimum point of a quadratic function by completing the square. You will learn to identify the exact x-coordinate of the vertex and calculate the corresponding minimum value of the expression. Solved: Find the minimum value of the quadratic function 8x^2 + 32x + 35 and state the value of x at which this minimum occurs. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1188/EqdK9AIZFSQ8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/q0pAy8tyOAqY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/q0pAy8tyOAqY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Calculate the tension in the cable at B required to support the load of 200 kg. The cable passes over a frictionless pulley located at C. Neglect the size of this pulley and weight of the boom. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/q0pAy8tyOAqY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736824008016.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ST_MeDGI8iir</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/ST_MeDGI8iir.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems of the third kind. Solved: A spring AB is attached to a support at A and to a collar. The unstretched length of the spring is l . Knowing that the collar is released from rest at x=x_0 and has an acceleration defined by the relation a=-100(x-lx/\sqrt{l^2+x^2)} , determine the velocity of the collar as it passes through point C 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/ST_MeDGI8iir.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xQgSJhHeI7VQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/318/xQgSJhHeI7VQ.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/318/xQgSJhHeI7VQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9CJtjIbgFRB1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/9CJtjIbgFRB1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The 20-kg uniform rectangular plate is supported by an ideal pivot at O and a spring which must be compressed prior to being slipped into place at point A. If the modulus of the spring is k=2kN/m, what must be its undeformed length L? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/9CJtjIbgFRB1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736826554894.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/qOr0jaJ3XpIM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/qOr0jaJ3XpIM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The smooth pipe rests against the wall at the points of contact A, B, and C. Determine the reactions at these points needed to support the vertical force of 45lb . Neglect the pipe's thickness in the calculation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/qOr0jaJ3XpIM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736859225786.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sciiptSYz_56</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/sciiptSYz_56.jpg</video:thumbnail_loc>

            <video:title>Similar matrices</video:title>

            <video:description><![CDATA[
Characteristic polynomial and eigenvalues of similar matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/sciiptSYz_56.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_mIAg7bgI_oz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/_mIAg7bgI_oz.jpg</video:thumbnail_loc>

            <video:title>Powers of diagonal matrices</video:title>

            <video:description><![CDATA[
Evaluating powers of diagonal matrices and matrices similar to them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/_mIAg7bgI_oz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i-RN1PiIdJHW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/i-RN1PiIdJHW.jpg</video:thumbnail_loc>

            <video:title>Simple non-linear equations (2)</video:title>

            <video:description><![CDATA[
Solution of Riccati's ordinary differential equation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/i-RN1PiIdJHW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q0--zxjiqiYr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/Q0--zxjiqiYr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Determine the magnitude and direction \theta of the minimum force P needed to pull the 50-kg roller over the smooth step. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/Q0--zxjiqiYr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736863180597.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/usdNwaYWoP5b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/usdNwaYWoP5b.jpg</video:thumbnail_loc>

            <video:title>Inequality of means (2)</video:title>

            <video:description><![CDATA[
Follow a second walkthrough on the inequality of means to master more complex proofs and optimisations. You will learn to manipulate multi-variable expressions to establish bounds and verify equality conditions. This reinforces the practical application of arithmetic and geometric relationships. Solved: 14. If a and b are positive real numbers, prove that (a+b)\left(\frac{1}{a} + \frac{1}{b}\right) \ge 4. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/usdNwaYWoP5b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HgOiiogMl9VK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/526/HgOiiogMl9VK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on diagonalization of symmetric matrices involving the use of Gram-Schmidt procedure. Solved: Obtain an orthogonal diagonalizing matrix P and the corresponding diagonal matrix D forA=\left[ \begin{array}{ccc} 0 & 1 & 1\\ 1 & 0 & 1\\ 1 &1 & 0 \end{array} \right] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/526/HgOiiogMl9VK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vBnIVppAogct</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/vBnIVppAogct.jpg</video:thumbnail_loc>

            <video:title>Worked examples (17)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The spanner shown is used to rotate a shaft. A pin fits in a hole at A, while a flat, frictionless surface rest against the shaft at B. If a 300-N force P is exerted on the spanner at D, find (a) the reaction at B, (b) the component of the reaction at A in a direction perpendicular to AC. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/vBnIVppAogct.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736866914958.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/wwPzl8CBctUS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/141/wwPzl8CBctUS.jpg</video:thumbnail_loc>

            <video:title>MS-Excel (Google Sheets)</video:title>

            <video:description><![CDATA[
Manipulating matrices with MS-Excel (Google Sheets) - algebra, transposes, determinants and inverse of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/141/wwPzl8CBctUS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wS5qZDNJS9VG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/526/wS5qZDNJS9VG.jpg</video:thumbnail_loc>

            <video:title>Gram-Schmidt procedure</video:title>

            <video:description><![CDATA[
Gram-Schmidt procedure for obtaining an orthonormal set of vectors from a linearly-independent set of vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/526/wS5qZDNJS9VG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J1aiha28Ce2g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/539/J1aiha28Ce2g.jpg</video:thumbnail_loc>

            <video:title>Image</video:title>

            <video:description><![CDATA[
Meaning of the image of an element or subset of the domain for a map, and how it differs from the range of the map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/539/J1aiha28Ce2g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VZaVsQoNRvak</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/528/VZaVsQoNRvak.jpg</video:thumbnail_loc>

            <video:title>Fields</video:title>

            <video:description><![CDATA[
Meaning and examples of fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/528/VZaVsQoNRvak.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/40ihVXJYAef_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/528/40ihVXJYAef_.jpg</video:thumbnail_loc>

            <video:title>Vector spaces</video:title>

            <video:description><![CDATA[
Definition of [linear] vector spaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/528/40ihVXJYAef_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a0AQ_vC12JbL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/539/a0AQ_vC12JbL.jpg</video:thumbnail_loc>

            <video:title>Examples of maps (1)</video:title>

            <video:description><![CDATA[
Some examples of maps and their notations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/539/a0AQ_vC12JbL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QbBOHRO_8qRZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/539/QbBOHRO_8qRZ.jpg</video:thumbnail_loc>

            <video:title>Examples of maps (2)</video:title>

            <video:description><![CDATA[
More examples of maps and their notations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/539/QbBOHRO_8qRZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D9aSrAcBHHNo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/539/D9aSrAcBHHNo.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of map or mapping between two sets, domain and co-domain of a map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/539/D9aSrAcBHHNo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tui2tPygLPEu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/539/tui2tPygLPEu.jpg</video:thumbnail_loc>

            <video:title>Range</video:title>

            <video:description><![CDATA[
Meaning of the range of a map and how it differs from its co-domain.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/539/tui2tPygLPEu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JzsqeXpAEhdO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/566/JzsqeXpAEhdO.jpg</video:thumbnail_loc>

            <video:title>Quotient set</video:title>

            <video:description><![CDATA[
Meaning of the quotient set of a given set with respect to an equivalence relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/566/JzsqeXpAEhdO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wi6Eck_1rhzf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/wi6Eck_1rhzf.jpg</video:thumbnail_loc>

            <video:title>Equation from roots</video:title>

            <video:description><![CDATA[
This lesson explains how to build a quadratic equation when the roots are known. You will learn to use the sum and product of the roots to correctly place coefficients in the general equation form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/wi6Eck_1rhzf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eLaImZ2CpRj7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/eLaImZ2CpRj7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: The spring of constant k = 200 N/m is attached to both the support and the 2-kg cylinder, which slides freely on the horizontal guide. If a constant 10 N force is applied to the cylinder at time t = 0 when the spring is undeformed and the system is at rest, determine the velocity of the cylinder when x = 40 mm. Also determine the maximum displacement of the cylinder. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/eLaImZ2CpRj7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742299008786.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/EFyEGMiVVSPD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/EFyEGMiVVSPD.jpg</video:thumbnail_loc>

            <video:title>Conditions for common roots</video:title>

            <video:description><![CDATA[
This lesson explains the algebraic conditions required for two quadratic equations to share one or both roots. You will learn to use cross-multiplication or coefficient ratios to identify these relationships without solving the individual equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/EFyEGMiVVSPD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bOSciuXcSfhr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/527/bOSciuXcSfhr.jpg</video:thumbnail_loc>

            <video:title>Matrices</video:title>

            <video:description><![CDATA[
Review of some matrix concepts required for the course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/527/bOSciuXcSfhr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W0F7pRqlWMNr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/W0F7pRqlWMNr.jpg</video:thumbnail_loc>

            <video:title>Non-uniform charge density</video:title>

            <video:description><![CDATA[
Calculate the field of a rod with non-uniform charge density. How do you substitute the variable lambda into the integral? Watch the worked solution. Solved: A thin rod of length L = 20.0\text{ cm} lies along the x-axis from x = 0 to x = L. The rod has a non-uniform linear charge density given by \lambda = \alpha x, where \alpha = 5.00\text{ }\mu\text{C/m}^2. Calculate the magnitude of the electric field at a point P on the x-axis at x = -10.0\text{ cm}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/W0F7pRqlWMNr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mhemeWbEpveH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/mhemeWbEpveH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (22)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The rig shown consists of a 1200-lb horizontal member ABC and a vertical member DBE welded together at B. The rig is being used to raise a 3600-lb crate at a distance x=12ft from the vertical member DBE. If the tension in the cable is 4 kips, determine the reaction at E, assuming that the cable is (a) anchored as F as shown in the figure, (b) attached to the vertical member at a point located 1ft above E. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/mhemeWbEpveH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736939454827.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WPIIYvJo39ep</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/95/WPIIYvJo39ep.jpg</video:thumbnail_loc>

            <video:title>Worked examples II</video:title>

            <video:description><![CDATA[
More worked examples graphing in 3 dimensions. Solved: Graph y=2x+3 in R2 and R3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/95/WPIIYvJo39ep.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t_mvFo5L_wow</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/t_mvFo5L_wow.jpg</video:thumbnail_loc>

            <video:title>Worked examples (21)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The semicircular rod ABCD is maintained in equilibrium by the small wheel at D and the rollers at B and C. Knowing that \alpha=45^{\circ}, determine the reactions at B, C, and D. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/t_mvFo5L_wow.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736938863809.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/kjJ32Djcf9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/kjJ32Djcf9.jpg</video:thumbnail_loc>

            <video:title>Finding continuity constants</video:title>

            <video:description><![CDATA[
Find the value of an unknown constant that forces two parts of a piecewise function to meet. This walkthrough ensures the left and right limits equal the central value. Solved: Find the value of the constant k for which the following function is continuous at x = 2: f(x) = \begin{cases} kx + 1 & \text{if } x \le 2 \\ x^2 - 1 & \text{if } x > 2 \end{cases}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/kjJ32Djcf9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_wTT6Vjr5L8b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/399/_wTT6Vjr5L8b.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on sample examination problems on limits of functions. Solved: 1.Evaluate \lim_{x\to 0} (\sqrt\frac{1-x^3}{1+x^2} -\sqrt\frac{1-x}{1+x} )2.Evaluate \lim_{x\to 1}(\frac{1-x^2}{|x-1|})3.Evaluate \lim_{h\to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}4.Evaluate \lim_{x\to 0}\frac{\arcsin2x}{\arcsin3x}5.Evaluate \lim_{x\to a} \frac{x^n-a^n}{x-a},a>0, n is a rational number.6.Evaluate \lim_{x\to\frac{x}{2} }\sec\theta(\cos\theta-\sin2\theta)7.Evaluate \lim_{x\to 0}\frac{2^x-1}{(1+x)^\frac{1}{2}-1} 8.Evaluate \lim_{\alpha\to \beta}\frac{\sin\alpha-\sin\beta}{\alpha-\beta}9.Evaluate \lim_{x\to 3^-}\frac{|4x-12|}{x-3}10.Which of the following statements is true concerning K: \lim_{x\to 0}(x+\frac{x}{|x|}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/399/_wTT6Vjr5L8b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zeNqOAyQmhFw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/zeNqOAyQmhFw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (19)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The exercise machine consists of a rigid bar, pin connected to the frame at A. As the man pushes up on the bar it stretches the rubber band BC. If the stiffness of the rubber band is K=500lb/ft, determine the applied vertical force F needed to hold the bar in position \theta=30^{\circ}. The rubber band is unstretched when \theta=0^{\circ}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/zeNqOAyQmhFw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736935314730.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/37kWd2QfIjEq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/90/37kWd2QfIjEq.jpg</video:thumbnail_loc>

            <video:title>Exponential growth and decay</video:title>

            <video:description><![CDATA[
Modelling exponential growth and decay with first-order ordinary differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/90/37kWd2QfIjEq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KfdUa_FAv7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/KfdUa_FAv7.jpg</video:thumbnail_loc>

            <video:title>Identifying discontinuity points</video:title>

            <video:description><![CDATA[
Locate the exact points where a function breaks by finding values that make the expression undefined. This walkthrough focuses on points where the denominator becomes zero. Solved: Locate the points of discontinuity for f(x) = \frac{x - 3}{x^2 - 9} and classify them as removable or essential (non-removable). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/KfdUa_FAv7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pA1rOFm2bmip</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/pA1rOFm2bmip.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: If F = 80 N, determine the magnitude and coordinate direction angles of the couple moment. The pipe assembly lies in the x-y plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/pA1rOFm2bmip.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738866160179.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/l8YVVS5_fUAu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/l8YVVS5_fUAu.jpg</video:thumbnail_loc>

            <video:title>Evaluation (2)</video:title>

            <video:description><![CDATA[
Execute the systematic evaluation of cubic and higher-order polynomials through advanced numerical substitution. You will master the mechanical processing of exponents and signs to determine precise functional values for complex algebraic expressions. Solved: 2. Determine if x = \frac{1}{2} is a root of the polynomial f(x) = 4x^3 - 4x^2 + x + 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/l8YVVS5_fUAu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vuNHQJjKAGx1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/vuNHQJjKAGx1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: (a) If the coefficient of kinetic friction between the 50-kg crate and the ground is \mu_k = 0.3, determine the distance the crate travels and its velocity when t = 3 s. The crate starts from rest and P = 200 N.(b) If the 50-kg crate starts from rest and achieves a velocity of v = 4 m/s when it travels a distance of 5 m to the right, determine the magnitude of force P acting on the crate. The coefficient of kinetic friction between the crate and the ground is \mu_k = 0.3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/vuNHQJjKAGx1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742297228580.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/EiBZmPq9nCz3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/EiBZmPq9nCz3.jpg</video:thumbnail_loc>

            <video:title>Precedence and dominance</video:title>

            <video:description><![CDATA[
Meaning of precedence and dominance in a partially-ordered set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/EiBZmPq9nCz3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xkj9RD9i6VC7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/xkj9RD9i6VC7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (17)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Determine the magnitude of the projection of the force F_1 along cable AC. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/xkj9RD9i6VC7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739871800589.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/cH1pL90Cn_Kn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/cH1pL90Cn_Kn.jpg</video:thumbnail_loc>

            <video:title>Equations from roots (2)</video:title>

            <video:description><![CDATA[
This lesson shows how to build a quadratic equation using the reciprocals of existing roots. You will learn to find the new sum and product of roots to determine the final equation coefficients. Solved: If \alpha and \beta are roots of 3x^2 - 8x + 2 = 0, find the quadratic equation whose roots are \frac{1}{\alpha} and \frac{1}{\beta}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/cH1pL90Cn_Kn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/28ris_GzyIv6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/28ris_GzyIv6.jpg</video:thumbnail_loc>

            <video:title>Power and efficiency</video:title>

            <video:description><![CDATA[
Power is the rate of doing work, and efficiency is the ratio of useful output to total input. Calculate these values using watts and percentages to measure mechanical performance and system losses. This lesson provides the core formulas required for machine analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/28ris_GzyIv6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_XE_dbSNw9w9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/_XE_dbSNw9w9.jpg</video:thumbnail_loc>

            <video:title>Axial field of a disk (1)</video:title>

            <video:description><![CDATA[
Derive the field of a charged disk on its axis. How do you sum concentric rings to get the total field? Watch the integration steps. Solved: Consider a flat circular disk of radius R with a uniform surface charge density \sigma. By treating the disk as a set of concentric rings, derive the formula for the electric field at a point P on the central axis at distance z. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/_XE_dbSNw9w9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m49tS8Rs_qN6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UR7vNInezV/Thumbnails/681/m49tS8Rs_qN6.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the [Beginner] Modern Web Development Foundations learning track.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UR7vNInezV/Previews/681/m49tS8Rs_qN6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M_JD4Oo7wXnC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/961/M_JD4Oo7wXnC.jpg</video:thumbnail_loc>

            <video:title>Preparing for CSS</video:title>

            <video:description><![CDATA[
This is a practical lesson on setting up your styling environment. We will create a style.css file and use the <link> tag to connect it to our index.html document.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/961/M_JD4Oo7wXnC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XObnKN07ZN1D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/XObnKN07ZN1D.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: The two couples shown are to be replaced with an equivalent couple. Determine:(a) the couple vector representing the equivalent couple.(b) the two forces acting at B and C that can be used to form that couple. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/XObnKN07ZN1D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738867201653.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/aoeTjE7Okujf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/aoeTjE7Okujf.jpg</video:thumbnail_loc>

            <video:title>Introduction to GitHub</video:title>

            <video:description><![CDATA[
Git is the tool that tracks your code; GitHub is the online service that hosts your code. This lesson defines GitHub's role as the industry-standard platform for storing your repositories, enabling remote backup, and facilitating team collaboration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/aoeTjE7Okujf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rTWaJg3uFeqv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/rTWaJg3uFeqv.jpg</video:thumbnail_loc>

            <video:title>Work of a constant force</video:title>

            <video:description><![CDATA[
Calculate mechanical work when a constant force acts at an angle to the direction of motion. This example shows how to find the useful part of the force and determine the total energy transferred over a distance. Solved: A student pulls a heavy travel bag across a terminal floor with a force of 85 \, N using a strap held at an angle of 35^\circ to the horizontal. If the bag is moved a distance of 15 \, m, calculate the work done by the student on the bag. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/rTWaJg3uFeqv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4G9LEL0i-q9S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/4G9LEL0i-q9S.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: A movable bin and its contents have a combined weight of 2.8 kN. Determine the shortest chain sling ACB that can be used to lift the loaded bin if the tension in the chain is not to exceed 5 kN. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/4G9LEL0i-q9S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739472185263.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/1QZaVq5GoxQ_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/961/1QZaVq5GoxQ_.jpg</video:thumbnail_loc>

            <video:title>CSS language basics</video:title>

            <video:description><![CDATA[
This lesson covers the fundamental syntax of CSS. We will explain the core concepts of selectors, properties, and values, which are the building blocks of all styling.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/961/1QZaVq5GoxQ_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OnwTZp4kdgt8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/OnwTZp4kdgt8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the equilibrium of a particle in two dimensions. Solved: Knowing that \alpha = 20^\circ, determine the tension in (a) cable AC, (b) rope BC. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/OnwTZp4kdgt8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739470790797.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Ki75-3uWlTk0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/Ki75-3uWlTk0.jpg</video:thumbnail_loc>

            <video:title>Principal minors</video:title>

            <video:description><![CDATA[
Meaning of principal minors in general, and principal minors of a given order.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/Ki75-3uWlTk0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ICVrQ7H54h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/ICVrQ7H54h.jpg</video:thumbnail_loc>

            <video:title>Double constant continuity</video:title>

            <video:description><![CDATA[
Solve a system of equations to find two different constants that make a three-part piecewise function continuous. This walkthrough ensures a smooth connection at both boundary points. Solved: Determine the constants a and b that make the function f(x) = \begin{cases} x^2, & x < 2 \\ ax+b, & 2 \le x < 4 \\ 9, & x \ge 4 \end{cases} continuous everywhere. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/ICVrQ7H54h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VBFREqwOxgDX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/VBFREqwOxgDX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: Determine the maximum weight that can be supported in the position shown if each chain AC and AB can support a maximum tension of 600 lb before it fails. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/VBFREqwOxgDX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739471908153.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/07bSkEDplGpu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/07bSkEDplGpu.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/07bSkEDplGpu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WjXoR4Hze99k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/921/WjXoR4Hze99k.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson explains why energy and momentum methods are faster than Newton's laws for solving motion problems. You will understand the course structure and how to use scalar and vector methods in mechanics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/921/WjXoR4Hze99k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Tr8API2_J6Im</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/Tr8API2_J6Im.jpg</video:thumbnail_loc>

            <video:title>Common roots (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to determine constants when two quadratic equations share both roots. You will learn to use coefficient ratios to establish equality and solve for missing parameters efficiently. Solved: The equations x^2 + px + q = 0 and 3x^2 + 12x + 15 = 0 have both roots in common. Calculate p and q. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/Tr8API2_J6Im.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2PdP5eFbcJc2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/2PdP5eFbcJc2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: The 30-kg block is supported by two springs having the stiffness shown. Determine the unstretched length of each string after the block is removed. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/2PdP5eFbcJc2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739472518181.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/pAfj_RT0gtxd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/pAfj_RT0gtxd.jpg</video:thumbnail_loc>

            <video:title>Addition</video:title>

            <video:description><![CDATA[
Addition of linear maps and its linearity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/pAfj_RT0gtxd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KO1GXFcBglb7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/KO1GXFcBglb7.jpg</video:thumbnail_loc>

            <video:title>Composition</video:title>

            <video:description><![CDATA[
Composition of linear maps - definition and proof of its linearity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/KO1GXFcBglb7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RGS2Kxo4e94y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/RGS2Kxo4e94y.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: Collar A is connected as shown to a 50-lb load and can slide on a frictionless horizontal rod. Determine the magnitude of the force P required to maintain the equilibrium of the collar when (a) x=4.5 in., (b) x=15 in. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/RGS2Kxo4e94y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739784902976.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/W3TVV6apZ7lA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/W3TVV6apZ7lA.jpg</video:thumbnail_loc>

            <video:title>Vector space of linear maps</video:title>

            <video:description><![CDATA[
Vector space of all linear maps between two vector spaces over the same field of scalars.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/W3TVV6apZ7lA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5_0K6mbuYkTK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/5_0K6mbuYkTK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: The winch takes in cable at the constant rate of 200 mm/s. If the cylinder mass is 100 kg, determine the tension in cable 1. Neglect all friction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/5_0K6mbuYkTK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739783183709.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/W3aSNJKt3oNw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/202/W3aSNJKt3oNw.jpg</video:thumbnail_loc>

            <video:title>Modulus and argument</video:title>

            <video:description><![CDATA[
Modulus (magnitude) and general argument of a complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/202/W3aSNJKt3oNw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V4UynSYx4Bzb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/V4UynSYx4Bzb.jpg</video:thumbnail_loc>

            <video:title>Work in vector form</video:title>

            <video:description><![CDATA[
Calculate the work done by a force expressed in unit vector notation moving an object between two points. This walkthrough applies the dot product between the force vector and the displacement vector to determine the total energy transfer in a 2D coordinate system. Solved: A heavy box is pushed across a workshop floor from the origin (0,0) to a final position at coordinates (10.0, 5.0) m. The constant force applied is \vec{F} = (12\hat{i} + 6\hat{j}) \, N. Calculate the work done by this force. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/V4UynSYx4Bzb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/upIFLEl5MA0I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/upIFLEl5MA0I.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: What weight W_B will cause the system to be in equilibrium? Neglect all friction, and state any other assumptions. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/upIFLEl5MA0I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739782939643.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/II62hAAK2W0i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/II62hAAK2W0i.jpg</video:thumbnail_loc>

            <video:title>Newton's third law</video:title>

            <video:description><![CDATA[
Every stationary charge exerts an equal opposite force on its partner. How do we replace whole charged spheres with single points without breaking this force balance? Watch the video to see the proof.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/II62hAAK2W0i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N_fKe6KxE6tF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/528/N_fKe6KxE6tF.jpg</video:thumbnail_loc>

            <video:title>Vector subspaces</video:title>

            <video:description><![CDATA[
Review of the definition of linear vector subspaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/528/N_fKe6KxE6tF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Cw2mPU2dVVKz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/Cw2mPU2dVVKz.jpg</video:thumbnail_loc>

            <video:title>Equations of motion</video:title>

            <video:description><![CDATA[
Equations of motion and procedure for force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/Cw2mPU2dVVKz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mm-g4UyLEynB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/517/mm-g4UyLEynB.jpg</video:thumbnail_loc>

            <video:title>Studying MTH202</video:title>

            <video:description><![CDATA[
General guide on how to take this class, and combine with your school tutorials and lectures.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/517/mm-g4UyLEynB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xFptu0crv_hI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Thumbnails/302/xFptu0crv_hI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on forces in three dimensions - solutions to some exercises on three-dimensional coordinates. Solved: Write out the coordinates of all the lettered points on the figures. (a) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Previews/302/xFptu0crv_hI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740296402665.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/51IizzdA6SfL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/541/51IizzdA6SfL.jpg</video:thumbnail_loc>

            <video:title>Illustration</video:title>

            <video:description><![CDATA[
Solving problems involving derivation of the definition of a linear map from some known images.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/541/51IizzdA6SfL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fkZXorySo7rV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/862/fkZXorySo7rV.jpg</video:thumbnail_loc>

            <video:title>Calculating reaction rates</video:title>

            <video:description><![CDATA[
Use experimental data to calculate reaction rates by tracking concentration changes over time. This lesson explains how to find average and instantaneous rates using graph slopes and stoichiometric ratios.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/862/fkZXorySo7rV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w83RHa_oFWlp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/221/w83RHa_oFWlp.jpg</video:thumbnail_loc>

            <video:title>Change of bases (3)</video:title>

            <video:description><![CDATA[
How a change of bases of both the domain and co-domain affects the matrix representation of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/221/w83RHa_oFWlp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aPdfthQmFFJK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/aPdfthQmFFJK.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the composition or product of linear maps - associativity, identity and distributivity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/aPdfthQmFFJK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Nwt5jzJOf6SM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/Nwt5jzJOf6SM.jpg</video:thumbnail_loc>

            <video:title>Calculating the sum of a series</video:title>

            <video:description><![CDATA[
A step-by-step walkthrough of calculating the sum of a finite arithmetic series. The problem requires correct identification of variables and application of the sum formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/Nwt5jzJOf6SM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wENd6EBIOxON</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/518/wENd6EBIOxON.jpg</video:thumbnail_loc>

            <video:title>Crash course</video:title>

            <video:description><![CDATA[
Summary of key concepts on calculus of scalar and vector fields using the Cartesian coordinate system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/518/wENd6EBIOxON.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t9oNoC5J0Ynj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/982/t9oNoC5J0Ynj.jpg</video:thumbnail_loc>

            <video:title>Alkaline medium (1)</video:title>

            <video:description><![CDATA[
This lesson introduces the specific protocol for balancing redox reactions occurring in alkaline (basic) medium using the half-reaction method. You will learn the final step of adding OH- ions to neutralise the H+ ions used in the acidic balancing process. Mastering this technique is necessary for accurately quantifying reactions in non-acidic aqueous environments. Solved: For example: Balance the redox reactions below in basic mediumNO_{2(aq)}^{-} + Al_{(s)} \rightarrow NH_{3(g)} + AlO_{2(aq)}^{-} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/982/t9oNoC5J0Ynj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dSZ15NqKjVvO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/dSZ15NqKjVvO.jpg</video:thumbnail_loc>

            <video:title>Isolated modification</video:title>

            <video:description><![CDATA[
Isolated series capacitors trap charge on inner plates. How does changing one gap affect the total voltage? We calculate the new potential difference using constant charge. Solved: Two identical parallel-plate capacitors, each with a capacitance of 8.00 \text{ }\mu\text{F}, are connected in series across a 40.0\text{-V} battery. The battery is then disconnected, leaving the capacitors charged and isolated as a series string. If the plate separation of one of the capacitors is subsequently doubled, determine (a) the magnitude of the charge on each capacitor and (b) the new potential difference across the entire series string. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/dSZ15NqKjVvO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CCu_FMyPCXwS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/CCu_FMyPCXwS.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General procedure for analysis of motion of a particle by relating their kinetic energy with the work done by the external forces acting on it.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/CCu_FMyPCXwS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KLjbnYErB8DQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/863/KLjbnYErB8DQ.jpg</video:thumbnail_loc>

            <video:title>Concentration and rate law</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step calculation of a rate law using experimental concentration and rate data. You will master the algebraic process of comparing trials to isolate reaction orders and solving for the specific rate constant. Solved: 1. Consider the reaction:2\text{NO }(g) + \text{O}_2(g) \rightarrow 2\text{NO}_2(g)Experiments show that doubling the concentration of NO quadruples the rate. Doubling the concentration of \text{O}_2 doubles the rate. What is the rate law?2. Consider the reaction:\text{CH}_3\text{Br }(aq) + \text{OH}^-(aq) \rightarrow \text{CH}_3\text{OH }(aq) + \text{Br}^-(aq)It is observed that when the concentration of \text{CH}_3\text{Br} is tripled, the rate triples. When the concentration of \text{OH}^- is doubled, the rate doubles. What is the rate law? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/863/KLjbnYErB8DQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PCWMBBHsGlwD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/221/PCWMBBHsGlwD.jpg</video:thumbnail_loc>

            <video:title>Change of bases (2)</video:title>

            <video:description><![CDATA[
How a change of the co-domain basis affects the matrix representation of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/221/PCWMBBHsGlwD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kq7cYnhWJPeN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/220/Kq7cYnhWJPeN.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
How to find the matrix representation of a linear map with respect to given bases of the domain and co-domain.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/220/Kq7cYnhWJPeN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rH1vcPQBcpXF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/220/rH1vcPQBcpXF.jpg</video:thumbnail_loc>

            <video:title>Theorem</video:title>

            <video:description><![CDATA[
Existence of matrix representation of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/220/rH1vcPQBcpXF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mfy1r8Yu7N5c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/221/mfy1r8Yu7N5c.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of the transition matrix between two bases of a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/221/mfy1r8Yu7N5c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d6jIzBZMf0qs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/218/d6jIzBZMf0qs.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on kernels of linear maps. Solved: For T: M_{22} \to M_{22} defined by T(A) = A^T, determine ker(T) and a basis for it. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/218/d6jIzBZMf0qs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nlY2sPqprGKa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/nlY2sPqprGKa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using parameters measured relative to a reference frame in rotation. Solved: The wheel is rotating with the angular velocity and angular acceleration at the instant shown. Determine the angular velocity and angular acceleration of the rod at this instant. The rod slides freely through the smooth collar. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/nlY2sPqprGKa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745662105456.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/6aY7NoNr6fir</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/220/6aY7NoNr6fir.jpg</video:thumbnail_loc>

            <video:title>Proof</video:title>

            <video:description><![CDATA[
Proof of the existence of matrix representation of a linear map.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/220/6aY7NoNr6fir.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vo_1TH3i3NGg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/vo_1TH3i3NGg.jpg</video:thumbnail_loc>

            <video:title>Symmetric identities</video:title>

            <video:description><![CDATA[
This lesson explains how to express symmetric functions of roots using only their sum and product. You will learn to manipulate expressions like the sum of squares or cubes into forms that can be calculated directly from the equation coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/vo_1TH3i3NGg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zqFKoxPFGyBG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/211/zqFKoxPFGyBG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on linear combinations of vectors in a vector space. Solved: Write u=3t^2+8t-5 as a linear combination of v=2t^2+3t-4 and w=t^2-2t-3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/211/zqFKoxPFGyBG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6cuaF3vP8QY7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/686/6cuaF3vP8QY7.jpg</video:thumbnail_loc>

            <video:title>Your next step</video:title>

            <video:description><![CDATA[
This final lesson concludes the course. It directs you to the immediate next step in your learning path: the HTML5 Foundations course, where you will use your new toolkit to build your first webpage.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/686/6cuaF3vP8QY7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8HEEaSSE3iVY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/8HEEaSSE3iVY.jpg</video:thumbnail_loc>

            <video:title>Natural numbers and integers</video:title>

            <video:description><![CDATA[
Meaning of and differences between natural numbers and integers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/8HEEaSSE3iVY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QVbkdt7ug9-_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/299/QVbkdt7ug9-_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on addition of vectors in three dimensions. Solved: Four forces applied to an object are concurrent at O as shown. Determine the magnitude of the resultant F_R of the four forces. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/299/QVbkdt7ug9-_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739872693712.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5hiTuXpj18uT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/5hiTuXpj18uT.jpg</video:thumbnail_loc>

            <video:title>Evaluation</video:title>

            <video:description><![CDATA[
Master the systematic substitution of numerical values into polynomial variables to determine specific outputs. You will execute precise calculations using functional notation, establishing the mechanical accuracy required for testing roots and applying the Remainder Theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/5hiTuXpj18uT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9Clgdny1mbCh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/9Clgdny1mbCh.jpg</video:thumbnail_loc>

            <video:title>Properties (1)</video:title>

            <video:description><![CDATA[
Properties of partially-ordered sets - first or least element, last or greatest element, minimal and maximal elements.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/9Clgdny1mbCh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b5JNiGZ-_Nap</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/b5JNiGZ-_Nap.jpg</video:thumbnail_loc>

            <video:title>Comparability</video:title>

            <video:description><![CDATA[
When are two elements of a poset said to be comparable?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/b5JNiGZ-_Nap.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wnR-Ncjp9sDX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/517/wnR-Ncjp9sDX.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/517/wnR-Ncjp9sDX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gt5LyzZ00j1o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/Gt5LyzZ00j1o.jpg</video:thumbnail_loc>

            <video:title>Solving equations with unknown index (2)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving equations with variables in the exponent by taking the logarithm of both sides. You will learn to isolate the unknown index when bases cannot be equated directly and apply substitution to resolve equations that reduce to a quadratic form. Solved: 2. Solve the equation 5^{2x} - 5^{1+x} + 6 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/Gt5LyzZ00j1o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9VTCDTol9Hy1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/9VTCDTol9Hy1.jpg</video:thumbnail_loc>

            <video:title>Superposition of distributed sources</video:title>

            <video:description><![CDATA[
Find the charge for zero net field from two rings. How do you balance opposing axial fields using superposition? Watch the calculation steps. Solved: Two concentric thin rings are placed in the yz-plane. The inner ring has radius R_1 = 3.00\text{ cm} and charge Q_1 = +8.00\text{ nC}. The outer ring has radius R_2 = 6.00\text{ cm}. Determine the charge Q_2 required on the outer ring such that the net electric field is zero at a point P located 4.00\text{ cm} from the centre along the central axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/9VTCDTol9Hy1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wmUbeNMulHWI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/wmUbeNMulHWI.jpg</video:thumbnail_loc>

            <video:title>Speed of a pendulum</video:title>

            <video:description><![CDATA[
Apply the principle of conservation of mechanical energy to determine the speed of a pendulum Bob at its lowest point. This walkthrough shows how to calculate the vertical height change from the cable length and angle to equate potential energy loss to kinetic energy gain. Solved: A metal wrecking ball of mass 80 \, kg is pulled back until its 5 \, m cable makes an angle of 45^\circ with the vertical. If the ball is released from rest, calculate its speed at the lowest point of the swing. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/wmUbeNMulHWI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RaYh0r6Xpf6O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/686/RaYh0r6Xpf6O.jpg</video:thumbnail_loc>

            <video:title>What you have learnt</video:title>

            <video:description><![CDATA[
We will now consolidate your achievements from this course. This lesson provides a final review of the core web concepts and the professional toolkit - the command line, VS Code, and Git - that you now have at your command.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/686/RaYh0r6Xpf6O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m0dS2Q2ozwC_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1189/m0dS2Q2ozwC_.jpg</video:thumbnail_loc>

            <video:title>Range of rational expressions (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to find the impossible values for a rational expression. You will learn to rearrange the expression into a quadratic equation in x and apply the discriminant condition for real roots to identify the excluded range of y. Solved: If x is a real number, determine the range of values that the expression y = \frac{x^2 - 15}{2x - 8} cannot take. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1189/m0dS2Q2ozwC_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hZqU2jnz0_Sg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/hZqU2jnz0_Sg.jpg</video:thumbnail_loc>

            <video:title>Solving equations with unknown index (4)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving exponential equations with mixed bases. You will learn to use the change of base formula and logarithms to isolate the unknown index for a precise solution. Solved: 4. Solve for x if\log_5 x + \log_3 x = 1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/hZqU2jnz0_Sg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rT64GYnr_e5a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/968/rT64GYnr_e5a.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
This lesson provides a final, consolidated overview of the entire course. It serves as the definitive course recap before outlining your next steps.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/968/rT64GYnr_e5a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ma_Rj6FUgLLy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/569/ma_Rj6FUgLLy.jpg</video:thumbnail_loc>

            <video:title>Sub-lattice</video:title>

            <video:description><![CDATA[
Meaning and examples of a sub-lattice.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/569/ma_Rj6FUgLLy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/poqv6QR0Y775</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/569/poqv6QR0Y775.jpg</video:thumbnail_loc>

            <video:title>Distributivity</video:title>

            <video:description><![CDATA[
When is a lattice said to be distributive?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/569/poqv6QR0Y775.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KShHJJ8t9SUQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/KShHJJ8t9SUQ.jpg</video:thumbnail_loc>

            <video:title>Force and torque</video:title>

            <video:description><![CDATA[
A uniform field exerts zero net force on a dipole. Why does it still spin? Watch to see how torque aligns the dipole moment with the field lines.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/KShHJJ8t9SUQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZbvSVJhpQ_hH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/ZbvSVJhpQ_hH.jpg</video:thumbnail_loc>

            <video:title>Equations of motion</video:title>

            <video:description><![CDATA[
Equations of motion for force-acceleration analysis of curvilinear motion of particles in rectangular coordinates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/ZbvSVJhpQ_hH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WlzFYGWTKiSX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/WlzFYGWTKiSX.jpg</video:thumbnail_loc>

            <video:title>Work of a weight</video:title>

            <video:description><![CDATA[
Calculate the work done by gravity when an object moves vertically or along an incline. This walkthrough explains how to use the weight component and displacement to determine the energy change in these systems. Solved: A technician at a telecommunications mast pulls a 22 \, kg equipment box vertically upwards to a height of 8 \, m at a constant speed. Calculate the work done by the force of gravity on the box. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/WlzFYGWTKiSX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QwM9HIf3SWxv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/QwM9HIf3SWxv.jpg</video:thumbnail_loc>

            <video:title>Evaluation (3)</video:title>

            <video:description><![CDATA[
Execute the systematic evaluation of polynomials containing literal coefficients and multiple variables through a rigorous problem walkthrough. You will master the mechanical substitution of complex expressions to resolve functional values with absolute algebraic precision. Solved: 3. Given Q(x) = x^2 - 3x, evaluate Q(5) - 2Q(-1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/QwM9HIf3SWxv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lVNWseYdS7Bq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/lVNWseYdS7Bq.jpg</video:thumbnail_loc>

            <video:title>Calculating pH or pOH (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate pH and pOH using negative logarithms of ion concentrations. You will learn to use the relationship between pH and pOH to find unknown values for strong acids and bases. Follow these worked examples to master the basic arithmetic of the pH scale. Solved: A research chemist adds a measured amount of HCl gas to pure water at 25??C and obtains a solution with [\text{H}_3\text{O}^+] = 3.0 \times 10^{-4} \text{ M}. Calculate the [\text{OH}^-]. Is the solution neutral, acidic, or basic? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/lVNWseYdS7Bq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vx2HTIJeyRLd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/vx2HTIJeyRLd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: The jet belt and man has a total weight of 210 lb. If the engine provides a constant thrust having x and y components of F_x = 35 lb anf F_y = 300 lb, determine the total distance the man travels when t = 5 s after takeoff. What is his velocity at this instant? Neglect air resistance and the loss of fuel. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/vx2HTIJeyRLd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744387305143.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/x0onuIBU52Gy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/x0onuIBU52Gy.jpg</video:thumbnail_loc>

            <video:title>Remainder theorem</video:title>

            <video:description><![CDATA[
Master the application of the Remainder Theorem to determine the result of polynomial division without executing long division. You will learn to calculate the remainder f(c) when a polynomial is divided by (x - c), establishing the essential test for factor identification.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/x0onuIBU52Gy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FnGozWFbU1qK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/569/FnGozWFbU1qK.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
General properties of lattices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/569/FnGozWFbU1qK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l0n8qliaJNzC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1189/l0n8qliaJNzC.jpg</video:thumbnail_loc>

            <video:title>Range of rational expressions</video:title>

            <video:description><![CDATA[
This lesson explains how to identify the possible values a rational expression can take. You will learn to rearrange the expression into a quadratic equation and apply the discriminant to determine valid numerical ranges for the output.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1189/l0n8qliaJNzC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PkXW4CnYU1H1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/PkXW4CnYU1H1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the vector equation of a straight line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/PkXW4CnYU1H1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yN8KoPRnaDlI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/13/yN8KoPRnaDlI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar product of two vectors. Solved: 1.Given any three vectors a, b and c, find the value of ((b.c)a-(a.c)b).c.2.Calculate the length of the sides and sizes of the angle of the triangle whose vertices are A(-3, 5, 2), B(6, -8, -7) and C(-4, 9, -11). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/13/yN8KoPRnaDlI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ihhjGdmqJmJ1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/ihhjGdmqJmJ1.jpg</video:thumbnail_loc>

            <video:title>Special integers (1)</video:title>

            <video:description><![CDATA[
Special integer subsets - positive, nonzero, etc.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/ihhjGdmqJmJ1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zS7wfe_EvC4E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Thumbnails/292/zS7wfe_EvC4E.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on modelling of conservative mechanical systems by the method of Lagrange's equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Previews/292/zS7wfe_EvC4E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XGawBGyp83LZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/XGawBGyp83LZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the vector equation of a straight line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/XGawBGyp83LZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pr0kd1RhvpJK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/686/pr0kd1RhvpJK.jpg</video:thumbnail_loc>

            <video:title>The bigger picture</video:title>

            <video:description><![CDATA[
This lesson puts your new skills into a professional context. We will briefly introduce more advanced tools, like package managers and Git branching, showing how they build upon the foundation you have now mastered.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/686/pr0kd1RhvpJK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YPLvilfK0THf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/YPLvilfK0THf.jpg</video:thumbnail_loc>

            <video:title>Speed on compressed spring</video:title>

            <video:description><![CDATA[
Calculate the launch speed of a toy car using the conservation of energy principle. This walkthrough demonstrates how to convert stored elastic potential energy from a compressed spring into the kinetic energy of the moving car. Solved: A 2.0 \, kg pinball is pressed against a horizontal spring in a launcher, which has a stiffness constant k = 800 \, N/m. If the spring is compressed by 0.15 \, m and then released, calculate the speed of the ball as it leaves the spring, assuming the surface is frictionless. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/YPLvilfK0THf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VGYz231aDlWG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/VGYz231aDlWG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the vector equation of a straight line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/VGYz231aDlWG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3o8ctjuvMzbL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/3o8ctjuvMzbL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the vector equation of a straight line - how to obtain the shortest (perpendicular) distance from a point to a given straight line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/3o8ctjuvMzbL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VDA2zS_xFInk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/VDA2zS_xFInk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let A be an mxn matrix and let T:\mathbb{R}^n\to\mathbb{R}^n be defined by T(V)=A_V. Is it linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/VDA2zS_xFInk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2QKccje10dAL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/2QKccje10dAL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let T:V\to{V} such that T(V)=mv, where m is a fixed scalar. Show that T is linear. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/2QKccje10dAL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ruSv5hzPOONb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/551/ruSv5hzPOONb.jpg</video:thumbnail_loc>

            <video:title>Equation of motion</video:title>

            <video:description><![CDATA[
Newton's second law equation for a system of particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/551/ruSv5hzPOONb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gI0ErweA1C1C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/gI0ErweA1C1C.jpg</video:thumbnail_loc>

            <video:title>Length dimensions</video:title>

            <video:description><![CDATA[
This lesson explains absolute units like px and relative units like em, rem, and percentages. We will focus on rem as the professional standard for scalable design.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/gI0ErweA1C1C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SBKrq1u58bK9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1189/SBKrq1u58bK9.jpg</video:thumbnail_loc>

            <video:title>Basic quadratic inequality</video:title>

            <video:description><![CDATA[
This lesson shows how to solve a quadratic inequality by identifying critical values and testing intervals. You will learn to determine the exact set of values for which the expression is negative. Solved: Find the set of values of x for which x^2 - 9x + 14 < 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1189/SBKrq1u58bK9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lDDK7FjoaGxO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/lDDK7FjoaGxO.jpg</video:thumbnail_loc>

            <video:title>Types of sets (1)</video:title>

            <video:description><![CDATA[
Types of sets - finite, infinite sets and their order or cardinality.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/lDDK7FjoaGxO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ng_Pcxw07JQi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/321/ng_Pcxw07JQi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of planar trusses by the method of sections. Solved: Determine the force in members BC, FC, and FE and state if the members are in tension or compression. Hint: The force acting at the pin G is directed along member GD. Why? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/321/ng_Pcxw07JQi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1739014708334.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/SALSIPA8gfR1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/321/SALSIPA8gfR1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of planar trusses by the method of sections. Solved: Determine the force in member GK of the loaded symmetrical truss. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/321/SALSIPA8gfR1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1739014942331.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/zuxiVh0Mw_yo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/zuxiVh0Mw_yo.jpg</video:thumbnail_loc>

            <video:title>More examples</video:title>

            <video:description><![CDATA[
More examples of relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/zuxiVh0Mw_yo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4r68ASGtDJCn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/4r68ASGtDJCn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of higher-order derivatives using the Leibnitz's formula. Solved: Given that 4(x+1)\frac{d^2y}{dx^2} +2\frac{dy}{dx} +\pi ^2y=0, show that 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/4r68ASGtDJCn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OY_L0x9O_QOd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/OY_L0x9O_QOd.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Define Venn diagrams as geometric representations of set relationships within a universal set. You will establish the spatial logic of regions to map memberships and inclusions, providing a visual framework for verifying algebraic identities and solving complex data overlaps.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/OY_L0x9O_QOd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZfZqb4Phe9mH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/ZfZqb4Phe9mH.jpg</video:thumbnail_loc>

            <video:title>Power and inverse laws</video:title>

            <video:description><![CDATA[
This lesson explains the power law for shifting exponents to the front of a logarithm and the inverse law for cancelling logarithms with their bases. You will learn to use these rules to simplify complex expressions and isolate variables when solving exponential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/ZfZqb4Phe9mH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nlM4rlY7TKl2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/nlM4rlY7TKl2.jpg</video:thumbnail_loc>

            <video:title>Work and energy</video:title>

            <video:description><![CDATA[
Rotating a dipole stores energy. How do we calculate the work done against the electric torque? Watch to master the potential energy formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/nlM4rlY7TKl2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pAW9KYE4ToCm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/pAW9KYE4ToCm.jpg</video:thumbnail_loc>

            <video:title>The work-energy theorem (2)</video:title>

            <video:description><![CDATA[
Apply the work-energy theorem to determine the final speed of a trolley pushed from rest. This walkthrough calculates total work done by a constant force and equates it to the change in kinetic energy to find the final velocity. Solved: A 15 \, kg trolley, initially at rest on a smooth supermarket floor, is pushed with a constant horizontal force of 40 \, N. Calculate the speed of the trolley after it has been pushed over a distance of 6 \, m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/pAW9KYE4ToCm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8hHUV1Eu-oB1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/8hHUV1Eu-oB1.jpg</video:thumbnail_loc>

            <video:title>Relations</video:title>

            <video:description><![CDATA[
Definition and examples of relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/8hHUV1Eu-oB1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JsSikOLuBfS2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/JsSikOLuBfS2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: A torque applied to a flywheel causes it to accelerate uniformly from a speed of 300 rev\min to a speed of 900rev\min in 6 seconds. Determine the number of revolutions N through which the wheel turns during this interval. (Suggestions: Use revolutions and minutes for units in your calculations.) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/JsSikOLuBfS2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QG23_3ItvR_y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/QG23_3ItvR_y.jpg</video:thumbnail_loc>

            <video:title>Factorisation (2)</video:title>

            <video:description><![CDATA[
Execute the systematic factorisation of cubic and higher-degree polynomials by synthesising the Factor Theorem with polynomial long division. You will master the mechanical identification of initial roots to reduce complex expressions into solvable quadratic factors with absolute precision. Solved: 6. Solve the equation 2x^3 - 3x^2 - 11x + 6 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/QG23_3ItvR_y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z6_uDkYt5xGA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/z6_uDkYt5xGA.jpg</video:thumbnail_loc>

            <video:title>Finite union</video:title>

            <video:description><![CDATA[
This lesson defines the finite union. It demonstrates the notation and method for combining a finite number of sets into a single set, with duplicate elements removed.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/z6_uDkYt5xGA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mt6X6FmxSH_o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/mt6X6FmxSH_o.jpg</video:thumbnail_loc>

            <video:title>Roots of compound surds</video:title>

            <video:description><![CDATA[
This lesson explains the theory for finding the square root of a compound surd by converting it into a perfect square. You will learn to use the identity for the square of a binomial to resolve these nested radicals into simpler separate surds.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/mt6X6FmxSH_o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/maSUsSdVz4tM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/552/maSUsSdVz4tM.jpg</video:thumbnail_loc>

            <video:title>Work and energy</video:title>

            <video:description><![CDATA[
Work-Energy principle and conservation of mechanical energy for systems of particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/552/maSUsSdVz4tM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A_jPZIzOtmln</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/A_jPZIzOtmln.jpg</video:thumbnail_loc>

            <video:title>Introduction to responsiveness</video:title>

            <video:description><![CDATA[
This is a conceptual introduction to responsive design. We will explain why websites need to adapt to different screen sizes and briefly introduce the media query as the tool for doing so.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/A_jPZIzOtmln.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_59M1wOnDwE5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/_59M1wOnDwE5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n\to \infty} (\frac{-1}{n})^n=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/_59M1wOnDwE5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9JVkY2fruwmt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/8/9JVkY2fruwmt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on position vectors. Solved: What is the sum of vectors \vec{30A}, \vec{6BZ}, \vec{2AD}, \vec{AB}, and \vec{50B} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/8/9JVkY2fruwmt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i4yUivf1mtUF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/551/i4yUivf1mtUF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on Newton's second law equation for a system of particles. Solved: Calculate the acceleration of the center of mass of the system of the four 10-kg cylinders. Neglect friction and the mass of the pulleys and cables. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/551/i4yUivf1mtUF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1750748143288.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0iDg3eSUlfLp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/0iDg3eSUlfLp.jpg</video:thumbnail_loc>

            <video:title>Angular impulse-momentum principle</video:title>

            <video:description><![CDATA[
Principle of angular impulse and momentum.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/0iDg3eSUlfLp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mzidkUZuy4wZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/mzidkUZuy4wZ.jpg</video:thumbnail_loc>

            <video:title>Work of a variable force</video:title>

            <video:description><![CDATA[
Calculating work done by a variable force.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/mzidkUZuy4wZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2NW5S5H5FC5Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/2NW5S5H5FC5Z.jpg</video:thumbnail_loc>

            <video:title>Solving equations with unknown index (3)</video:title>

            <video:description><![CDATA[
This lesson demonstrates solving exponential equations where bases cannot be matched by taking logarithms of both sides. You will learn to isolate the unknown index and use the change of base formula to calculate precise numerical solutions for mixed-base problems. Solved: 3. Solve for x if \frac{e^x + e^{-x}}{2} = 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/2NW5S5H5FC5Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xM7K2WomWmZ6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/xM7K2WomWmZ6.jpg</video:thumbnail_loc>

            <video:title>Solution of differential equations (2)</video:title>

            <video:description><![CDATA[
How to obtain a differential equation from its known general solution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/xM7K2WomWmZ6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UeTAGuNKXUI2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/510/UeTAGuNKXUI2.jpg</video:thumbnail_loc>

            <video:title>Energy and momentum methods</video:title>

            <video:description><![CDATA[
Motivation for energy and momentum methods for the analysis of kinetics of particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/510/UeTAGuNKXUI2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/doX6NiNDvFey</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/339/doX6NiNDvFey.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of frictional forces (rolling resistance) on wheels. Solved: Knowing that a 6-in -diameter disk rolls at a constant velocity down a 2 percent incline, determine the coefficient of rolling resistance between the disk and the incline. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/339/doX6NiNDvFey.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V_H4WNDJV_2s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/V_H4WNDJV_2s.jpg</video:thumbnail_loc>

            <video:title>Power and efficiency</video:title>

            <video:description><![CDATA[
Calculate the electrical power needed to lift a heavy load at constant speed. This walkthrough shows how to find the useful power output using force and velocity, then applies the efficiency percentage to determine the total input power required from the motor. Solved: An electric winch with an efficiency of 65\% is used to lift a 120 \, kg car engine vertically at a constant speed of 0.8 \, m/s. Calculate the total electrical power that must be supplied to the motor. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/V_H4WNDJV_2s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RfOXmEkHBGWN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/335/RfOXmEkHBGWN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of frictional forces on square-threaded screws. Solved: The hand clamp is constructed using a square - threaded screw having a mean diameter of 36mm , a lead of 4mm , and a coefficient of static friction at the screw of \mu_s=0.3 . If the clamping force in the board AB is 300N , determine the reversed force -F that must be applied perpendicular to the handle in order to loosen the screw. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/335/RfOXmEkHBGWN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746867480906.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/pbBcREF2b3YU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/pbBcREF2b3YU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/pbBcREF2b3YU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yzcSXLpQS0KA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/510/yzcSXLpQS0KA.jpg</video:thumbnail_loc>

            <video:title>Kinetics of particles</video:title>

            <video:description><![CDATA[
Review of the fundamental concepts of kinetics of particles - Newton's second law.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/510/yzcSXLpQS0KA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pr8DVYvbrzjy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/Pr8DVYvbrzjy.jpg</video:thumbnail_loc>

            <video:title>Moment of a force and angular momentum</video:title>

            <video:description><![CDATA[
Relationship between the moment of a force and the angular moment of the particle on which it acts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/Pr8DVYvbrzjy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fpPoK9Gyv8z5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/fpPoK9Gyv8z5.jpg</video:thumbnail_loc>

            <video:title>Definitions</video:title>

            <video:description><![CDATA[
Meaning, scalar and vector formulations of angular momentum and angular impulse.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/fpPoK9Gyv8z5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HHMnKhfHuqoW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/HHMnKhfHuqoW.jpg</video:thumbnail_loc>

            <video:title>Zero-work forces</video:title>

            <video:description><![CDATA[
Identifying forces that do no work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/HHMnKhfHuqoW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nNmMhxI4MP7B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/nNmMhxI4MP7B.jpg</video:thumbnail_loc>

            <video:title>Conservation of angular momentum</video:title>

            <video:description><![CDATA[
Principle of conservation of angular momentum of a particle.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/nNmMhxI4MP7B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0Z5xIVOWnkUf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/0Z5xIVOWnkUf.jpg</video:thumbnail_loc>

            <video:title>Membership notations</video:title>

            <video:description><![CDATA[
The membership notation of a set helps us express whether a particular object belongs to a given set or not. Using the symbols ??? (is an element of) and ??? (is not an element of), we can clearly show the relationship between elements and sets.

By the end of this lesson, students will be able to interpret and use membership notation correctly to identify whether or not an element belongs to a set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/0Z5xIVOWnkUf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a1GCj_mlh9Fz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/a1GCj_mlh9Fz.jpg</video:thumbnail_loc>

            <video:title>Field scaling and symmetry</video:title>

            <video:description><![CDATA[
Dipole fields fade faster than point charges. Why does the strength drop by the cube of distance and flip direction on the axis? See the logic behind this rapid decay.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/a1GCj_mlh9Fz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qybiHp0tLa4S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/qybiHp0tLa4S.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
To deepen understanding, we will now look at a worked example that demonstrates how membership notation is applied in practice. This example will show step by step how to determine whether given elements belong to a set or not, using the symbols ??? and ???.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/qybiHp0tLa4S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/p41YFxUxYYLs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/p41YFxUxYYLs.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
We will now consider a worked example that uses notation together with the listing of set elements. This will help illustrate how elements are written explicitly in a set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/p41YFxUxYYLs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nUltTMeUsZv5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/60/nUltTMeUsZv5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the intermediate-value theorem. Solved: Show that the equation x=cosx has at least one solution in the interval [0,\frac{\Pi}{2}]. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/60/nUltTMeUsZv5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VE3Z7S_tnQXc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/VE3Z7S_tnQXc.jpg</video:thumbnail_loc>

            <video:title>Chemical formulae (1)</video:title>

            <video:description><![CDATA[
This problem walkthrough uses the percentage of water in a metal sulfate decahydrate and the metal's known valency to determine the unknown metal's atomic mass. Solved: Illustration:A metal sulfate decahydrate contains 31.48% water. Which is the atomic mass of the metal (Note: the metal is trivalent) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/VE3Z7S_tnQXc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FFlrfAaaVjuk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/FFlrfAaaVjuk.jpg</video:thumbnail_loc>

            <video:title>Rational equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of rational equations by clearing denominators through the least common multiple or cross-multiplication. You will master the mechanical isolation of variables and the critical verification of solutions to exclude undefined values. Solved: 3. Solve the equation\frac{x + 2}{x - 2} = \frac{3x - 1}{x + 1} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/FFlrfAaaVjuk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CizLrpimuC8A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7qZafmufII/Thumbnails/641/CizLrpimuC8A.jpg</video:thumbnail_loc>

            <video:title>Directly-integrable equations</video:title>

            <video:description><![CDATA[
Solving higher-order ODEs that are directly integrable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7qZafmufII/Previews/641/CizLrpimuC8A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dHCxlkvY1ioR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7qZafmufII/Thumbnails/641/dHCxlkvY1ioR.jpg</video:thumbnail_loc>

            <video:title>Dependent variable absent</video:title>

            <video:description><![CDATA[
Solving higher-order ODEs by reduction to lower-order ones when the dependent variable is absent.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7qZafmufII/Previews/641/dHCxlkvY1ioR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pe5pCPK1ooQe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/Pe5pCPK1ooQe.jpg</video:thumbnail_loc>

            <video:title>Types of sets (2)</video:title>

            <video:description><![CDATA[
Types of sets - empty, singleton and universal and complement sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/Pe5pCPK1ooQe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RV_1ayDjyvsr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/RV_1ayDjyvsr.jpg</video:thumbnail_loc>

            <video:title>Maximum spring compression</video:title>

            <video:description><![CDATA[
Calculate the maximum compression of a vertical spring when hit by a falling mass. This walkthrough uses the conservation of energy to equate the total gravitational potential energy lost to the elastic potential energy gained by the spring. Solved: A 5.0 \, kg safety test block is dropped from a height of 1.2 \, m above the top of a vertical emergency spring. The spring has a constant k = 3000 \, N/m. Calculate the maximum compression of the spring as it stops the block. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/RV_1ayDjyvsr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Yw4hJZ_2fJ8y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/Yw4hJZ_2fJ8y.jpg</video:thumbnail_loc>

            <video:title>Equilibrium states</video:title>

            <video:description><![CDATA[
Zero torque means equilibrium, but not all states are safe. Why does one orientation hold firm while the other flips at a slight nudge? Watch to distinguish stable from unstable equilibrium.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/Yw4hJZ_2fJ8y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JmKEB707wm-1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/510/JmKEB707wm-1.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course, course outline and references.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/510/JmKEB707wm-1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mP3P2euZNHmW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/mP3P2euZNHmW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on producing free-body diagrams for the force analysis of rigid bodies in three dimensions. Solved: Two tape spools are attached to an axle supported by bearings at A and D. The radius of spool B is 1.5 in. and the radius of spool C is 2 in. Knowing that T_B=20lb and that the system rotates at a constant rate, draw the free-body diagram needed to determine the reaction at A and D. Assume that the bearing at A does not exert any axial thrust and neglect the weights of the spools and axle. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/mP3P2euZNHmW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1737370857197.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/G251uK8iARxu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/G251uK8iARxu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: The 30-lb block A is placed on top of two nested springs B and C and then pushed down to the position shown. If it is then released, determine the maximum height h to which it will rise. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/G251uK8iARxu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747310811292.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/HGoH5xA2J2pE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/HGoH5xA2J2pE.jpg</video:thumbnail_loc>

            <video:title>Work of a spring force</video:title>

            <video:description><![CDATA[
Calculating the work done to stretch or compress a spring.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/HGoH5xA2J2pE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lvFeLfxfy8Fa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/394/lvFeLfxfy8Fa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on producing free-body diagrams for the force analysis of rigid bodies in two dimensions. Solved: Draw the free-body diagram to determine the reactions at the smooth contact points A, B and C on the bar. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/394/lvFeLfxfy8Fa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736822755601.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nCD_2gR0Za4k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/nCD_2gR0Za4k.jpg</video:thumbnail_loc>

            <video:title>Radical equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of equations involving square roots by isolating the radical and squaring both sides. You will master the mechanical elimination of surds and the mandatory verification of results to detect extraneous solutions. Solved: 4. Solve the equation \sqrt{2x + 3} - \sqrt{x + 1} = 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/nCD_2gR0Za4k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MfnYdGLbdAJe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/MfnYdGLbdAJe.jpg</video:thumbnail_loc>

            <video:title>Basic theorem on empty set</video:title>

            <video:description><![CDATA[
Here, we prove that an empty set is a subset of every set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/MfnYdGLbdAJe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BWt8ypoPzqvF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/BWt8ypoPzqvF.jpg</video:thumbnail_loc>

            <video:title>Finding turning points</video:title>

            <video:description><![CDATA[
Locate the points where a particle reverses direction by equating its total mechanical energy to the potential energy function. This walkthrough shows how to solve the resulting quadratic equation to find the exact coordinates where kinetic energy becomes zero. Solved: A particle has a constant total mechanical energy of 20 \, J. It moves in a region where its potential energy is defined as U(x) = 3x^2 - 12x. Determine the x-coordinates of the turning points where the particle reverses its direction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/BWt8ypoPzqvF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nCWAWT_fnlmN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/nCWAWT_fnlmN.jpg</video:thumbnail_loc>

            <video:title>Irrational numbers</video:title>

            <video:description><![CDATA[
Meaning of irrational numbers and how they differ from rational ones.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/nCWAWT_fnlmN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/teUqGnIiNTfi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/teUqGnIiNTfi.jpg</video:thumbnail_loc>

            <video:title>Complex numbers</video:title>

            <video:description><![CDATA[
Meaning and identification of complex numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/teUqGnIiNTfi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0_P4YazqfhU3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/0_P4YazqfhU3.jpg</video:thumbnail_loc>

            <video:title>The box model</video:title>

            <video:description><![CDATA[
This is a critical lesson on the core concept of CSS layout. We will use simple examples to explain how every element is a box, and how to control its size and space with padding, border, and margin.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/0_P4YazqfhU3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/54_ofNSHMOQC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1024/54_ofNSHMOQC.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson outlines the course structure and the specific sequence of proof techniques you will learn. It provides a clear roadmap of the topics covered, including series, divisibility, and inequalities, to guide your progress through the curriculum.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1024/54_ofNSHMOQC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R65VWdlyKE3w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/R65VWdlyKE3w.jpg</video:thumbnail_loc>

            <video:title>Sum and product</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the sum and product of roots using equation coefficients. You will learn to apply the formulas directly to identify these values without solving for the individual roots. Solved: Find the sum and product of the roots for the quadratic equation 4x^2 - 11x + 3 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/R65VWdlyKE3w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QiM3W8PSeSdg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/413/QiM3W8PSeSdg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on theorems on Jacobians. Solved: If u = \frac {x + y} {1 - xy} and v = tan^{-1}x + tan^{-1}y,(a) Find \frac {\partial (u, v)} {\partial (x, y)}(b) are u and v functionally related? If so, find the relationship. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/413/QiM3W8PSeSdg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gBDko6L9vij5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/413/gBDko6L9vij5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on theorems on Jacobians. Solved: If x = u - v + w, y = u^2 - v^2 -w^2 and z = u^3 + v,(a) evaluate \frac {\partial (x, y, z)} {\partial (u, v, w)}(b) what can you make of the result in (a) ? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/413/gBDko6L9vij5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pJlqR3DQWoUA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/pJlqR3DQWoUA.jpg</video:thumbnail_loc>

            <video:title>Torque and stable equilibrium</video:title>

            <video:description><![CDATA[
Calculate the torque on a dipole in a uniform field. How do you apply the cross product formula with the correct angle? Watch the solution steps. Solved: A dipole with charges q = \pm 5.00 \text{ nC} and separation d = 4.00 \text{ }\mu\text{m} is placed in a uniform external field of E = 2.50 \times 10^4 \text{ N/C}. Calculate the magnitude of the torque exerted on the dipole when it is oriented at an angle of 30.0^\circ relative to the field lines. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/pJlqR3DQWoUA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BgWy5BTbWm8w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/661/BgWy5BTbWm8w.jpg</video:thumbnail_loc>

            <video:title>Our approach</video:title>

            <video:description><![CDATA[
See how the journey is structured, what matters, what does not, and why we teach real tools, not abstract theory.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/661/BgWy5BTbWm8w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WDOAlEoDEyVM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/139/WDOAlEoDEyVM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on diagonalization of matrices. Solved: DiagonalizeA=\left[ \begin{array}{ccc} 1 & 2 \\ 2 & 1 \\ \end{array} \right] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/139/WDOAlEoDEyVM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nyVuuW1DRVgH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/nyVuuW1DRVgH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the vector product of two vectors and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/nyVuuW1DRVgH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1egMG3SPcnJC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/1egMG3SPcnJC.jpg</video:thumbnail_loc>

            <video:title>Power</video:title>

            <video:description><![CDATA[
Instantaneous and average power generated by a force when it does a work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/1egMG3SPcnJC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c8OpRUbi7pYl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/195/c8OpRUbi7pYl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the gradient in orthogonal curvilinear coordinates. Solved: Determine the gradient of the scalar \theta=r\cos\theta+2z 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/195/c8OpRUbi7pYl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zMqF5q9hOhgt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/zMqF5q9hOhgt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: Each cord can sustain a maximum tension of 500 N. Determine the largest mass of pipe that can be supported. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/zMqF5q9hOhgt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739472349458.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/voKsq_tPlEqr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/195/voKsq_tPlEqr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the gradient in orthogonal curvilinear coordinates. Solved: 1)Suppose that in an orthogonal coordinate system (u1,u2,u3),u1,u2,u3 each strictly positive with basis (\vec{\hat{e}}_1,\vec{\hat{e}}_2,\vec{\hat{e}}_3) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/195/voKsq_tPlEqr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e80L2KSeHMIQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Thumbnails/292/e80L2KSeHMIQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on modelling of conservative mechanical systems by the method of Lagrange's equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vNvVjmmvBR/Previews/292/e80L2KSeHMIQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/odZT3SbuLhRQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Thumbnails/643/odZT3SbuLhRQ.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
How to study MTH 104 and prepare for the exam.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Previews/643/odZT3SbuLhRQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gg4LCdCBUpVB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/gg4LCdCBUpVB.jpg</video:thumbnail_loc>

            <video:title>Common roots (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to find unknown constants when two quadratic equations share a single root. You will learn to use the method of elimination or substitution to satisfy the condition for a common root and solve for the missing values. Solved: Find the condition that x^2 + px + q = 0 and x^2 + qx + p = 0 have a common root. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/gg4LCdCBUpVB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gQVmk4SYHaXW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/gQVmk4SYHaXW.jpg</video:thumbnail_loc>

            <video:title>Special rationals and reals</video:title>

            <video:description><![CDATA[
Special subsets of rational numbers and real numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/gQVmk4SYHaXW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8-lFYlc1e2Zq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Thumbnails/647/8-lFYlc1e2Zq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculus of vectors - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Previews/647/8-lFYlc1e2Zq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rDabCSGWtsCb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/rDabCSGWtsCb.jpg</video:thumbnail_loc>

            <video:title>Inverse relation</video:title>

            <video:description><![CDATA[
Meaning of the inverse of a relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/rDabCSGWtsCb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8sifqvTAsxFH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/8sifqvTAsxFH.jpg</video:thumbnail_loc>

            <video:title>Collision in two dimensions</video:title>

            <video:description><![CDATA[
Calculate the final speed and direction of a combined wreck following a two-dimensional collision. This walkthrough applies the conservation of momentum separately along the x and y axes to determine the final velocity components and the resulting impact angle. Solved: At a junction, a 1200 \, kg saloon car moving East at 22 \, m/s is struck by a 3000 \, kg delivery truck moving North at 14 \, m/s. The vehicles stick together upon impact. Calculate the speed and the direction (angle) of the wreckage immediately after the collision. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/8sifqvTAsxFH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eLXmoGKZZG9f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/eLXmoGKZZG9f.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: Determine the x, y, z components of reaction acting on the ball-and-socket at A, the reaction at roller B, and the tension in the cord CD required for equilibrium of the plate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/eLXmoGKZZG9f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738675741524.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dIqm6Yh4RWGj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/dIqm6Yh4RWGj.jpg</video:thumbnail_loc>

            <video:title>Linear impulse-momentum principle</video:title>

            <video:description><![CDATA[
Relation between the linear momentum of a particle and the impulse of forces acting on it.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/dIqm6Yh4RWGj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AqapYHJdyaWp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/AqapYHJdyaWp.jpg</video:thumbnail_loc>

            <video:title>Impulsive forces and motion</video:title>

            <video:description><![CDATA[
Meaning of impulsive forces and motion, and how to identify impulsive and non-impulsive forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/AqapYHJdyaWp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sb7lra6MGl4d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/sb7lra6MGl4d.jpg</video:thumbnail_loc>

            <video:title>Equality of sets</video:title>

            <video:description><![CDATA[
Meaning, condition for and implications of the equality of two sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/sb7lra6MGl4d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sCvZVapiOtyb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/sCvZVapiOtyb.jpg</video:thumbnail_loc>

            <video:title>Mass flow</video:title>

            <video:description><![CDATA[
Definitions and equations of mass and volumetric flow rates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/sCvZVapiOtyb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s26qjJomBsB2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/s26qjJomBsB2.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/s26qjJomBsB2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TrePbEQBvRHM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/TrePbEQBvRHM.jpg</video:thumbnail_loc>

            <video:title>Power set</video:title>

            <video:description><![CDATA[
Meaning and cardinality of the power set of a given set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/TrePbEQBvRHM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RvvOP4G3ZFkx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/RvvOP4G3ZFkx.jpg</video:thumbnail_loc>

            <video:title>Domain and range</video:title>

            <video:description><![CDATA[
Meaning of domain and range of a relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/RvvOP4G3ZFkx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H5inRIvOmqh8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/H5inRIvOmqh8.jpg</video:thumbnail_loc>

            <video:title>Logarithmic functions</video:title>

            <video:description><![CDATA[
Logarithmic integrals require a specific technique. How do you handle the integration of ln x and log x? This lesson shows the standard result for these functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/H5inRIvOmqh8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2pZQW8mRWMYL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/2pZQW8mRWMYL.jpg</video:thumbnail_loc>

            <video:title>Equations from roots (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to build a new quadratic equation using modified roots of an existing one. You will learn to find the new sum and product of roots to determine the coefficients of the required equation. Solved: If \alpha and \beta are roots of x^2 - 5x + 2 = 0, find the quadratic equation whose roots are \alpha^2 and \beta^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/2pZQW8mRWMYL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1YsK2hgMeh-V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/550/1YsK2hgMeh-V.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/550/1YsK2hgMeh-V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8HEp_NLxgo1L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/562/8HEp_NLxgo1L.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of symmetric relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/562/8HEp_NLxgo1L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/do6waB-YRM2O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/do6waB-YRM2O.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of real sequences. Solved: Determine whether or not the following sequences converge. If they do, find the limit. 8.{n\arctan(\frac{1}{n})} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/do6waB-YRM2O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VS7FQyW_6isK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/550/VS7FQyW_6isK.jpg</video:thumbnail_loc>

            <video:title>Centre of mass</video:title>

            <video:description><![CDATA[
Meaning and location of the centre of mass of systems of particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/550/VS7FQyW_6isK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EM0epZgM5fzb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/EM0epZgM5fzb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (23)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Determine the reaction on the bent rod which is supported by a smooth surface at B and by a collar at A, which is fixed to the rod and is free to slide over the fixed inclined rod. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/EM0epZgM5fzb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736939710344.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/J8BEcAcYM1g_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/561/J8BEcAcYM1g_.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
When is a relation said to be reflexive?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/561/J8BEcAcYM1g_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qFkVrGhSxDW5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/557/qFkVrGhSxDW5.jpg</video:thumbnail_loc>

            <video:title>Equation of motion</video:title>

            <video:description><![CDATA[
General analysis of systems of particles gaining or losing mass.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/557/qFkVrGhSxDW5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OK3uZ0PpjYX6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/OK3uZ0PpjYX6.jpg</video:thumbnail_loc>

            <video:title>Finite intersection</video:title>

            <video:description><![CDATA[
This lesson defines the finite intersection and disjoint sets. It covers the notation and method for identifying all elements common to a finite collection of sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/OK3uZ0PpjYX6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EtlCRh3Lav31</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/557/EtlCRh3Lav31.jpg</video:thumbnail_loc>

            <video:title>Thrust implications</video:title>

            <video:description><![CDATA[
Resultant thrust due to particles being absorbed or ejected by systems of particles gaining or losing mass.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/557/EtlCRh3Lav31.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xFxjvSmtuHs8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/xFxjvSmtuHs8.jpg</video:thumbnail_loc>

            <video:title>Trigonometric functions</video:title>

            <video:description><![CDATA[
Mixed trigonometric integrands require precise pattern matching for each term. How do you integrate sine, cosine and secant tangent products in one sweep? We apply standard rules to resolve this combination. Solved: Evaluate the indefinite integral \int (4 \sin x - 6 \cos x + 3 \sec x \tan x) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/xFxjvSmtuHs8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UxuV1p2fA4i9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/564/UxuV1p2fA4i9.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of equivalence relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/564/UxuV1p2fA4i9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v2exoK68_k_t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/1189/v2exoK68_k_t.jpg</video:thumbnail_loc>

            <video:title>Range of rational expressions (2)</video:title>

            <video:description><![CDATA[
This lesson proves the range of a complex rational expression by forming a quadratic equation and applying the discriminant. You will learn to solve the resulting quadratic inequality to verify the specific interval of values that the expression cannot take. Solved: Given that x is a real number, prove that the expression \frac{(x-3)^2 + 36}{2(x+3)} cannot take any real values lying between -6(1+\sqrt{2}) and 6(\sqrt{2}-1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/1189/v2exoK68_k_t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OpwCIsI_xq1P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/OpwCIsI_xq1P.jpg</video:thumbnail_loc>

            <video:title>Stopping potential</video:title>

            <video:description><![CDATA[
Kinetic energy fights electric potential. How far does a proton travel before the field brings it to a halt? Watch to solve for distance. Solved: A proton enters a uniform electric field of magnitude 1.80 \times 10^4 V/m directed opposite to its motion. If the proton has an initial speed of 2.20 \times 10^5 m/s, calculate the distance the proton travels before it is brought to a halt by the electric field. (Take the mass of a proton as 1.67 \times 10^{-27} kg and its charge as 1.60 \times 10^{-19} C). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/OpwCIsI_xq1P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4iyS3jayTPn5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/963/4iyS3jayTPn5.jpg</video:thumbnail_loc>

            <video:title>Global CSS variables</video:title>

            <video:description><![CDATA[
Establish a centralized design system by defining global colors, font families, and spacing units as CSS variables, directly from your design for consistency.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/963/4iyS3jayTPn5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UGNbzZ6ejmRU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/410/UGNbzZ6ejmRU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on gradients and directional derivatives. Solved: If f(x ,y, z) =x\sin yz, (a) Find the gradient of f and(b) Find the directional derivative of f at (1, 3, 0) in the direction \vec{v} =i+2j-k 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/410/UGNbzZ6ejmRU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8VtSO1TNfAq7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/8VtSO1TNfAq7.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
What number systems are and why they matter in mathematics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/8VtSO1TNfAq7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j8ooKz0O3N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/j8ooKz0O3N.jpg</video:thumbnail_loc>

            <video:title>Basic force calculation</video:title>

            <video:description><![CDATA[
Coulomb's law links charge and distance to force. How do you handle unit conversions and the inverse square relationship to get the correct magnitude? Watch the video for the step-by-step calculation. Solved: Two small metallic spheres are given charges of +4.50 \times 10^{-6} \text{ C} and -2.20 \times 10^{-6} \text{ C}. If they are separated by a distance of 15.0 \text{ cm}, calculate the magnitude of the electrostatic force acting between them. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/j8ooKz0O3N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wxVSRAa_GG7f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/wxVSRAa_GG7f.jpg</video:thumbnail_loc>

            <video:title>Real numbers</video:title>

            <video:description><![CDATA[
Meaning and identification of real numbers - and 'unreal' ones.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/wxVSRAa_GG7f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mWKG_84cUZrC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1025/mWKG_84cUZrC.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson breaks down the exact sequence for proving summation formulas. You will learn how to set up the base case, state the inductive hypothesis, and add the next term to both sides to prove the identity for n equals k plus one.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1025/mWKG_84cUZrC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HUlGq9qidfdz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/HUlGq9qidfdz.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course and outline of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/HUlGq9qidfdz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2W2rJu387Zqc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/2W2rJu387Zqc.jpg</video:thumbnail_loc>

            <video:title>Subsets</video:title>

            <video:description><![CDATA[
Meaning and examples of subsets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/2W2rJu387Zqc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/79aKb328NC25</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/79aKb328NC25.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of set and set membership notation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/79aKb328NC25.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0gKMvC5Rx77A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/0gKMvC5Rx77A.jpg</video:thumbnail_loc>

            <video:title>Description</video:title>

            <video:description><![CDATA[
Different ways to clearly define the membership of a set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/0gKMvC5Rx77A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N8LGcO3mgO1s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/N8LGcO3mgO1s.jpg</video:thumbnail_loc>

            <video:title>Rational numbers</video:title>

            <video:description><![CDATA[
Meaning of rational numbers and how to identify them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/N8LGcO3mgO1s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ynr-HbjGXdfP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/Ynr-HbjGXdfP.jpg</video:thumbnail_loc>

            <video:title>Special integers (2)</video:title>

            <video:description><![CDATA[
Special subsets of integers involving modular arithmetics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/Ynr-HbjGXdfP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-wLqDYBFQyof</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/-wLqDYBFQyof.jpg</video:thumbnail_loc>

            <video:title>Impulsive forces</video:title>

            <video:description><![CDATA[
Identifying impulsive forces in the analysis of systems (control volumes) subjected to mass flow.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/-wLqDYBFQyof.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XYEepKjZTiPl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/558/XYEepKjZTiPl.jpg</video:thumbnail_loc>

            <video:title>Venn diagrams</video:title>

            <video:description><![CDATA[
An introduction to Venn diagrams and their use in illustrating sets and their subsets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/558/XYEepKjZTiPl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OXN5LnE-sv3S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/OXN5LnE-sv3S.jpg</video:thumbnail_loc>

            <video:title>Steady flow</video:title>

            <video:description><![CDATA[
Meaning of steady flow and analysis of control volumes under steady flow.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/OXN5LnE-sv3S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E4xbl1SjkS0K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/E4xbl1SjkS0K.jpg</video:thumbnail_loc>

            <video:title>Ordered pairs</video:title>

            <video:description><![CDATA[
Meaning and equality of ordered pairs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/E4xbl1SjkS0K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nYggLufD0Fqi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Thumbnails/559/nYggLufD0Fqi.jpg</video:thumbnail_loc>

            <video:title>Polynomials and rational functions</video:title>

            <video:description><![CDATA[
Meaning and examples of polynomials and rational functions with real coefficients.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2RQEZa2QYu/Previews/559/nYggLufD0Fqi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2UuUciUb1IZn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/95/2UuUciUb1IZn.jpg</video:thumbnail_loc>

            <video:title>Worked examples I</video:title>

            <video:description><![CDATA[
Worked examples graphing in 3 dimensions. Solved: Graph x=5 in R, R2 and R3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/95/2UuUciUb1IZn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zx9aJ4Yo4Tk0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Thumbnails/890/Zx9aJ4Yo4Tk0.jpg</video:thumbnail_loc>

            <video:title>Symmetric identities (2)</video:title>

            <video:description><![CDATA[
This lesson shows how to calculate the sum of the squares of the roots using the equation coefficients. You will learn to expand the square of the sum of roots to isolate the required expression and find its numerical value. Solved: If \alpha and \beta are the roots of 2x^2 - 10x + 5 = 0, find the value of \alpha^2 + \beta^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JQVEGfVl5Y/Previews/890/Zx9aJ4Yo4Tk0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GPWxD8enP_ds</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/GPWxD8enP_ds.jpg</video:thumbnail_loc>

            <video:title>Arrhenius' definition</video:title>

            <video:description><![CDATA[
Learn how Svante Arrhenius defined acids and bases by their ability to produce hydrogen or hydroxide ions in water. This lesson covers the essential requirements for Arrhenius behavior and the specific role of aqueous solvents. Master these foundational definitions to identify simple electrolytes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/GPWxD8enP_ds.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MozdrIzGc9w8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/MozdrIzGc9w8.jpg</video:thumbnail_loc>

            <video:title>Equality of relations</video:title>

            <video:description><![CDATA[
When are two relations said to be equal?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/MozdrIzGc9w8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jojcl6-Sjay5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/jojcl6-Sjay5.jpg</video:thumbnail_loc>

            <video:title>Cartesian product</video:title>

            <video:description><![CDATA[
Meaning and cardinality of the Cartesian product of two sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/jojcl6-Sjay5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1HgzAJi_KfBA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/1HgzAJi_KfBA.jpg</video:thumbnail_loc>

            <video:title>Work done in rotation</video:title>

            <video:description><![CDATA[
Calculate the work to rotate a dipole in a field. How do you find the change in potential energy between equilibrium positions? Watch the solution. Solved: How much work must an external agent perform to rotate a dipole (p = 4.50 \times 10^{-30} \text{ C}\cdot\text{m}) from its stable equilibrium position (\theta = 0^\circ) to its unstable equilibrium position (\theta = 180^\circ) in a uniform field of E = 6.00 \times 10^5 \text{ N/C}? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/1HgzAJi_KfBA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/shih46b9KQvW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/shih46b9KQvW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A 30-lb vertical force P is applied at A to the bracket shown, which is held by screws at B and C. (a) Replace P with an equivalent force-couple system at B. (b) Find the two horizontal forces at B and C that are equivalent to the couple obtained in part a. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/shih46b9KQvW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739178804629.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/y7wL3f2pGzbW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/418/y7wL3f2pGzbW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating line or double integrals using Green's theorem. Solved: Evaluate\oint_C\, (y^2dx + 3xydy), where C is the boundary of the semi-annular region D bounded by x^2 +y^2=1 and x^2+y^2=4 as shown below 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/418/y7wL3f2pGzbW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747320248118.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/6f1ei4nQOm22</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/63/6f1ei4nQOm22.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on the Rolle's and mean-value theorems. Solved: Use the MVT to show that \sqrt{y}-\sqrt{x}<\frac{y-x}{2\sqrt{x}} if 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/63/6f1ei4nQOm22.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cLEUSUiM8MAR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1146/cLEUSUiM8MAR.jpg</video:thumbnail_loc>

            <video:title>Axial potentials</video:title>

            <video:description><![CDATA[
Dipole potential varies sharply with position. Why does the value vanish on the bisector yet persist on the axis? We derive the exact axial formula to resolve this contrast.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1146/cLEUSUiM8MAR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VBMHObg7uc57</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/VBMHObg7uc57.jpg</video:thumbnail_loc>

            <video:title>Improper fractions (1)</video:title>

            <video:description><![CDATA[
Decompose improper rational functions where the numerator degree matches the denominator. This walkthrough shows how to perform long division to obtain a polynomial and a proper remainder before applying standard partial fraction rules. Master this step to avoid fundamental errors. Solved: 5. Resolve \frac{x^2+2x-4}{x^2-4} into partial fractions. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/VBMHObg7uc57.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x62eZ0P2JEbq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/x62eZ0P2JEbq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A worker tries to move a rock by applying a 360-N force to steel bar as shown. (a) Replace that force with an equivalent force-couple system at D. (b) Two workers attempt to move the same rock by applying a vertical force at A and another force at D. Determine these two forces if they are to be equivalent to the single force of part a. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/x62eZ0P2JEbq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739181268579.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ZIGxXQNubHGw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/563/ZIGxXQNubHGw.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of transitive relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/563/ZIGxXQNubHGw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OAMy_hiCCjPk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/OAMy_hiCCjPk.jpg</video:thumbnail_loc>

            <video:title>Far-field perpendicular symmetry</video:title>

            <video:description><![CDATA[
Derive the far-field on the perpendicular bisector. Why is the resultant vector antiparallel to the dipole moment? Watch the symmetry analysis. Solved: A dipole with moment \vec{p} (pointing from -q to +q) is centered at the origin. For a point P located on the perpendicular bisector at a distance z from the centre, derive the far-field expression for the electric field vector. Explicitly demonstrate why the field is antiparallel to \vec{p}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/OAMy_hiCCjPk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/75HXWtUaXVPC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/75HXWtUaXVPC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the evaluation of higher-order derivatives. Solved: Obtain the nth derivative of y=\frac{1}{1+x}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/75HXWtUaXVPC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_2YaBdk2YDAq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/_2YaBdk2YDAq.jpg</video:thumbnail_loc>

            <video:title>Axial and bisector comparison</video:title>

            <video:description><![CDATA[
Compare the field strength on the axis and bisector. How do you apply the distinct formulas for each position? Watch the calculation steps. Solved: A molecular dipole has a moment of p = 6.20 \times 10^{-30} \text{ C}\cdot\text{m}. Calculate the magnitude of the electric field at a point 5.00 \text{ nm} away from the centre of the molecule:(a) along the dipole axis and(b) along the perpendicular bisector. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/_2YaBdk2YDAq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8x-rW-nA6vCC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/55/8x-rW-nA6vCC.jpg</video:thumbnail_loc>

            <video:title>Odd and even functions</video:title>

            <video:description><![CDATA[
Meaning and examples of odd and even functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/55/8x-rW-nA6vCC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/msq4Hei5BkoD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/55/msq4Hei5BkoD.jpg</video:thumbnail_loc>

            <video:title>Meaning</video:title>

            <video:description><![CDATA[
An introduction to transcendental functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/55/msq4Hei5BkoD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/__6LrxX6BqPx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/__6LrxX6BqPx.jpg</video:thumbnail_loc>

            <video:title>Lewis' definition</video:title>

            <video:description><![CDATA[
This lesson defines acids as electron pair acceptors and bases as electron pair donors. You will learn to identify these species using Lewis dot structures and understand how this definition includes reactions without protons. Focus on coordinate covalent bond formation to master this concept.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/__6LrxX6BqPx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nqhfvAVeDB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/nqhfvAVeDB.jpg</video:thumbnail_loc>

            <video:title>An unknown charge</video:title>

            <video:description><![CDATA[
Three charges interact on a line. Given the net force on one, how do you deduce the magnitude and sign of an unknown charge? Watch the video to see the vector logic unfold. Solved: A point charge q_1 = +5.00 \mu\text{C} is fixed at the origin. An unknown charge q_2 is placed on the x-axis at x = -5.00 \text{ cm}. A third test charge q_3 = +2.50 \mu\text{C} is placed at x = 5.00 \text{ cm}. If the net electrostatic force on q_3 is 100.0 \text{ N} directed along the positive x-axis, determine the magnitude and sign of the unknown charge q_2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/nqhfvAVeDB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_NGgUMglCz1P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/_NGgUMglCz1P.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson defines surds as irrational roots that cannot be simplified to whole numbers or fractions. You will learn to distinguish between rational and irrational roots and understand why keeping exact values is vital for engineering and scientific precision.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/_NGgUMglCz1P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rAJobbmxEC-s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/rAJobbmxEC-s.jpg</video:thumbnail_loc>

            <video:title>General equation</video:title>

            <video:description><![CDATA[
General analysis of systems (control volumes) subjected to mass flow.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/rAJobbmxEC-s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7flsFm5LmYl8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/7flsFm5LmYl8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exert at B a 175-N force directed along line AB. Replace that force with an equivalent force-couple system at C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/7flsFm5LmYl8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739185495468.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ShoMHB35KV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1146/ShoMHB35KV.jpg</video:thumbnail_loc>

            <video:title>Axial dipole potential</video:title>

            <video:description><![CDATA[
Axial potential requires careful sign handling. How do you sum contributions from unequal distances on the dipole axis? This walkthrough applies superposition to find the exact value. Solved: An electric dipole consists of two point charges, q_1 = +15.0 \text{ nC} and q_2 = -15.0 \text{ nC}, separated by a distance of d = 8.00 \text{ cm}. Calculate the resultant electric potential at a point B located on the dipole axis, at a distance of r_1 = 4.00 \text{ cm} from the positive charge and r_2 = 12.0 \text{ cm} from the negative charge. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1146/ShoMHB35KV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xjTh5ZbM62ug</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/xjTh5ZbM62ug.jpg</video:thumbnail_loc>

            <video:title>Closed surfaces</video:title>

            <video:description><![CDATA[
Closed surfaces define inside and outside. Why must the area vector point outward to get the right sign for net flux? Watch to see how this rule reveals hidden charge.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/xjTh5ZbM62ug.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hVcqGPbqYqaJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/396/hVcqGPbqYqaJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on producing free-body diagrams for the force analysis of rigid bodies in three dimensions. Solved: Draw the free-body diagram to determine the components of reaction that the thrust bearing A and the cable BC exert on the bar. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/396/hVcqGPbqYqaJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737406611268.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/6BDBcNTNNvFi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/6BDBcNTNNvFi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on equations of lines, planes, curves and surfaces in three dimensions. Solved: Find equations of the tangent plane and normal line to the surfacex^4 + y^4 + z^4 = 3x^2 y^2 z^2at the point (1,1,1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/6BDBcNTNNvFi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ku3QO6P3ITlI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/Ku3QO6P3ITlI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: Block A has a mass of 40 kg, and block B has a mass of 8 kg. The coefficients of friction between all surfaces of contact are \mu_s = 0.20 and \mu_k = 0.15. If P = 40 N, determine(a) the acceleration of block B,(b) the tension in the cord. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/Ku3QO6P3ITlI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742304685666.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/G4GOdgCfUrkM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/G4GOdgCfUrkM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on equations of lines, planes, curves and surfaces in three dimensions. Solved: At what points does the normal line through the point (1,2,1) on the ellipsoid 4x^2 + y^2 + 4z^2 = 12 intersect the sphere x^2 + y^2 + z^2 = 102 ? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/G4GOdgCfUrkM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1xguTEpjlPAm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/1xguTEpjlPAm.jpg</video:thumbnail_loc>

            <video:title>Hydrolysis of salts</video:title>

            <video:description><![CDATA[
This lesson explains how salt ions react with water to alter the pH of a solution. You will learn why salts from weak acids or bases undergo hydrolysis while those from strong parents do not. Master these reaction mechanisms to predict if a salt solution will be acidic, basic, or neutral.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/1xguTEpjlPAm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/krLMTPzgx6UH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/krLMTPzgx6UH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on simplifying distributed loads on rigid bodies. Solved: Replace the distributed loading with an equivalent resultant force, and specify its location on the beam, measured from O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/krLMTPzgx6UH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740300814829.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Jo8T6ihCSw0b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/Jo8T6ihCSw0b.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying distributed loads on rigid bodies. Solved: Replace the distributed loading by an equivalent resultant force and couple moment acting at point A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/Jo8T6ihCSw0b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740300991380.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/k25t-SmV8tFB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/k25t-SmV8tFB.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
General analysis procedure for systems of particles under steady flow.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/k25t-SmV8tFB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w4mZgrfGjhPE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/w4mZgrfGjhPE.jpg</video:thumbnail_loc>

            <video:title>Types of collision</video:title>

            <video:description><![CDATA[
Collisions are classified as elastic or inelastic based on whether kinetic energy is conserved. This lesson explains the differences between objects bouncing apart or sticking together and shows how kinetic energy is lost to heat, sound or deformation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/w4mZgrfGjhPE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MuvFBDA_juZ1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/MuvFBDA_juZ1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying distributed loads on rigid bodies. Solved: The form is used to cast a concrete wall having a width of 5m. Determine the equivalent resultant force the wet concrete exerts on the form AB if the pressure distribution due to the concrete can be approximated as shown. Specify the location of the resultant force, measured from point B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/MuvFBDA_juZ1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740302152080.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Ji9j0s1LYBF8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/Ji9j0s1LYBF8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying distributed loads on rigid bodies. Solved: Currently eighty-five percent of all neck injuries are caused by rear-end car collisions. To alleviate this problem, an automobile seat restraint has been developed that provides additional pressure contact with the cranium. During dynamic tests the distribution of load on the cranium has been plotted and shown to be parabolic. Determine the equivalent resultant force and its location, measured from A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/Ji9j0s1LYBF8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740302879785.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Y2QDQMlZTnmc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/Y2QDQMlZTnmc.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying distributed loads on rigid bodies. Solved: Replace the loading by an equivalent resultant force and specify its location measured from A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/Y2QDQMlZTnmc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740303329322.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/UTNBaZI1-A2O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/403/UTNBaZI1-A2O.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on series - 2023/2024 mid-semester examination questions. Solved: Which of the following statements is not true about \sum_{n=1}^{\infty}x_n of real numbers? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/403/UTNBaZI1-A2O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/stv_8h5zpafH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/stv_8h5zpafH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: The tool is used to shut off gas valves that are difficult to access. If the force F is applied to the handle, determine the component of the moment created about the z axis of the valve. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/stv_8h5zpafH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738694239240.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/KVanjFXR7Qaq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/KVanjFXR7Qaq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: A multiple-drilling machine is used to drill simultaneously six holes in the steel plate shown. Each drill exert a clockwise couple of magnitude 40 lb.in. on the plate. Determine an equivalent couple formed by the smallest possible forces acting (a) at A and C, (b) at A and D, (c) on the plate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/KVanjFXR7Qaq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738752320963.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/96_cuat7u8Xe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/96_cuat7u8Xe.jpg</video:thumbnail_loc>

            <video:title>Systems with varying mass</video:title>

            <video:description><![CDATA[
Analyze systems where mass changes over time, such as a rocket or a leaking cart. This lesson applies the momentum principle to derive the equation of motion for these cases, showing how changing mass creates a thrust force that affects acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/96_cuat7u8Xe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hOx0VsRJ9Ax7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1008/hOx0VsRJ9Ax7.jpg</video:thumbnail_loc>

            <video:title>Simplifying indices (2)</video:title>

            <video:description><![CDATA[
Execute the systematic reduction of expressions involving negative and fractional indices through a detailed calculation. You will master the mechanical conversion of powers into reciprocal and radical forms to ensure absolute precision in complex algebraic simplification. Solved: 2. Simplify (16x^8)^{1/4} \times x^{-5}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1008/hOx0VsRJ9Ax7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YRMBgx0p_BcV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/YRMBgx0p_BcV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of real sequences. Solved: Determine whether or not the following sequences converge. If they do, find the limit.6.{\frac{\cos n}{n} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/YRMBgx0p_BcV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lGvxsBkzxk1B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/lGvxsBkzxk1B.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of real sequences. Solved: Determine whether or not the following sequences converge. If they do, find the limit. 10.{\frac{x^n}{n!}}, x\in IR. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/lGvxsBkzxk1B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7rBgnMGuZByL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/7rBgnMGuZByL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of real sequences. Solved: Determine whether or not the following sequences converge. If they do, find the limit. 12.{\sqrt{n^2+2n}-n}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/7rBgnMGuZByL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iFM1x3tL7NHq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/iFM1x3tL7NHq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of real sequences. Solved: Determine whether or not each of the following sequences converge. If they do, find the limit.14 \{{\frac {e^n - e^{-n}} {e^n + e^{-n}}}\}15 \{{\frac{n} {2n}}\} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/iFM1x3tL7NHq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vyhwiDoIFoTV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Thumbnails/387/vyhwiDoIFoTV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on boundedness of subsets of real numbers. Solved: Find the supremum and infimum for the following, if they exist:1.[-1,5] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Previews/387/vyhwiDoIFoTV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4FiK_RcfuaAW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/4FiK_RcfuaAW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of planar trusses by the method of joints. Solved: Using the method of joints, determine the force in each member of the truss shown. State whether each member is in tension (T) or compression (C). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/4FiK_RcfuaAW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1738920570035.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/PDsJ8k2YulYa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/PDsJ8k2YulYa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of planar trusses by the method of joints. Solved: Determine the force in each member of the truss and state if the members are in tension or compression. Assume all members are pin connected. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/PDsJ8k2YulYa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1738920965834.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/HlpA16pFSk1E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/HlpA16pFSk1E.jpg</video:thumbnail_loc>

            <video:title>Conductor in equilibrium</video:title>

            <video:description><![CDATA[
Inside a conductor at rest, the electric field is zero. Why does excess charge hide only on the surface and pile up at sharp points? Watch to see the physics of equilibrium.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/HlpA16pFSk1E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WP2RxAWuoN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1146/WP2RxAWuoN.jpg</video:thumbnail_loc>

            <video:title>Angular dipole potential</video:title>

            <video:description><![CDATA[
Dipole potential varies with angle. How do you calculate the value at an arbitrary position off the axis? This example applies the far-field formula to solve it. Solved: A certain polar molecule has a permanent electric dipole moment p = 2.40 \text{ D}, where 1 \text{ D} = 1 \text{ debye unit} = 3.34 \times 10^{-30} \text{ C}\cdot\text{m}. Calculate the electric potential due to this molecule at a point r = 25.0 \text{ nm} away at an angle of \theta = 45.0^\circ to the dipole axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1146/WP2RxAWuoN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XgxMTLOfvdRQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/XgxMTLOfvdRQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of planar trusses by the method of joints. Solved: Determine the forces in members AB, BC, and BD of the loaded truss. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/XgxMTLOfvdRQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1739013080053.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/QJJErEWpZKBj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Thumbnails/387/QJJErEWpZKBj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on boundedness of subsets of real numbers. Solved: Find the supremum and infimum for the following, if they exist:4.{n!:n\in IN} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Previews/387/QJJErEWpZKBj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S2j2_O4jbXTL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Thumbnails/387/S2j2_O4jbXTL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on boundedness of subsets of real numbers. Solved: Find the supremum and infimum for the following, if they exist:6.{\frac{(-1)^nn}{2n+1} } 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3vVUTeNGFa/Previews/387/S2j2_O4jbXTL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SoxkXgY-6rR0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/SoxkXgY-6rR0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of planar trusses by the method of joints. Solved: For the given loading, determine the zero-force members in each of the trusses shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/SoxkXgY-6rR0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1739013756698.JPEG</image:loc>
            </image:image>
            
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1739013724258.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/k9DvNnJDE0D_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/415/k9DvNnJDE0D_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of space trusses - using method of joints for space trusses. Solved: The truss shown consist of six members and is supported by a short link at A, two short links at B, and a ball-and-socket at D. Determine the force in each of the members for the given loading. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/415/k9DvNnJDE0D_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739184977188.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sXLab4LNFl6V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/sXLab4LNFl6V.jpg</video:thumbnail_loc>

            <video:title>Conservation of momentum</video:title>

            <video:description><![CDATA[
Calculate recoil velocity using the law of conservation of momentum. This walkthrough shows how to equate the initial zero momentum to the final sum of momenta to find the resulting backwards motion after throwing an anchor. Solved: An 85 \, kg fisherman stands still in a 120 \, kg boat on calm water. He throws a 15 \, kg anchor horizontally away from the boat at a speed of 4.0 \, m/s. Neglecting water resistance, calculate the recoil velocity of the boat and the fisherman. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/sXLab4LNFl6V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/35q_f7_XpY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/35q_f7_XpY.jpg</video:thumbnail_loc>

            <video:title>Surface angle</video:title>

            <video:description><![CDATA[
Angle determines flux. How do you handle a field that strikes a surface at a slant instead of head-on? Watch to see the correct angle for your calculation. Solved: A uniform electric field of magnitude E = 750 \text{ } \text{N/C} makes an angle of 30.0^{\circ} with a flat rectangular sheet of area A = 5.20\text{ }m^2. Calculate the electric flux through this sheet. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/35q_f7_XpY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CIqh1Y_Br8BR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/CIqh1Y_Br8BR.jpg</video:thumbnail_loc>

            <video:title>Non-conservative force</video:title>

            <video:description><![CDATA[
Calculate the magnitude of friction by accounting for the work done by non-conservative forces within the energy balance. This walkthrough shows how to find the energy lost to the environment by comparing the initial kinetic energy with the final potential energy at the stopping point. Solved: A 12 \, kg crate is launched up a ramp inclined at 25^\circ to the horizontal with an initial speed of 10 \, m/s. The crate slides up the ramp and stops after covering a distance of 4.5 \, m along the surface. Calculate the magnitude of the constant frictional force acting on the crate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/CIqh1Y_Br8BR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7zc3OIR4e9V1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/7zc3OIR4e9V1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: A 500-lb cylindrical tank, 8ft in diameter ,is to be raised over a 2-ft obstruction. A cable is wrapped around the tank and pulled horizontally as shown. Knowing that the corner of the obstruction at a is rough, find the required tension in the cable and the reaction at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/7zc3OIR4e9V1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736944528223.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/M_RwhPGe4knY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/M_RwhPGe4knY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: A 12-ft ladder, weighing 40 lb, leans against a frictionless vertical wall. The lower end of the ladder rest on rough ground, 4-ft away from the wall. determine the reactions at both ends. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/M_RwhPGe4knY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736946142191.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Zv71rU6x4iV0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/Zv71rU6x4iV0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: The uniform rod has a length l and weight W. It is supported at one end A by a smooth wall and the other end by a cord of length s which is attached to the wall. Determine the placement h for equilibrium. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/Zv71rU6x4iV0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737027949620.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/9LmTr2Ls791_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/9LmTr2Ls791_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: Determine the reactions at B and D when b=60mm. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/9LmTr2Ls791_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737303611305.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/tH9FzVnVp8Ps</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/tH9FzVnVp8Ps.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: Knowing that \theta=30^{\circ}, determine the reaction (a) at B, (b) at C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/tH9FzVnVp8Ps.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737303875752.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/rnFZZBm7WVpg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/rnFZZBm7WVpg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: The 50-kg homogeneous smooth sphere rests on the 30^\circ incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/rnFZZBm7WVpg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739472800173.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/2UO3iWBN_U8t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/2UO3iWBN_U8t.jpg</video:thumbnail_loc>

            <video:title>Safety bottleneck</video:title>

            <video:description><![CDATA[
Series capacitors split voltage unevenly. Which component hits its breakdown limit first in a mixed network? We identify the bottleneck to find the maximum safe input. Solved: A network consists of three capacitors. Capacitors C_1 = 15.0 \mu\text{F} and C_2 = 10.0 \mu\text{F} are connected in parallel. This parallel pair is then connected in series with a third capacitor, C_3 = 20.0 \mu\text{F}. If every capacitor in the network has a maximum safety rating (breakdown voltage) of 150 \text{ V}, determine (a) the maximum safe potential difference that can be applied across the entire network and (b) the maximum total energy that can be stored by the system without any component failing. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/2UO3iWBN_U8t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CSp8k_umIXtt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/CSp8k_umIXtt.jpg</video:thumbnail_loc>

            <video:title>Difference of sets</video:title>

            <video:description><![CDATA[
This lesson defines the set difference operation. It covers the notation and method for creating a set containing only the elements of one set that are not in another.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/CSp8k_umIXtt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ewzHfuDggh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/ewzHfuDggh.jpg</video:thumbnail_loc>

            <video:title>Charge redistribution</video:title>

            <video:description><![CDATA[
Touching identical conductors shares charge equally. How does sequential contact with a neutral sphere alter the initial charges and the final force? Watch the video to track the redistribution steps. Solved: Three identical metal spheres A, B, and C are used. Sphere A initially carries a charge of +8Q, sphere B carries -12Q, and sphere C is neutral. Spheres A and B are fixed at a distance r. In Procedure 1, sphere C is touched to sphere A, then touched to sphere B, and finally removed. In Procedure 2, starting with the original initial charges, sphere C is touched to sphere B, then touched to sphere A, and finally removed. Find the ratio of the final electrostatic force F_2 (after Procedure 2) to the force F_1 (after Procedure 1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/ewzHfuDggh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lcmeTHVeYM0D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/lcmeTHVeYM0D.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: The check valve is used to regulate pressure in the pipe. If the stiffness of the spring is k=80 kN/m and its uncompressed length is 120mm, determine the maximum pressure in the tank if the lever is to remain in the horizontal position as shown. The plug at A is circular. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/lcmeTHVeYM0D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737327303399.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/6DDdm_Bkoiwd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/511/6DDdm_Bkoiwd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating the work of a force. Solved: When s=0 , the block is at rest and the spring is uncompressed. The contact surface is smooth. Determine the workdone by each force acting on the block when s=0.5m 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/511/6DDdm_Bkoiwd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1747300769156.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/SjvUdkKBd0jB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/SjvUdkKBd0jB.jpg</video:thumbnail_loc>

            <video:title>Onto functions</video:title>

            <video:description><![CDATA[
This lesson defines onto or surjective functions where every element in the target set is mapped from at least one input. You will learn to verify this property by ensuring the range is equal to the codomain.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/SjvUdkKBd0jB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Yh_b_kI5l9gm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/Yh_b_kI5l9gm.jpg</video:thumbnail_loc>

            <video:title>Elastic collision</video:title>

            <video:description><![CDATA[
Calculate the final velocities of two balls after a head-on elastic collision. This walkthrough applies the conservation of both momentum and kinetic energy to solve a system of simultaneous equations for the individual velocities after impact. Solved: A 0.25 \, kg billiard ball moving at 3.5 \, m/s makes a head-on elastic collision with a stationary 0.40 \, kg ball. Calculate the final velocities of both balls after the impact. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/Yh_b_kI5l9gm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MSfIFagvi_qP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/MSfIFagvi_qP.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: To unload a bound stack of plywood from a truck, the driver first tilts the bed of the truck and then accelerates from rest. Knowing that the coefficients of friction between the bottom sheet of plywood and the bed are \mu_s = 0.40 and \mu_k = 0.30, determine(a) the smallest acceleration of the truck which will cause the stack of plywood to slide,(b) the acceleration of the truck which causes corner A of the stack to reach the end of the bed in 0.9 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/MSfIFagvi_qP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742301927634.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/FaIoOC7aE74i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/FaIoOC7aE74i.jpg</video:thumbnail_loc>

            <video:title>Improper fractions (2)</video:title>

            <video:description><![CDATA[
Apply polynomial long division to resolve improper fractions where the numerator degree exceeds the denominator. This advanced walkthrough demonstrates how to extract the quotient and decompose the resulting proper remainder into partial fractions. Accuracy in division is critical for success. Solved: 6. Resolve \frac{x^3+x^2+2}{(x-1)(x+2)} into partial fractions. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/FaIoOC7aE74i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w3iF5HiS1_r3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/w3iF5HiS1_r3.jpg</video:thumbnail_loc>

            <video:title>Calculating pH or pOH (2)</video:title>

            <video:description><![CDATA[
This lesson provides another worked example on determining pH and pOH from molar concentrations. You will learn to calculate ion concentrations from given pH values using antilogarithms. Master these multi-step problems to handle complex acidic and basic solution data with precision. Solved: Calculate [\text{H}_3\text{O}^+], pH, [\text{OH}^-], and pOH for each solution at 25??C: (a) 0.20 M HCl(b) 0.0012 M Mg(OH)2, used as an antacid in the treatment of heartburns 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/w3iF5HiS1_r3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t4FZYJTAdgts</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/t4FZYJTAdgts.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: A 10-kg box is dropped onto the body of a truck moving 50 km/h horizontally. If the coefficient of friction is 0.5, calculate how far the truck will move before the box stops slipping. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/t4FZYJTAdgts.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742303366152.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/MkqyzvR1pxtY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/MkqyzvR1pxtY.jpg</video:thumbnail_loc>

            <video:title>One-to-one functions</video:title>

            <video:description><![CDATA[
A one-to-one function ensures every input has its own unique output. You will learn to identify these mappings by confirming that different domain elements never share the same image. This rule is essential for reversing functions later in the chapter.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/MkqyzvR1pxtY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aNfZG9Z0hV9L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/aNfZG9Z0hV9L.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: The conveyor belt is moving at 6 m/s. If the coefficient of static friction between the conveyor belt and the 10-kg box B \mu_s = 0.2, determine the shortest time the conveyor can stop so that the box does not slip or move on the belt. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/aNfZG9Z0hV9L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742302837367.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dkQPmO8dh7am</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/dkQPmO8dh7am.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: Boxes A and B are at rest on a conveyor belt which is initially at rest. The belt is suddenly started in an upward direction so that slipping occurs between the belt and the boxes. Knowing that the coefficient of kinetic friction between the belt and the boxes are (\mu_k)_A = 0.30 and (\mu_k)_B = 0.32, determine the initial acceleration of each box. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/dkQPmO8dh7am.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742303173139.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/oqOccvDi3iRD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/oqOccvDi3iRD.jpg</video:thumbnail_loc>

            <video:title>Proper fractions</video:title>

            <video:description><![CDATA[
Define proper rational functions by comparing the degree of the numerator to the denominator. You must ensure the numerator's highest power is strictly less than the denominator's before beginning decomposition. This classification is the mandatory first step in solving any partial fraction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/oqOccvDi3iRD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_G8e1crTps1U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/_G8e1crTps1U.jpg</video:thumbnail_loc>

            <video:title>Inverse functions</video:title>

            <video:description><![CDATA[
This lesson explains how to reverse a function to find the original input from a given output. You will learn the conditions for a function to be invertible and how to derive its inverse formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/_G8e1crTps1U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KMnsAeXSZqIK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/KMnsAeXSZqIK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: A uniform cylinder is placed in a V -notched cradle. What is the largest horizontal acceleration that the cradle may have without causing the cylinder to climb out of the cradle? Neglect friction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/KMnsAeXSZqIK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742303550475.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/kO4AWWJFoSUG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/kO4AWWJFoSUG.jpg</video:thumbnail_loc>

            <video:title>Strength of an electrolyte</video:title>

            <video:description><![CDATA[
This lesson explains the difference between strong and weak electrolytes based on their degree of dissociation in water. You will learn how complete or partial ionisation affects electrical conductivity and chemical reactivity. Distinguishing these helps predict the behaviour of ionic solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/kO4AWWJFoSUG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XTk6c--4OGDD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/518/XTk6c--4OGDD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculus of scalar and vector fields - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/518/XTk6c--4OGDD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bEp5ZKWqX8m_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/bEp5ZKWqX8m_.jpg</video:thumbnail_loc>

            <video:title>Other kinds of functions</video:title>

            <video:description><![CDATA[
Classify functions by their equations, domains, and ranges. This lesson explains identity, polynomial, trigonometric, and modulus types. Recognising these specific forms is essential for solving higher-level mathematical problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/bEp5ZKWqX8m_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M_JwNxEUAfRM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/M_JwNxEUAfRM.jpg</video:thumbnail_loc>

            <video:title>Energy dissipation</video:title>

            <video:description><![CDATA[
Calculate the thermal energy dissipated by friction as a toolbox is dragged at an angle. This walkthrough shows how to determine the normal force and friction to calculate the total work done against motion. Solved: A 6.0 \, kg toolbox is dragged a distance of 5.0 \, m across a workshop floor by a rope exerting a force of 30 \, N at an angle of 25^\circ above the horizontal. If the coefficient of kinetic friction is 0.35, calculate the energy dissipated as heat (thermal energy) during this movement. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/M_JwNxEUAfRM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ziT6W_ZYFg8V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/421/ziT6W_ZYFg8V.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of problems involving dry friction - for rigid bodies. Solved: A 200-lb sliding door is mounted on a horizontal rail as shown. The coefficients of static friction between the rail and the door at A and B are 0.15 and 0.25 respectively. Determine the horizontal force that must be applied to the handle C in order to move the door to the right. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/421/ziT6W_ZYFg8V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741107149991.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/1Hn4WFAy3BSW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/1Hn4WFAy3BSW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: The water sprinkler positioned at the base of a hill releases a stream of water with the velocity of 15ft/s as shown. Determine the point B(x, y) where the water strikes the ground on the hill. Assume that the hill is defined by the equation y = (0.05x^2) ft and neglect the size of the sprinkler. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/1Hn4WFAy3BSW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742214390106.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/huv9_ZY5x7wR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/421/huv9_ZY5x7wR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of problems involving dry friction - for rigid bodies. Solved: The crate has a weight of 200 lb and a center of gravity at G. Determine the height h of the tow rope so that the crates slips and tips at the same time. What horizontal force P is required to do this? Take \mu_s = 0.4. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/421/huv9_ZY5x7wR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741109643477.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/_dJj1YG4AdV-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/541/_dJj1YG4AdV-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on problems involving derivation of the definition of a linear map from some known images. Solved: Let F: \mathbb{R}^2 \to \mathbb{R}^2 be a linear mapping such that F(1, 3) = (2, 4) and F(0, 1) = (1, 1). Find F(1, 2). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/541/_dJj1YG4AdV-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QIlwTsdoFGir</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/QIlwTsdoFGir.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on composition of linear maps. Solved: Define linear transformations S: P_n \to P_n and T: P_n \to P_n by S(p(x)) = p(x + 1) and T(p(x)) = xp'(x). Find (S . T) (p(x)) and (T . S) (p(x)). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/QIlwTsdoFGir.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nH-5nlaCzyHL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/nH-5nlaCzyHL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: Determine the normal floor reaction on each wheel of the engine stand. The engine weighs 750 lb and has a center of gravity at G. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/nH-5nlaCzyHL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738572892449.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/GaOfH8i9k26o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/GaOfH8i9k26o.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The small 0.6-kg block slides with a small amount of friction on the circular path of radius 3m in the vertical plane . If the speed of the block is 5m/s as it passes point A and 4m/s as it passes point B , determine the normal force exerted on the block by the surface at each of these two locations. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/GaOfH8i9k26o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744970136182.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dgHZXozUDUMs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/dgHZXozUDUMs.jpg</video:thumbnail_loc>

            <video:title>Force optimisation</video:title>

            <video:description><![CDATA[
Splitting a fixed charge changes the force between the parts. What specific ratio of the split yields the maximum repulsive force at a constant distance? Watch the video to see the calculus trick. Solved: A charge of 14.0 \mu\text{C} is to be split into two parts which are then separated by a distance of 7.0 \text{ mm}. Calculate the maximum possible magnitude of the electrostatic force that can act between these two parts. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/dgHZXozUDUMs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y_BGKlV8VbP3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/y_BGKlV8VbP3.jpg</video:thumbnail_loc>

            <video:title>Linear trig quotient</video:title>

            <video:description><![CDATA[
Spot a complex trigonometric quotient with mixed terms. Why split fractions when a master formula solves it instantly? This walkthrough shows you how to apply the coefficient rule by sight. Solved: Find \int \frac{4 \sin x + 2 \cos x}{3 \sin x + 5 \cos x} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/y_BGKlV8VbP3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E2UrnztiRurx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/E2UrnztiRurx.jpg</video:thumbnail_loc>

            <video:title>Inelastic collision</video:title>

            <video:description><![CDATA[
Calculate the final velocity of objects that stick together after a head-on collision. This walkthrough applies momentum conservation to an inelastic system, accounting for opposite directions and combined mass to determine the final magnitude and direction. Solved: A 2200 \, kg SUV travelling North at 18 \, m/s collides head-on with a 1300 \, kg car moving South at 25 \, m/s. The two vehicles lock bumpers and move together as a single unit after the crash. Calculate the final velocity (magnitude and direction) of the combined wreck. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/E2UrnztiRurx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jkUXaEUmzhXx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/jkUXaEUmzhXx.jpg</video:thumbnail_loc>

            <video:title>Shell induction</video:title>

            <video:description><![CDATA[
Conductors shield internal fields. How does a charge inside a cavity induce charge on the inner and outer surfaces? Watch to see the distribution logic. Solved: A solid conducting block contains a hollow cavity. A point charge of +5.50\text{ }\text{nC} is placed inside the cavity without touching the walls. The conducting block itself carries a net excess charge of -15.0\text{ }\text{nC}. Determine the amount of charge residing on(a) the inner wall of the cavity and(b) the outer surface of the block. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/jkUXaEUmzhXx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0KNnV_ZQH6HL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/0KNnV_ZQH6HL.jpg</video:thumbnail_loc>

            <video:title>The impulse-momentum theorem</video:title>

            <video:description><![CDATA[
Calculate the impulse and average force during a football collision by applying the impulse-momentum theorem. This walkthrough demonstrates how to account for direction changes when finding momentum difference and relates this change to contact time to determine the impact force. Solved: A 0.45 \, kg football is kicked towards a goal at 15 \, m/s. The goalkeeper punches it directly back in the opposite direction with a speed of 22 \, m/s. (a) Calculate the impulse delivered to the ball. (b) If the goalkeeper's fist is in contact with the ball for 8.0 \, ms, find the average force exerted on the ball. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/0KNnV_ZQH6HL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/u_bYXfzHhlHI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/u_bYXfzHhlHI.jpg</video:thumbnail_loc>

            <video:title>What is version control?</video:title>

            <video:description><![CDATA[
Version control is a time machine for your code. It is a system that tracks every change you make, allowing you to review a project's history and revert to any previous state without fear of losing work. This practice is non-negotiable for professionals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/u_bYXfzHhlHI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5xazPrn2qPo7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/140/5xazPrn2qPo7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on transformation of quadratic form to canonical forms. Solved: Express the quadratic form 5x_1^{2}-4x_1x_2+2x_2^2 in canonical form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/140/5xazPrn2qPo7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/24slLBSFDZgL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/24slLBSFDZgL.jpg</video:thumbnail_loc>

            <video:title>Symmetric difference of sets</video:title>

            <video:description><![CDATA[
This lesson defines the symmetric difference of two sets. It covers the notation and method for identifying the set of elements present in exactly one of the two sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/24slLBSFDZgL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DwiClZo6x6gG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1077/DwiClZo6x6gG.jpg</video:thumbnail_loc>

            <video:title>Priority on aromatic ring</video:title>

            <video:description><![CDATA[
Multiple functional groups on an aromatic ring compete for the parent name. Which group takes priority when assigning the principal suffix and numbering? This lesson establishes the strict IUPAC hierarchy for resolving these naming conflicts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1077/DwiClZo6x6gG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CmYlWWa2Wu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/CmYlWWa2Wu.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson introduces the core goals of the course and the essential role of trigonometry in engineering and science. You will see how angles and triangles form the basis for modelling waves, cycles, and rotations. Understand the course structure and the practical skills you will gain.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/CmYlWWa2Wu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BSL5dAQlX2ei</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/816/BSL5dAQlX2ei.jpg</video:thumbnail_loc>

            <video:title>Physical and chemical changes</video:title>

            <video:description><![CDATA[
This lesson defines and provides examples of physical changes, which alter form but not identity, and contrasts them with chemical changes (reactions), which result in new substances.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/816/BSL5dAQlX2ei.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lo7goAucoBxI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/140/lo7goAucoBxI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on applications of quadratic and canonical forms to conic sections. Solved: Show that the equation 9x^2-4xy+6y^2-2\sqrt{5}x-4\sqrt{5y}=15 is the equation of an ellipse. Determine the lengths of its major and minor axes. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/140/lo7goAucoBxI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kowGcTVBpfQ6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/526/kowGcTVBpfQ6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on Gram-Schmidt orthonormalization algorithm. Solved: Given the vectors v_1={(1,1,0)}, v_2={(2,1,1)},v_3={(3,0,2)}, obtain a set of orthonormal vectors which opan the same vector space, using the Gran-Schmidt procedure 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/526/kowGcTVBpfQ6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nPLlVrWuvkPW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/nPLlVrWuvkPW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: Determine the magnitude H_o of the angular momentum of the 2-kg sphere about point O (a) by using the vector definition of angular momentum and (b) by using an equivalent scalar approach. The center of the sphere lies in the x-y plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/nPLlVrWuvkPW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748951791541.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/jLJ3Ho6YCzlD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/jLJ3Ho6YCzlD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: Determine the angular momentum H_p of the particle about point P. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/jLJ3Ho6YCzlD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749043617974.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ez4H7JZ-4Q34</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/96/ez4H7JZ-4Q34.jpg</video:thumbnail_loc>

            <video:title>Worked examples II</video:title>

            <video:description><![CDATA[
More worked examples on transformation of coordinates. Solved: A line is defined by 3x+y=-5 in the x-y coordinates system. What is its equation in the t1-t2 coordinates system formed by rotating the x-y coordinates system by \theta=\frac{\pi}{6} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/96/ez4H7JZ-4Q34.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iJNH_wP68Nqn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/977/iJNH_wP68Nqn.jpg</video:thumbnail_loc>

            <video:title>Relative velocity (4)</video:title>

            <video:description><![CDATA[
This advanced walkthrough analyses how heading choice dictates the shortest crossing time versus the shortest crossing distance for a boat in a flowing current. You will resolve vector components to optimise transit parameters through analytical differentiation and geometric reasoning. Mastery of these optimisations is essential for precision in dynamics and navigation. Solved: 4. A boat with speed v_b needs to cross a river of width D. The current flows at speed v_c.(a) Which heading gives the shortest crossing time?(b) Which heading gives the shortest crossing distance? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/977/iJNH_wP68Nqn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LejBIM_txc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/LejBIM_txc.jpg</video:thumbnail_loc>

            <video:title>Angle measurement</video:title>

            <video:description><![CDATA[
Learn to measure rotation using degrees, minutes, seconds, radians, and gradians. You will master converting between these systems to maintain accuracy in engineering and surveying tasks. Understanding these units is the first step toward describing angles precisely in physics and advanced mathematics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/LejBIM_txc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4gS_iH8ruf-w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/4gS_iH8ruf-w.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: The 800-lb roller-coaster car start from rest on the track having the shape of a cylindrical helix. If the normal force of the tracks on the car has a transverse component of N_\theta=68lb, determine the transverse component of its velocity in t=4s. Also, what is the car's velocity when it descends 8ft? Neglect the size of the car. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/4gS_iH8ruf-w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749045826522.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/FHdVbmCRPqzu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1076/FHdVbmCRPqzu.jpg</video:thumbnail_loc>

            <video:title>More examples (1)</video:title>

            <video:description><![CDATA[
Polyfunctional compounds require strict priority rules. How do you choose the parent suffix when a ketone, alcohol, and carboxylic acid compete? This example applies the IUPAC hierarchy to resolve the naming conflict. Solved: \mathrm{CH_3COCH(OH)(CH_2)_2COOH}\begin{array}{ccccccccccccc} & & & & \mathrm{OH} & & & & & & & & \mathrm{O} \\ & & & & | & & & & & & & // & \\ \mathrm{CH_3} & - & \mathrm{C} & - & \mathrm{CH} & - & \mathrm{CH_2} & - & \mathrm{CH_2} & - & \mathrm{C} & & \\ & & || & & & & & & & & & \backslash & \\ & & \mathrm{O} & & & & & & & & & & \mathrm{O-H} \end{array} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1076/FHdVbmCRPqzu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nrxWQFj62P7l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/nrxWQFj62P7l.jpg</video:thumbnail_loc>

            <video:title>Battery-connected squeeze</video:title>

            <video:description><![CDATA[
Compressing a capacitor changes its storage. How does constant voltage affect charge flow and energy when plate separation shrinks? We calculate the exact increase in both quantities. Solved: A parallel-plate capacitor with a capacitance of 8.00 \text{ }\mu\text{F} is connected to a 25.0 \text{-V} DC power supply. While the power supply remains connected, the capacitor is compressed such that the separation distance between its plates is reduced to 20.0\% of its original value. Determine (a) the magnitude of the additional charge that flows from the power supply onto the plates and (b) the total increase in electrical potential energy stored in the capacitor. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/nrxWQFj62P7l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2dVPk04ISPeH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/2dVPk04ISPeH.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (1)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of some questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/2dVPk04ISPeH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QVAC8SOp2n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/QVAC8SOp2n.jpg</video:thumbnail_loc>

            <video:title>Inverse ratios</video:title>

            <video:description><![CDATA[
Use inverse functions to calculate an unknown angle when side lengths are given. This lesson explains how to reverse the primary ratios to find angles in degrees or radians. This skill is essential for solving practical problems in surveying, navigation, and structural engineering.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/QVAC8SOp2n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/db5swSlmOExZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1077/db5swSlmOExZ.jpg</video:thumbnail_loc>

            <video:title>More cyclic compounds</video:title>

            <video:description><![CDATA[
Complex cyclic structures with multiple substituents or unsaturation test naming precision. How do you assign correct locants when alkyl groups and double bonds compete for priority? This lesson applies strict IUPAC rules to resolve these structural edge cases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1077/db5swSlmOExZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2dID24X64u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/2dID24X64u.jpg</video:thumbnail_loc>

            <video:title>Angle measurement</video:title>

            <video:description><![CDATA[
Convert degree-minute-second values into decimal degrees and then into radians and gradians. Follow this step-by-step calculation to master exact unit conversions. These skills ensure high precision when handling angular measurements in technical surveying and engineering projects. Solved: Convert 75^{\circ}\text{ } 30^\prime \text{ } 45^{\prime\prime} to decimal degrees. Express your result in both radians (in terms of \pi) and in gradians. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/2dID24X64u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mR0Wy44sxK0g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/543/mR0Wy44sxK0g.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on graphical solution of erratic rectilinear motion problems. Solved: A motorcycle starts from rest at S=0 and travels along a straight road with the speed shown by the v-t graph. Determine the total distance the motorcycle travels until it stops when t=15s. Also plot the a-t and s-t graph. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/543/mR0Wy44sxK0g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742043098800.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/p0ok8xnNBd7h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/p0ok8xnNBd7h.jpg</video:thumbnail_loc>

            <video:title>Null point</video:title>

            <video:description><![CDATA[
Two like charges create a balance point between them. Where exactly must a third charge sit for the opposing forces to cancel out completely? Watch the video to find the null point. Solved: Two positive point charges are fixed on the x-axis: q_1 = +25.0 \mu\text{C} is at x = 3.00 \text{ m} and q_2 = +9.00 \mu\text{C} is at the origin. At what position x on the axis must a third charge q_3 be placed such that the net electrostatic force acting on it is zero? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/p0ok8xnNBd7h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SCWucRpuufb2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/561/SCWucRpuufb2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on identifying reflexive relations. Solved: Which of the following relations on the set of integers is reflexive?(a) a R b means that a\le b(b) a R b means that a(c) a R b means a=2b(d) a R b means a+b\ge 5(e) a R b means a and b have the same parity. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/561/SCWucRpuufb2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mzTDaEXzf2Mr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/mzTDaEXzf2Mr.jpg</video:thumbnail_loc>

            <video:title>Angular position and displacement</video:title>

            <video:description><![CDATA[
Measure a spinning body’s position using angles instead of metres. Calculate angular displacement as the change in this angle during rotation. This lesson explains how radians define distance along a circular path.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/mzTDaEXzf2Mr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_IKttN84sXDY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1076/_IKttN84sXDY.jpg</video:thumbnail_loc>

            <video:title>More examples (2)</video:title>

            <video:description><![CDATA[
Polyfunctional naming demands strict priority application. How do you assign locants when aldehyde, ketone, amino, and hydroxyl groups compete? This walkthrough applies the IUPAC hierarchy to resolve these conflicts correctly. Solved: Example 2:\mathrm{CH_3C(Cl)CHCH_2COCH_3}\begin{array}{ccccccccccc} \mathrm{H_3C} & - & \mathrm{C} & = & \mathrm{CH} & - & \mathrm{CH_2} & - & \mathrm{C} & - & \mathrm{CH_3} \\ & & | & & & & & & || & & \\ & & \mathrm{Cl} & & & & & & \mathrm{O} & & \end{array} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1076/_IKttN84sXDY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1x2VTpCVSkMh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1077/1x2VTpCVSkMh.jpg</video:thumbnail_loc>

            <video:title>Poly-aromatic compounds</video:title>

            <video:description><![CDATA[
Fused aromatic rings form complex poly-aromatic systems. How do you apply IUPAC rules to name these multi-ring structures correctly? This lesson defines the precise nomenclature for fused benzene derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1077/1x2VTpCVSkMh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9kjFwXRFchIm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/9kjFwXRFchIm.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (7)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/9kjFwXRFchIm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P92r_fDl9wQe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/P92r_fDl9wQe.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (4)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/P92r_fDl9wQe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_9Mkm8KOh60W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/61/_9Mkm8KOh60W.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Some examples on the determination of the derivative of a function at a given point. Solved: Given f:IR\to IR defined by f(x)=x^2. Is f differentiable at x=2? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/61/_9Mkm8KOh60W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1d6ZIdyT136D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/963/1d6ZIdyT136D.jpg</video:thumbnail_loc>

            <video:title>Web fonts</video:title>

            <video:description><![CDATA[
Integrate custom web fonts, like Google Fonts, into your project, ensuring your font variables correctly display the intended typefaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/963/1d6ZIdyT136D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ovbCYMSSA4zw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/ovbCYMSSA4zw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on calculating eigenvalues and eigenvectors. Solved: Obtain the eigenvalues and corresponding eigenvectors of the matrixA=\left[ \begin{array}{ccc} 3 & -5 \\ 1 & -1\\ \end{array} \right] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/ovbCYMSSA4zw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iz6Xh8F9PspQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/iz6Xh8F9PspQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of systems of particles under steady flow. Solved: A jet-engine noise suppressor consists of a movable duct which is secured directly behind the jet exhaust by cable A and deflects the blast directly upward. During a ground test, the engine sucks in air at the rate of 43kg/s and burns fuel at the rate of 0.8kg/s. The exhaust velocity is 720m/s. Determine the tension T in the cable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/iz6Xh8F9PspQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1752747868662.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/TlzKz_7i2GOe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/TlzKz_7i2GOe.jpg</video:thumbnail_loc>

            <video:title>Angular velocity and speed</video:title>

            <video:description><![CDATA[
Angular velocity measures how fast an object spins and its direction along an axis. Calculate this rate in radians per second and distinguish between scalar angular speed and the velocity vector. This fundamental quantity replaces linear velocity for all rotating systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/TlzKz_7i2GOe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Xv4Mizf4zW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/Xv4Mizf4zW.jpg</video:thumbnail_loc>

            <video:title>Inverse ratios</video:title>

            <video:description><![CDATA[
Calculate the sun’s angle of elevation using the inverse tangent ratio from a mast's height and shadow length. This step-by-step walkthrough shows how to find unknown angles from vertical and horizontal sides. This is a vital skill for surveying and civil engineering. Solved: A telecommunications mast 32 \text{ m} high casts a shadow 14 \text{ m} long on level ground. Calculate the angle of elevation of the sun to the nearest degree. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/Xv4Mizf4zW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1qVulPLu3U9J</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/816/1qVulPLu3U9J.jpg</video:thumbnail_loc>

            <video:title>Definition and states</video:title>

            <video:description><![CDATA[
This lesson defines matter and its classification by physical state - into solid, liquid, or gas.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/816/1qVulPLu3U9J.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_sik5Qtf2Lzb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/_sik5Qtf2Lzb.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (6)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/_sik5Qtf2Lzb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WIZUcbpCgl2L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/562/WIZUcbpCgl2L.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on identifying symmetric and anti-symmetric relations. Solved: Which of the following relation of the set Z of integers is symmetric?(a) aRb means that a\le b(b) aRb means that a(c) aRb means a=2b(d) aRb means a+b\ge 5(e) aRb means a and b has the same parity. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/562/WIZUcbpCgl2L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nSn-uUK3CPBF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/562/nSn-uUK3CPBF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on identifying symmetric and anti-symmetric relations. Solved: Which of the following relation is symmetric ?(a) The relation R on a set of university students where xRy if and only if x and y are in the same department. (b) The relation "is the brother of" on the children of a family.(c) The relation R in {1,2,3}, where R ={(1,1), (1,2), (3,2), (3,3)}.(d) The relation "is the mother of" on a set of residents in a country.(e) The relation R in IR where xRy if and only if x=y. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/562/nSn-uUK3CPBF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qS7tv5s_I36k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/564/qS7tv5s_I36k.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on identifying equivalence relations. Solved: Show that the relation R defined on the set \mathbb{Z}^+ by mRn implies that m and n have the same digits is an equivalence relation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/564/qS7tv5s_I36k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d8AYb6gh1ggA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/d8AYb6gh1ggA.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (5)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/d8AYb6gh1ggA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XYXc1PpkJTFv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/563/XYXc1PpkJTFv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on identifying transitive relations. Solved: Which of the following is transitive?(a) The relation R on a set of university students where xRy if and only if x and y are in the same department. (b) The relation "is the brother of" on the children of a family.(c) The relation R in {1,2,3}, where R ={(1,1), (1,2), (3,2), (3,3)}.(d) The relation "is the mother of" on a set of residents in a country.(e) The relation R in IR where xRy if and only if x=y. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/563/XYXc1PpkJTFv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BkcwK4v89OJS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/566/BkcwK4v89OJS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating equivalence classes and quotient sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/566/BkcwK4v89OJS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/p4pqy4M4eHe4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1078/p4pqy4M4eHe4.jpg</video:thumbnail_loc>

            <video:title>Isomerism</video:title>

            <video:description><![CDATA[
Same molecular formula does not guarantee identical compounds. Why do substances with matching atoms show different physical and chemical properties? This lesson defines isomerism and distinguishes structural from stereoisomerism based on atomic arrangement.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1078/p4pqy4M4eHe4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1VTkfZEzFSr_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/1VTkfZEzFSr_.jpg</video:thumbnail_loc>

            <video:title>Relations with linear variables</video:title>

            <video:description><![CDATA[
Connect linear displacement, velocity, and acceleration to their angular counterparts using the radius of rotation. Apply these conversion formulas to determine how fast a point on a spinning body moves along its curved path. These links are vital for switching between linear and rotational frames.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/1VTkfZEzFSr_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sofxYi7IWzTp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/566/sofxYi7IWzTp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating equivalence classes and quotient sets. Solved: Consider the set S = {1, 2, 3,.., 20} and the relation R = {xRy if x and y have the same remainder when divided by 4}; i . e, R = {xRy \to x - y = 4k : x, y \epsilon S, k \epsilon\mathbb{Z} }.(a) Show that R is an equivalence relation.(b) Obtain its equivalence classes. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/566/sofxYi7IWzTp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RLKIKIbGmbuT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/566/RLKIKIbGmbuT.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating equivalence classes and quotient sets. Solved: Let R be an equivalence relation on a set S and let [a] be the equivalence class of element a\in S . Show that (a) a\in[a] for all a\in S(b) [a]=[b] if and only if a\space R \space b(c) If [a] \ne[b] , then [a]\space n \space [b]=\emptyset 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/566/RLKIKIbGmbuT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KRtZSbmJJuZq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/KRtZSbmJJuZq.jpg</video:thumbnail_loc>

            <video:title>Properties (2)</video:title>

            <video:description><![CDATA[
Properties of partially-ordered sets - upper and lower bounds.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/KRtZSbmJJuZq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D6SLZP3aBZ28</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/D6SLZP3aBZ28.jpg</video:thumbnail_loc>

            <video:title>Totally-ordered sets</video:title>

            <video:description><![CDATA[
Meaning and examples of totally-ordered sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/D6SLZP3aBZ28.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/46dDb58dl1ZJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/46dDb58dl1ZJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (18)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: A bicyclist applies a 40-N force to the brake lever of her bicycle as shown. Determine the corresponding tension T transmitted to the brake cable. Neglect friction at the pivot O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/46dDb58dl1ZJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736930180900.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/AZOq8QT39La0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/AZOq8QT39La0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on identification and properties of partially-ordered sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/AZOq8QT39La0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K56IL17Iyz1K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/K56IL17Iyz1K.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on identification and properties of partially-ordered sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/K56IL17Iyz1K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GLFvwC8ZUS1m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/GLFvwC8ZUS1m.jpg</video:thumbnail_loc>

            <video:title>Well-ordered sets</video:title>

            <video:description><![CDATA[
Meaning and examples of well-ordered sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/GLFvwC8ZUS1m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K0PvanIPpwqp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/568/K0PvanIPpwqp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on identification and properties of partially-ordered sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/568/K0PvanIPpwqp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PNKdy6LTfM5D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/928/PNKdy6LTfM5D.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson explains rotation at a constant angular acceleration. Use equations based on linear motion formulas to solve problems. Calculate the position and speed of any steadily turning object.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/928/PNKdy6LTfM5D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/11Y0sYu_rvYP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/11Y0sYu_rvYP.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (9)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/11Y0sYu_rvYP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pAl1QG5a6uVr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/618/pAl1QG5a6uVr.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions</video:title>

            <video:description><![CDATA[
Evaluating limits of piecewise-defined functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/618/pAl1QG5a6uVr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/p9TdqXZhbTrJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/p9TdqXZhbTrJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on indeterminate forms. Solved: i) \lim_{x\to0}(\frac{\sin x}{x})^\frac{1}{x^2}=(\frac{0}{0})^\infty=1^\infty 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/p9TdqXZhbTrJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EiEjl9AppG0o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/EiEjl9AppG0o.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on indeterminate forms. Solved: i)\lim_{x\to0}\frac{10^x -e^x}{x} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/EiEjl9AppG0o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aShpYEtNkte9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/aShpYEtNkte9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on indeterminate forms. Solved: \lim_{x\to\infty}\frac{x^{\frac{3}{2}}logx}{\sqrt{1+x^4}} =\frac{\infty}{\infty} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/aShpYEtNkte9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f43TvLiTODCj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/f43TvLiTODCj.jpg</video:thumbnail_loc>

            <video:title>The complement of a set</video:title>

            <video:description><![CDATA[
Covers the definition of the complement of a set relative to a universal set. It explains how to determine the elements not present in a given set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/f43TvLiTODCj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FBo_tg0kBpBR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/614/FBo_tg0kBpBR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on removable discontinuities. Solved: How should the following functions be re-defined at the indicated point to be continuous there?(a) \frac{1+t^3}{1-t^2},t=-1 , (b) \frac{x^2-2}{x^4-4},x=\sqrt{2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/614/FBo_tg0kBpBR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S45bHtpMtk2B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/618/S45bHtpMtk2B.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of limits. Solved: Given that \lim_{x\to 0}\frac{\sin x}{x}=1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/618/S45bHtpMtk2B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BOcfyW6zYe1N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/BOcfyW6zYe1N.jpg</video:thumbnail_loc>

            <video:title>Acceleration vectors</video:title>

            <video:description><![CDATA[
This lesson defines the average acceleration vector and instantaneous acceleration, the derivative of the velocity vector. Any change in a velocity vector's magnitude or its direction constitutes an acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/BOcfyW6zYe1N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OR170p1IiVOz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/OR170p1IiVOz.jpg</video:thumbnail_loc>

            <video:title>Inverse trig pattern</video:title>

            <video:description><![CDATA[
Spot an inverse trig function multiplied by its derivative. Why use substitution when the power rule applies directly? This walkthrough shows you how to integrate by sight. Solved: Determine the integral \int \frac{\cos^{-1} x}{\sqrt{1 - x^{2}}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/OR170p1IiVOz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vTjyU7eMVhEP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/vTjyU7eMVhEP.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (11)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/vTjyU7eMVhEP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LqGALAy1argj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/LqGALAy1argj.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (16)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/LqGALAy1argj.mp4</video:content_loc>

          <video:duration>58</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zQuj8ecMYdEE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/613/zQuj8ecMYdEE.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on continuity of functions. Solved: Find the values of x for which the following functions are discontinuous:(a) f(x) = \begin{cases} 2x + 3, x \leq 4 \\ 7 + \frac {16} x, x > 4 \end {cases}(b) f(x) = \begin{cases} 0, x \leq 0 \\ \frac 1 2 - x, 0 < x < \frac 1 2 \\ \frac 1 2, x = \frac 1 2 \\ \frac 3 2 - x , \frac 1 2 < x < 1\end {cases} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/613/zQuj8ecMYdEE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dQy545muWVer</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/620/dQy545muWVer.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on evaluation of limits. Solved: \lim_{x \to 2} f(x) = \frac{|x-2|}{x^2 + x -6} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/620/dQy545muWVer.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4ryFZX2QlDlH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/613/4ryFZX2QlDlH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on continuity of functions. Solved: For what values of m will the following functions be continuous?(a) f(x) = \begin{cases} x^2, x \leq 2 \\ m- x^2, x > 2 \end {cases}(b) f(x) = \begin{cases} x^2 + 5, x > 2 \\ m(x + 1) + k, -1 < x \leq 2 \\ 2x^3 + x + 7, x \leq -1 \end {cases} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/613/4ryFZX2QlDlH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/81NJLbsO7M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/81NJLbsO7M.jpg</video:thumbnail_loc>

            <video:title>R or S assignment (2)</video:title>

            <video:description><![CDATA[
Chiral centres demand precise R-S assignment. How do you rank substituents and trace priorities when the lowest group faces forward? This walkthrough fixes the common wedge-dash trap. Solved: Questions: Do the following compounds have the R or the S configuration?(a)\begin{array}{ccc} & \mathrm{H} & \\ & | & \\ \mathrm{Br} - & \mathrm{C} & \cdots \mathrm{CH_3} \\ & \boldsymbol{\blacktriangle} & \\ & \mathrm{COOH} & \end{array} 2 - bromopropanoic acid 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/81NJLbsO7M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bIEgQMMtr2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/bIEgQMMtr2.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Get an overview of the course goals and the importance of static electricity in modern technology. This lesson sets the stage for mastering fundamental electromagnetic principles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/bIEgQMMtr2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/h7AFVr27tik7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/h7AFVr27tik7.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (12)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/h7AFVr27tik7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/k8ec_AJJcrgi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/k8ec_AJJcrgi.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (13)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/k8ec_AJJcrgi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J8o31_jwQ9X4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/662/J8o31_jwQ9X4.jpg</video:thumbnail_loc>

            <video:title>Clients and servers</video:title>

            <video:description><![CDATA[
The web operates on the client-server model, the fundamental architecture for all online communication. This lesson defines the client's role in requesting data and the server's role in responding to it. Mastering this request-response cycle is non-negotiable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/662/J8o31_jwQ9X4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3h92gnewIt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/3h92gnewIt.jpg</video:thumbnail_loc>

            <video:title>Atomic structure</video:title>

            <video:description><![CDATA[
Atoms consist of protons and electrons that determine the net electrical state of an object. Understand how the transfer of these subatomic particles creates ions and charged bodies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/3h92gnewIt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1uVd_IF_w0EV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/662/1uVd_IF_w0EV.jpg</video:thumbnail_loc>

            <video:title>IPs, domains and URLs</video:title>

            <video:description><![CDATA[
This lesson clarifies the relationship between the web's addressing components. We define the IP address as the server's true location, the **domain name** as its memorable alias, and the URL as the full, specific instruction to retrieve a resource.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/662/1uVd_IF_w0EV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i2uz7y0ubB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/i2uz7y0ubB.jpg</video:thumbnail_loc>

            <video:title>External charges</video:title>

            <video:description><![CDATA[
External charges create no net flux. Do charges outside the surface affect the total flux through it? See why they are ignored in this calculation. Solved: Charges of +4.00\text{ }\text{nC}, -3.00\text{ }\text{nC}, -9.00\text{ }\text{nC}, and +2.00\text{ }\text{nC} are contained inside a large rectangular container. Located just outside the container are additional charges of +5.00\text{ }\text{nC} and +8.00\text{ }\text{nC}. Determine the net electric flux passing through the surface of the container. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/i2uz7y0ubB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tlMBsAIzdlnh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1211/tlMBsAIzdlnh.jpg</video:thumbnail_loc>

            <video:title>Cylindrical capacitance</video:title>

            <video:description><![CDATA[
Curved conductors store energy differently. How does one derive capacitance when the field varies radially? This lesson resolves the geometry of the coaxial capacitor.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1211/tlMBsAIzdlnh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KOvfM4p7yCwG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7qZafmufII/Thumbnails/641/KOvfM4p7yCwG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on solving reducible higher-order ODEs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7qZafmufII/Previews/641/KOvfM4p7yCwG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ccc_Nudvz2fz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7qZafmufII/Thumbnails/641/Ccc_Nudvz2fz.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on solving reducible higher-order ODEs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7qZafmufII/Previews/641/Ccc_Nudvz2fz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E10Dgr8V4Gw-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7qZafmufII/Thumbnails/641/E10Dgr8V4Gw-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on solving reducible higher-order ODEs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7qZafmufII/Previews/641/E10Dgr8V4Gw-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4AqEsIrG8DjM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/4AqEsIrG8DjM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the collision of particles and their motion before and after collision. Solved: Car B weighing 3200 lb and travelling west at 30 mi/hr collides with car A weighing 3400 lb and travelling north at 20 mi/hr as shown. If the two cars become entangled and move together as a unit after the crash, compute the magnitude v of their common velocity immediately after the impact and the angle \theta made by the velocity vector with the north direction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/4AqEsIrG8DjM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748951100049.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JkfbqyKxXLv7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/164/JkfbqyKxXLv7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the collision of particles and their motion before and after collision. Solved: The 2-kg sphere is projected horizontally with a velocity of 10 m/s against the 10-kg carriage which is backed up by the spring with stiffness of 1600 N/m. The carriage is initially at rest with the spring un compressed. If the coefficient of restitution is 0.6, calculate the rebound velocity v, the rebound angle \theta, and the maximum travel of the carriage after impact. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/164/JkfbqyKxXLv7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748951526062.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/KlPGRVGwlUTB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/KlPGRVGwlUTB.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on solution of first-order ordinary differential equations. Solved: Solve the following differential equations:xydy=(y+1)(1-x)dx 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/KlPGRVGwlUTB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bIlQLrNvSfZW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/bIlQLrNvSfZW.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions</video:title>

            <video:description><![CDATA[
Piecewise functions use different rules for different parts of their domain. You will learn to identify these sub-domains and evaluate the function correctly for any given input. This is vital for defining functions that change behaviour across specific intervals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/bIlQLrNvSfZW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vugzd7o072Wa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/Vugzd7o072Wa.jpg</video:thumbnail_loc>

            <video:title>Stability of equilibrium</video:title>

            <video:description><![CDATA[
Zero net force does not guarantee stability. If you nudge the electron slightly, do the forces push it back or pull it further away? Watch the video to test the equilibrium. Solved: Two particles are fixed in place on an x-axis: a particle with charge q_1 = +9q is at the origin and a particle with charge q_2 = -q is at x = d. At what position x along the axis can a proton be placed so that it is in electrostatic equilibrium? Additionally, determine whether this equilibrium position is stable or unstable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/Vugzd7o072Wa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N-QNSXUTYm6a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/N-QNSXUTYm6a.jpg</video:thumbnail_loc>

            <video:title>More worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on solution of first-order ordinary differential equations. Solved: Solve the following DEs:(1+x^2)\frac{dy}{dx} +3xy=5x 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/N-QNSXUTYm6a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FiBd0NLFnCFD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/FiBd0NLFnCFD.jpg</video:thumbnail_loc>

            <video:title>One linear and one quadratic</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of mixed systems through substitution to determine points of intersection between linear and quadratic functions. You will master the reduction of two variables into a single quadratic equation to find precise coordinate solution sets. Solved: Worked Examples2. Solve the equationsy - x = 1x^2 + xy - 2y^2 = -5 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/FiBd0NLFnCFD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dZFdgkaP8eQk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/dZFdgkaP8eQk.jpg</video:thumbnail_loc>

            <video:title>Reciprocal transitions</video:title>

            <video:description><![CDATA[
Reciprocal integrands bridge trigonometric and logarithmic results. How do you handle secant integration versus definite integrals with negative bounds? We resolve both patterns with precise standard forms. Solved: Evaluate the following: (i) \int 4 \sec x \, dx. (ii) \int_{-e^{2}}^{-e} \frac{3}{x} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/dZFdgkaP8eQk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pjAbBKMjyhVu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/279/pjAbBKMjyhVu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the method of Lagrange multiplier for examining stationary points of a function of two variables subject to a constraint. Solved: Find the stationary points of the function V=x^2+y^2+z, subject to the condition x^2-z^2=1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/279/pjAbBKMjyhVu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l3H8a7vbW2x5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/54/l3H8a7vbW2x5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on the domain of real-valued functions. Solved: A function f: \mathbb{R} \rightarrow \mathbb{R} is defined such that f(x) = x^2. Describe the domain of f. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/54/l3H8a7vbW2x5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DIxWXNl1h8hv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/58/DIxWXNl1h8hv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on formal definition of limits at infinity. Solved: Prove that \lim_{x\to \infty}(\frac{1}{x}) =0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/58/DIxWXNl1h8hv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hmkZUNlopZWL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/669/hmkZUNlopZWL.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a direct overview of the course. We will define our objective - mastering HTML5 as a professional tool - and outline the structure we will follow to achieve it.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/669/hmkZUNlopZWL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t1Qy6k-UDcYc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/615/t1Qy6k-UDcYc.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on differentiation of functions. Solved: Show that \frac{d}{dx}|x|=\frac{x}{|x|} For x\ne0[Hint: |x|^2=x^2;\frac{d}{dx}|x|^2 =2|x|\frac{d}{dx}|x| ] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/615/t1Qy6k-UDcYc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vHia_zEZfPmf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/147/vHia_zEZfPmf.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of a rigid body undergoing general plane motion by locating an instantaneous centre of zero velocity. Solved: If C has a velocity of v_C = 3 m/s, determine the angular velocity of the wheel at the instant shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/147/vHia_zEZfPmf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744987250405.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/yVODAsSOm_8C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/88/yVODAsSOm_8C.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on boundary-value and initial-value problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/88/yVODAsSOm_8C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RoowC09Uip9x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/RoowC09Uip9x.jpg</video:thumbnail_loc>

            <video:title>Even and odd functions</video:title>

            <video:description><![CDATA[
Identify even and odd functions using symmetry. Even functions mirror across the y-axis; odd functions rotate through the origin. Spotting these patterns simplifies sketching and solving equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/RoowC09Uip9x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/31ubZvePnnU3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/31ubZvePnnU3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: Force P is supported by two cables and a bar. Point A lies in the yz plane, and points B and C lie in the xz plane. The compressive load that causes the bar to buckle and the breaking strength of each cable are specified below. If factors of safety against failure (see the footnote*) of 1.7 and 2.0 are to be used for cables and bars, respectively, determine the allowable force P that can be supported.MemberStrengthAO3000 lb compressionAB6000 lbAC5000 lbThe factor of safety against failure is defined to be the failure load for a member divided by the allowable load for the member. Thus, the largest load the member may be subjected to is its failure load divided by the factor of safety. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/31ubZvePnnU3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740069186116.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/1dbmIX92CsWo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/1dbmIX92CsWo.jpg</video:thumbnail_loc>

            <video:title>Rectangular superposition</video:title>

            <video:description><![CDATA[
Charges at rectangle corners pull in different directions. How do you resolve these diagonal and straight forces into components to find the true net push? Watch the video for the vector breakdown. Solved: Four identical point charges of +15.0 \mu\text{C} each are placed at the corners of a rectangular board. The board has a length of 80.0 \text{ cm} and a width of 20.0 \text{ cm}. Find the magnitude of the net electrostatic force acting on the charge located at the bottom-left corner due to the interactions with the other three charges. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/1dbmIX92CsWo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lm62QDNiZyFq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/84/lm62QDNiZyFq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on Newton's method of solution of equations in one variable. Solved: Verify that when Newton's method is used to compute \sqrt{R}, the sequence of iterates is defined by:x_{n+1} = \frac 1 2 (x_n + \frac R x_n ) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/84/lm62QDNiZyFq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kzfNh9tPv_VT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/669/kzfNh9tPv_VT.jpg</video:thumbnail_loc>

            <video:title>Generating your design</video:title>

            <video:description><![CDATA[
This lesson teaches you how to create a visual target for your project. You will use a professional AI prompt template to generate a high-quality UI Design for your personal portfolio website.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/669/kzfNh9tPv_VT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m2j0qSPFSC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/m2j0qSPFSC.jpg</video:thumbnail_loc>

            <video:title>Functions</video:title>

            <video:description><![CDATA[
A function is a rule that assigns exactly one output to every input. You will learn to distinguish functions from mere relations and use standard function notation correctly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/m2j0qSPFSC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xSydnxpQH_rN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/xSydnxpQH_rN.jpg</video:thumbnail_loc>

            <video:title>Two homogeneous quadratic equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of dual homogeneous quadratic systems by applying the y = mx substitution to reduce the system into a solvable single-variable quadratic. You will master the mechanical elimination of constant terms to determine all valid coordinate pairs with absolute precision. Solved: 3. Solve the equationsx^2 - xy + 7y^2 = 27x^2 - y^2 = 15 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/xSydnxpQH_rN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/isXaEz_YuFnj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/isXaEz_YuFnj.jpg</video:thumbnail_loc>

            <video:title>Hemisphere flux</video:title>

            <video:description><![CDATA[
Flux enters one side and leaves the other. How do you calculate flux through a curved surface when the field is uniform? Watch to see the symmetry trick. Solved: An imaginary Gaussian surface in the form of a hemisphere with a radius of 14.5\text{ }\text{cm} is placed in a uniform electric field of magnitude 6.20\text{ }\text{N/C}. The surface encloses no net charge. The field is perpendicular to the flat base and directed into the container. Calculate the electric flux through (a) the flat base and (b) the curved upper portion of the surface. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/isXaEz_YuFnj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EqMDnGNRbXtj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/EqMDnGNRbXtj.jpg</video:thumbnail_loc>

            <video:title>Work of external agent</video:title>

            <video:description><![CDATA[
Moving a charge takes work against the field. How do you calculate the energy needed to bring a charge from infinity? Watch to see the sign change. Solved: A 6\text{-}\mu\text{C} point charge is fixed at the origin, and a second point charge q_2 = -3 \text{ }\mu\text{C} is fixed on the x-axis at (4.00, 0) m. Calculate(i) The work done by an external agent to bring a 2\text{-}\mu\text{C} charge from infinity to point A at (0, 3.00) m at constant speed.(ii) The work done by the electric field on the 2\text{-}\mu\text{C} charge during this same move. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/EqMDnGNRbXtj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4h6_XcQEvJjY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/4h6_XcQEvJjY.jpg</video:thumbnail_loc>

            <video:title>Block and inline elements</video:title>

            <video:description><![CDATA[
This lesson explains the two main display behaviours of HTML elements. We will cover how block elements take up their own line, while inline elements sit within the flow of text.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/4h6_XcQEvJjY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/30b8jh98pohU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/30b8jh98pohU.jpg</video:thumbnail_loc>

            <video:title>Summing algebraic fractions</video:title>

            <video:description><![CDATA[
Review the addition of algebraic fractions by finding common denominators and combining numerators. This lesson establishes the forward process to ensure you understand how single rational expressions are formed before we begin the inverse process of decomposition into partial fractions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/30b8jh98pohU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OVpGbcqxeQ0c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/OVpGbcqxeQ0c.jpg</video:thumbnail_loc>

            <video:title>Planar superposition</video:title>

            <video:description><![CDATA[
Fields from sheets are uniform. How do you combine vectors from two parallel plates to find the net field in each region? Watch to see the superposition logic. Solved: Two large, parallel, non-conducting sheets carry uniform surface charge densities of \sigma_{1} = +9.4\mu C/m^{2} and \sigma_{2} = -6.1\mu C/m^{2} respectively. Find the magnitude of the net electric field in the regions (a) to the left of both sheets, (b) in the space between them, and (c) to the right of both sheets. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/OVpGbcqxeQ0c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/26XkmKqhoknF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/26XkmKqhoknF.jpg</video:thumbnail_loc>

            <video:title>Mixed integrand</video:title>

            <video:description><![CDATA[
Mixed transcendental integrands require separate standard forms for each term. How do you integrate logarithmic and inverse trigonometric functions in one sweep? We apply known results to resolve this combination. Solved: Evaluate the indefinite integral \int (2 \ln x + 3 \tan^{-1} x) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/26XkmKqhoknF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L2nbTOBQNx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/L2nbTOBQNx.jpg</video:thumbnail_loc>

            <video:title>Rational functions</video:title>

            <video:description><![CDATA[
Identify the values that make a denominator zero to determine the domain of a rational function. This walkthrough shows how to exclude these points to define the set of valid inputs. Solved: Let g(x) = \frac{15}{x-9}. Determine the domain of this function. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/L2nbTOBQNx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lXKMqt7Ax1Ru</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/788/lXKMqt7Ax1Ru.jpg</video:thumbnail_loc>

            <video:title>Project card (2)</video:title>

            <video:description><![CDATA[
In our second project card, we will implement the placeholder image we generated earlier, using the standard <img> element.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/788/lXKMqt7Ax1Ru.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vl3uzmKBTR15</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/vl3uzmKBTR15.jpg</video:thumbnail_loc>

            <video:title>HTML vocabulary</video:title>

            <video:description><![CDATA[
This lesson defines the core building blocks of any HTML page. We will clarify the difference between an element and a tag, and explain the roles of attributes, parents, children, and siblings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/vl3uzmKBTR15.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gjo4bKFraGmd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/Gjo4bKFraGmd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: The girl has a mass of 40 g and center of mass at G. If she is swinging to a maximum height defined by \theta = 60^\circ, determine the force developed along each of the four supporting posts such as AB at the instant \theta = 0^\circ. The swing is centrally located between the posts. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/Gjo4bKFraGmd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747071452940.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/UjhYnZ7QFHZc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/UjhYnZ7QFHZc.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions</video:title>

            <video:description><![CDATA[
Determine which interval contains the input to select the correct rule for calculation. This walkthrough demonstrates how to evaluate a piecewise function at a specific point. Precise matching ensures you obtain the correct output. Solved: A function is defined as f(x) = \begin{cases} 12-x, & x < 5 \\ 4x, & x \geq 5 \end{cases}. Evaluate the function at x = -3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/UjhYnZ7QFHZc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tKyduLGnSdlq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/tKyduLGnSdlq.jpg</video:thumbnail_loc>

            <video:title>Infinite line of charge</video:title>

            <video:description><![CDATA[
Field drops with distance from a line. How do you find the charge on a segment given the field strength? Watch to see the cylindrical Gaussian surface in action. Solved: The electric field measured at a perpendicular distance of 0.850\text{ }\text{m} from a very long uniform line of charge is 1500\text{ }\text{N/C}. Determine the amount of charge contained within a 4.50\text{ }\text{cm} segment of this line. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/tKyduLGnSdlq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UEITXXhmmAHi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/UEITXXhmmAHi.jpg</video:thumbnail_loc>

            <video:title>Algebraic inverse scaling</video:title>

            <video:description><![CDATA[
Algebraic fractions with sums and differences of squares yield inverse trigonometric results. How do you apply the correct scaling factor for arctan versus arcsin? We resolve this mixed integrand with precise standard forms. Solved: Evaluate the indefinite integral \int \left( \frac{5}{16 + x^{2}} + \frac{2}{\sqrt{7 - x^{2}}} \right) dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/UEITXXhmmAHi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kpcu8OYntcbl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/674/Kpcu8OYntcbl.jpg</video:thumbnail_loc>

            <video:title>Adding a favicon</video:title>

            <video:description><![CDATA[
This lesson covers how to add a custom icon to your browser tab. We will use the <link> tag to set the logo file we created earlier as our site's favicon.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/674/Kpcu8OYntcbl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UZhOXtryfysR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/UZhOXtryfysR.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (15)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/UZhOXtryfysR.mp4</video:content_loc>

          <video:duration>56</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RGhsFY6VfuUy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/671/RGhsFY6VfuUy.jpg</video:thumbnail_loc>

            <video:title>Generating placeholder media</video:title>

            <video:description><![CDATA[
We will use an AI image generator to create a professional placeholder image and a short video clip. These assets will be used for our project cards later in the course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/671/RGhsFY6VfuUy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MtJ_TyUMFhBP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/MtJ_TyUMFhBP.jpg</video:thumbnail_loc>

            <video:title>Insulating sphere</video:title>

            <video:description><![CDATA[
Charge fills the volume of an insulator. How does the field change from inside to outside the sphere? Watch to see the calculation logic. Solved: A solid plastic ball has a uniform distribution of positive charge throughout its volume. If the electric field magnitude at a distance r = R/2 from the centre (where R is the radius of the ball) is 1450\text{ } \text{N/C}, calculate the magnitude of the electric field at a point 3R from the centre. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/MtJ_TyUMFhBP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MW134yuSzg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/MW134yuSzg.jpg</video:thumbnail_loc>

            <video:title>Difference quotients</video:title>

            <video:description><![CDATA[
Calculate and simplify the change in a function over a small interval. This procedure is the essential algebraic bridge between basic functions and the definition of a derivative. Solved: For the function f(x) = 3x^2, evaluate the expression \frac{f(x+h) - f(x)}{h} and simplify your answer completely. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/MW134yuSzg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5LbXHCo9Cxbg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/5LbXHCo9Cxbg.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (17)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/5LbXHCo9Cxbg.mp4</video:content_loc>

          <video:duration>85</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gvYOyG7RQFsq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/671/gvYOyG7RQFsq.jpg</video:thumbnail_loc>

            <video:title>Choosing an icon library</video:title>

            <video:description><![CDATA[
This lesson explains why we use modern icon libraries instead of simple image files. We will choose a professional library and learn how to get the SVG code we will need to implement our icons later in this course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/671/gvYOyG7RQFsq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/euB7e_zErVCj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/euB7e_zErVCj.jpg</video:thumbnail_loc>

            <video:title>Mixed quadratic and reciprocal systems</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of simultaneous systems involving reciprocal and quadratic terms by applying algebraic identities and variable substitution. You will master the mechanical reduction of fractional constraints to solve for sum-product relationships and determine precise coordinate pairs. Solved: 4. Solve the equationsx^2 + y^2 = 25 \frac{1}{x} + \frac{1}{y} = \frac{7}{12} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/euB7e_zErVCj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C76kHAbkJRf5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/15/C76kHAbkJRf5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the scalar triple product of three vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/15/C76kHAbkJRf5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DjWhdiRc7PkN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/DjWhdiRc7PkN.jpg</video:thumbnail_loc>

            <video:title>Even and odd functions</video:title>

            <video:description><![CDATA[
Replace x with -x and simplify the expression to test for symmetry. This walkthrough demonstrates how to classify a function as even, odd, or neither. Mastering this check ensures accuracy when sketching graphs or solving calculus problems. Solved: Determine if the function g(x) = x^3 - 7x is even, odd, or neither. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/DjWhdiRc7PkN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uZ_c6wR_u6IY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/404/uZ_c6wR_u6IY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on partial derivatives - 2023/2024 mid-semester examination questions. Solved: Given the function f{(x,y)}=2x^3-3x^2y^2+ycosx . Find \frac{\partial^2 f} {\partial y 2 x} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/404/uZ_c6wR_u6IY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d2hlY7_s2P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/d2hlY7_s2P.jpg</video:thumbnail_loc>

            <video:title>Dielectric constant</video:title>

            <video:description><![CDATA[
An isolated capacitor sees its voltage drop when a dielectric fills the gap. How do you extract the material constant from this shift? We calculate kappa using conserved charge and reduced potential. Solved: An air-filled parallel-plate capacitor is charged such that the potential difference between its plates is 120\text{ V}. The capacitor is then disconnected from its power source, leaving it isolated. When a dielectric material is inserted to completely fill the gap between the plates, the potential difference is observed to drop to 30.0\text{ V}. Determine the dielectric constant of this material. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/d2hlY7_s2P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zCEB8dQwI1eM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/zCEB8dQwI1eM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: The tower crane is used to hoist a 2-Mg load upward at constant velocity. The 1.5-Mg jib BD and 0.5-Mg jib BC have centers of mass at G_1 and G_2 , respectively. Determine the required mass of the counterweight C so that the resultant moment produced by the load and the weights of the tower crane jibs about point A is zero. The center of mass for the counterweight is located at G_3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/zCEB8dQwI1eM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738689002743.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xi4jXph9tM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/xi4jXph9tM.jpg</video:thumbnail_loc>

            <video:title>Electron transfer count</video:title>

            <video:description><![CDATA[
Calculate the number of fundamental particles moved between surfaces during friction. This walkthrough applies the quantization formula to determine how many electrons produce a specific net charge. Solved: A student rubs a plastic ruler against a woollen sweater, resulting in a net charge of -4.80\text{ }\mu\text{C} on the ruler. Calculate the number of electrons transferred to the ruler. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/xi4jXph9tM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wRum1Z7ayb3u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/788/wRum1Z7ayb3u.jpg</video:thumbnail_loc>

            <video:title>Project card (3)</video:title>

            <video:description><![CDATA[
This lesson covers the <iframe> element. We will learn the professional method for embedding a third-party video into our final project card.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/788/wRum1Z7ayb3u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/14epoyh8393b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/14epoyh8393b.jpg</video:thumbnail_loc>

            <video:title>Off-axis potential</video:title>

            <video:description><![CDATA[
Rectangular charge arrangements require careful distance calculation. How do you apply the superposition principle to off-axis points? We sum the scalar potentials from each corner charge. Solved: Three point charges are fixed at the corners of a rectangular wooden frame. The frame has a width of 12.0 \text{ cm} and a height of 5.00 \text{ cm}. The charges are positioned as follows: a +6.00 \text{ } \mathrm{ \mu C} charge at the bottom-left corner, a +3.00 \text{ } \mathrm{ \mu C} charge at the top-left corner, and a -5.00 \text{ } \mathrm{ \mu C} charge at the bottom-right corner. Calculate the resultant electric potential at the empty top-right corner of the frame. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/14epoyh8393b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L6dRWoA5W0_S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/L6dRWoA5W0_S.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (10)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/L6dRWoA5W0_S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z8y7P7zr1DYL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/674/z8y7P7zr1DYL.jpg</video:thumbnail_loc>

            <video:title>What next?</video:title>

            <video:description><![CDATA[
You have now built the skeleton. This concluding lesson outlines your next logical step: learning CSS to add visual style to your structured HTML documents. The foundation is complete; the next stage is construction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/674/z8y7P7zr1DYL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QciqV8P5ljHA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/787/QciqV8P5ljHA.jpg</video:thumbnail_loc>

            <video:title>Adding icons</video:title>

            <video:description><![CDATA[
This lesson covers the professional way to add icons. We will learn how to get SVG code from a library like Heroicons and embed it in our HTML to create the skills and social media sections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/787/QciqV8P5ljHA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yzZ6EkpoZk2n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/787/yzZ6EkpoZk2n.jpg</video:thumbnail_loc>

            <video:title>Some refinements</video:title>

            <video:description><![CDATA[
This final lesson adds the professional finishing touches to our project. We will add our brand logo to the header and refactor our skills and social media links into semantic lists, using a specialised icon library for professional-grade accessibility.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/787/yzZ6EkpoZk2n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hvtafAvwEv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/hvtafAvwEv.jpg</video:thumbnail_loc>

            <video:title>Charge in mass</video:title>

            <video:description><![CDATA[
Link chemistry and physics by calculating the total positive charge within a known mass of a substance. Use molar mass and Avogadro's constant to find the number of protons present. Solved: A pure copper coin has a mass of 3.10\text{ g}. Given that the atomic mass of copper is 63.5\text{ g/mol} and its atomic number is 29, calculate the total positive charge contained in the protons of the coin. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/hvtafAvwEv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4cy1yfH-IBNj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/394/4cy1yfH-IBNj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on producing free-body diagrams for the force analysis of rigid bodies in two dimensions. Solved: Lifting Machine. Member AB of a machine weighs 40 lb with center of gravity at point C. Draw the FBD for member AB. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/394/4cy1yfH-IBNj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736822906291.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/laYkJY5AiFkR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/672/laYkJY5AiFkR.jpg</video:thumbnail_loc>

            <video:title>Main and section</video:title>

            <video:description><![CDATA[
This lesson covers how to structure the main content of our page. We will use the <main> element to wrap our primary content and <section> elements to create our distinct sections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/672/laYkJY5AiFkR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gO6AToFzIKqY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/gO6AToFzIKqY.jpg</video:thumbnail_loc>

            <video:title>Comments</video:title>

            <video:description><![CDATA[
This lesson covers the professional habit of writing comments in your code. We will explain the syntax for HTML comments and their critical role in documenting and debugging your work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/gO6AToFzIKqY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pe7OBsZdgXHZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/Pe7OBsZdgXHZ.jpg</video:thumbnail_loc>

            <video:title>Sets of numbers</video:title>

            <video:description><![CDATA[
In this lesson, we define the sets of natural numbers, integers, rational numbers, irrational numbers and real numbers along with their relationship using set inclusion. Standard notations for describing these sets are also mentioned.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/Pe7OBsZdgXHZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gicL55tZ0jIR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/814/gicL55tZ0jIR.jpg</video:thumbnail_loc>

            <video:title>What is chemistry?</video:title>

            <video:description><![CDATA[
This lesson formally defines our subject. We establish chemistry as the central science concerned with the composition, properties, and transformations of matter at the atomic and molecular level.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/814/gicL55tZ0jIR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ISpJ1sJTrv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/ISpJ1sJTrv.jpg</video:thumbnail_loc>

            <video:title>Non-uniform field</video:title>

            <video:description><![CDATA[
Flux changes when the field varies. How do you calculate flux through a cube face when the electric field depends on position? Watch to see the integration method. Solved: A Gaussian cube with an edge length of 2.20\text{ }\text{m} is placed with one corner at the origin and its edges along the x, y, z axes. The region contains a non-uniform electric field given by \vec{E} = (5.50x \hat{i} +2.50 \hat{j})\text{ }\text{N/C}, where x is in metres. Find (a) the net electric flux through the entire surface of the cube and (b) the net charge enclosed by the cube. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/ISpJ1sJTrv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IHrgS_kK6g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/IHrgS_kK6g.jpg</video:thumbnail_loc>

            <video:title>Radical functions</video:title>

            <video:description><![CDATA[
Ensure the expression under a square root is non-negative to find the domain of a radical function. You will solve a simple inequality to identify the range of allowed input values. Solved: Determine the domain of the function h(x) = \sqrt{x-18}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/IHrgS_kK6g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bAwb5kpjDrjq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/bAwb5kpjDrjq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cables DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at A and B. Assume that the hinge at B does not exert any axial thrust. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/bAwb5kpjDrjq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738571768656.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/I_dRmO_vYl3a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/816/I_dRmO_vYl3a.jpg</video:thumbnail_loc>

            <video:title>Atoms, molecules and ions</video:title>

            <video:description><![CDATA[
This lesson defines the fundamental particles constituting all matter. We establish the atom as an element's basic unit, a molecule as bonded atoms, and an ion as any atom or molecule with a net charge.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/816/I_dRmO_vYl3a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ta89mqeolir3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/Ta89mqeolir3.jpg</video:thumbnail_loc>

            <video:title>Solution of weak acids</video:title>

            <video:description><![CDATA[
This lesson examines the partial ionisation of weak acids and the use of the acid dissociation constant, Ka, to describe their equilibrium. You will learn to set up equilibrium expressions to determine the concentration of ions in solution. This theory is vital for calculating the pH of weak acids.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/Ta89mqeolir3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_3sCNdMboMMv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/816/_3sCNdMboMMv.jpg</video:thumbnail_loc>

            <video:title>Elements, compounds and mixtures</video:title>

            <video:description><![CDATA[
This lesson provides the formal definitions for elements, compounds, and mixtures. The key is to distinguish between the chemical bonds in compounds and the physical combination in mixtures.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/816/_3sCNdMboMMv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VLRIcGGXF7ZG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/VLRIcGGXF7ZG.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: The crossbar wrench is used to remove a lug nut from the automobile wheel. The machine applies a couple to the wrench such that his hands are a constant distant apart. Is it necessary that a=b in order to produce the most effective turning of the nut? Explain. Also, what is the effect of changing the shaft dimension c in this regard? The forces act in the vertical plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/VLRIcGGXF7ZG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738751632914.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WgTGeq_4v4gU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/WgTGeq_4v4gU.jpg</video:thumbnail_loc>

            <video:title>Redox reaction (1)</video:title>

            <video:description><![CDATA[
This lesson provides a worked solution for determining the volume of 0.500M potassium permanganate required to react completely with 20g of hydrated potassium oxalate. You will apply redox stoichiometry and molar mass calculations to resolve the titration volume required for full oxidation. Solved: Example 1:What volume of 0.500\text{M KMnO}_4 solution will react completely with 20g of \text{K}_2\text{C}_2\text{O}_4 \cdot \text{H}_2\text{O}? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/WgTGeq_4v4gU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f8wqWEyGSR_n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/816/f8wqWEyGSR_n.jpg</video:thumbnail_loc>

            <video:title>Characterization of matter</video:title>

            <video:description><![CDATA[
We characterise matter using its physical and chemical properties. This lesson defines these property types and explains how they correspond to physical and chemical changes, respectively.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/816/f8wqWEyGSR_n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ii5UYlSJ_5L_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/997/ii5UYlSJ_5L_.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Examine the non-commutative nature of Cartesian products and the distributive property over union and intersection operations. You will learn to calculate the cardinality of a product set by multiplying the sizes of individual sets and understand the null set property for empty collections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/997/ii5UYlSJ_5L_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/trJRp9xh4GPt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/trJRp9xh4GPt.jpg</video:thumbnail_loc>

            <video:title>Composite shapes</video:title>

            <video:description><![CDATA[
Break complex objects into simple parts like rectangles or circles to find their centre of mass. Treat each part as a point mass at its own centre and calculate the weighted average position. This lesson explains how to find the balance point for these combined shapes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/trJRp9xh4GPt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4XoaUFQHQO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/4XoaUFQHQO.jpg</video:thumbnail_loc>

            <video:title>Domains with inequalities</video:title>

            <video:description><![CDATA[
Find the domain when the variable is squared inside a square root. This walkthrough demonstrates how to solve quadratic inequalities to identify the valid interval for the function. Solved: Find the set of all real values of x for which h(x) = \sqrt{x^2 - 49} is defined. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/4XoaUFQHQO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P1BYDSB_JSEg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/P1BYDSB_JSEg.jpg</video:thumbnail_loc>

            <video:title>Surface-area-volume ratio</video:title>

            <video:description><![CDATA[
Small particles act differently. Why does shrinking a material boost its reactivity so much? See how the surface-area-volume ratio drives nanochemistry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/P1BYDSB_JSEg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/saH9Jn34FZLW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/saH9Jn34FZLW.jpg</video:thumbnail_loc>

            <video:title>Spin quantum number</video:title>

            <video:description><![CDATA[
This lesson defines the spin quantum number and explains how electron spin distinguishes paired and unpaired electrons within an orbital.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/saH9Jn34FZLW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gfzo7WzFY1So</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/Gfzo7WzFY1So.jpg</video:thumbnail_loc>

            <video:title>Similar surds</video:title>

            <video:description><![CDATA[
Similar surds are roots with the same value under the radical when in simplest form. This lesson teaches you to identify these like terms, which is the only way to correctly add or subtract surds in any algebraic expression.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/Gfzo7WzFY1So.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t4DrNbBYLrqI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Thumbnails/817/t4DrNbBYLrqI.jpg</video:thumbnail_loc>

            <video:title>Definition and classification</video:title>

            <video:description><![CDATA[
This lesson defines a chemical reaction as a rearrangement of atoms. We then introduce the primary classifications used to categorise these transformations, such as synthesis and decomposition.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qiZwBvwOkQ/Previews/817/t4DrNbBYLrqI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X1C3gahaQhAr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/X1C3gahaQhAr.jpg</video:thumbnail_loc>

            <video:title>Orientation of orbitals</video:title>

            <video:description><![CDATA[
This lesson explains how orbitals orient themselves in three-dimensional space. It relates each orientation to the magnetic quantum number and the distinct shapes of atomic orbitals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/X1C3gahaQhAr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fhzUvkVp2eea</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/820/fhzUvkVp2eea.jpg</video:thumbnail_loc>

            <video:title>Dalton's atomic theory</video:title>

            <video:description><![CDATA[
This lesson covers the four fundamental postulates of John Dalton's atomic theory, which established the first scientific model of the atom.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/820/fhzUvkVp2eea.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gi5twKqJQV5e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/gi5twKqJQV5e.jpg</video:thumbnail_loc>

            <video:title>Shortcomings of Rutherford's nuclear model</video:title>

            <video:description><![CDATA[
Rutherford's model is fundamentally unstable according to classical physics. An orbiting electron must radiate energy, causing it to rapidly spiral into the nucleus. This lesson explains why this contradiction forced the development of a quantum model of the atom.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/gi5twKqJQV5e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1Ywtanvd7wn6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/1Ywtanvd7wn6.jpg</video:thumbnail_loc>

            <video:title>Magnetic quantum number</video:title>

            <video:description><![CDATA[
This lesson defines the magnetic quantum number and its role in atomic structure. It explains how it determines the spatial orientation and distinction of orbitals within a subshell.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/1Ywtanvd7wn6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_aCs7KcPyKrV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/_aCs7KcPyKrV.jpg</video:thumbnail_loc>

            <video:title>The periodic table</video:title>

            <video:description><![CDATA[
This lesson reviews the structure of the modern periodic table, defining periods and groups. We establish the direct link between an element's position and its electronic configuration, which is the foundation for understanding periodicity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/_aCs7KcPyKrV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oSlmN7O71wFB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/819/oSlmN7O71wFB.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a brief overview of the course, outlining the key topics from Dalton's postulates to electronic configuration and periodic trends.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/819/oSlmN7O71wFB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D4_hTD7dhcms</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/D4_hTD7dhcms.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Is the operator T: \mathbb{C} \to \mathbb{C} defined by Tz = \bar {z} linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/D4_hTD7dhcms.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JnkRefsEfgRw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/829/JnkRefsEfgRw.jpg</video:thumbnail_loc>

            <video:title>Hybridization of orbitals</video:title>

            <video:description><![CDATA[
This lesson explains orbital hybridization - the mixing of atomic orbitals to form new, equivalent hybrid orbitals. Learn why this model is necessary to explain observed molecular geometries and bond angles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/829/JnkRefsEfgRw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Jc5e03uRO6qq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/Jc5e03uRO6qq.jpg</video:thumbnail_loc>

            <video:title>Spherical model</video:title>

            <video:description><![CDATA[
Carbon can form closed cages. How does a spherical shape change the stability of a molecule? Watch to see the geometry in action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/Jc5e03uRO6qq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wWW_TAfBNu2p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/wWW_TAfBNu2p.jpg</video:thumbnail_loc>

            <video:title>Classification (2)</video:title>

            <video:description><![CDATA[
This lesson expands on element classification by examining the periodic trends in metallic and non-metallic character. We will justify these trends across periods and down groups, linking them directly to effective nuclear charge and atomic size.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/wWW_TAfBNu2p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W_70ILfQ2X4j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/837/W_70ILfQ2X4j.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a brief overview of the course, outlining the key topics of the mole, chemical formulae, and solution concentration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/837/W_70ILfQ2X4j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Uf3TzA_Au64E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/Uf3TzA_Au64E.jpg</video:thumbnail_loc>

            <video:title>Electron affinity</video:title>

            <video:description><![CDATA[
This lesson defines electron affinity: the energy change when adding an electron to a neutral atom. We will then explain the periodic trends for this property, justifying them using effective nuclear charge and orbital stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/Uf3TzA_Au64E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ASHloc3L_dH_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/ASHloc3L_dH_.jpg</video:thumbnail_loc>

            <video:title>Ionic bonds</video:title>

            <video:description><![CDATA[
This lesson defines the ionic bond. We explain electron transfer from a metal to a non-metal - using Sodium chloride (NaCl) as a primary example. The resulting electrostatic attraction between the ions is the fundamental bonding force.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/ASHloc3L_dH_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/66ZiKfHlZl8A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/66ZiKfHlZl8A.jpg</video:thumbnail_loc>

            <video:title>Resonance structures</video:title>

            <video:description><![CDATA[
This lesson defines resonance for when a single Lewis structure fails. We examine Ozone (O3) and the Carbonate ion (CO32-). Learn to draw all valid contributing structures. Understand these average into a resonance hybrid - which represents the true electron delocalisation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/66ZiKfHlZl8A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B_ShD2It299c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/828/B_ShD2It299c.jpg</video:thumbnail_loc>

            <video:title>VSEPR theory</video:title>

            <video:description><![CDATA[
This lesson introduces Valence Shell Electron Pair Repulsion (VSEPR) theory. We use ABn notation - covering AB2, AB3, and AB4 domains - to predict electron and molecular geometry. Examples include Water (H2O), Beryllium chloride (BeCl2), Boron trifluoride (BF3), Methane (CH4), and Ammonia (NH3).  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/828/B_ShD2It299c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/70r_jC9Iccb1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/828/70r_jC9Iccb1.jpg</video:thumbnail_loc>

            <video:title>Examples (1)</video:title>

            <video:description><![CDATA[
This lesson is the first application of VSEPR theory. We demonstrate predicting molecular shapes for Tin(II) chloride (SnCl2), Sulfur tetrafluoride (SF4), Phosphorus pentafluoride (PF5), and Chlorine trifluoride (ClF3). Master the procedure for determining both electron and molecular geometry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/828/70r_jC9Iccb1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z2W2hNdLKM_m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/829/z2W2hNdLKM_m.jpg</video:thumbnail_loc>

            <video:title>Valence bond theory</video:title>

            <video:description><![CDATA[
This lesson introduces Valence Bond Theory, defining a chemical bond as the overlap of atomic orbitals. We explain the formation of sigma and pi bonds. This foundational theory is essential for understanding hybridization.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/829/z2W2hNdLKM_m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Dwt8xvtTIofk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/825/Dwt8xvtTIofk.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a brief overview of the course, outlining the key topics of chemical bonding, molecular geometry, and intermolecular forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/825/Dwt8xvtTIofk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/70Ji419D_7ns</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/829/70Ji419D_7ns.jpg</video:thumbnail_loc>

            <video:title>Examples (1)</video:title>

            <video:description><![CDATA[
This lesson provides initial examples of determining the hybridization (sp, sp2, sp3) of the central atom. We analyze the bonding in Methane (CH4), Ammonia (NH3), Ethene (C2H4), and Beryllium chloride (BeCl2). Master the method for identifying the correct hybridization from the Lewis structure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/829/70Ji419D_7ns.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nHxGwxQX64mg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/nHxGwxQX64mg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of higher-order derivatives using the Leibnitz's formula. Solved: Suppose y satisfies \frac{d^2y}{dx^2} +x^2y=\sin x 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/nHxGwxQX64mg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/un0x9nA3_FbP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/un0x9nA3_FbP.jpg</video:thumbnail_loc>

            <video:title>Cubic model (1)</video:title>

            <video:description><![CDATA[
Carbon atoms can form cubic cages. How does this box-like shape affect the strain within the structure? See the geometry explained here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/un0x9nA3_FbP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mzr0kDLd1OxU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/836/mzr0kDLd1OxU.jpg</video:thumbnail_loc>

            <video:title>Practice questions</video:title>

            <video:description><![CDATA[
Apply your knowledge to a comprehensive set of practice questions to confirm mastery of calculations and conceptual explanations. This practice is recommended before commencing 'Stoichiometry I'.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/836/mzr0kDLd1OxU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L6bQtWaElk_J</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/833/L6bQtWaElk_J.jpg</video:thumbnail_loc>

            <video:title>States of matter</video:title>

            <video:description><![CDATA[
This lesson differentiates the three primary states of matter - solid, liquid, and gas - based on particle separation and motion. We explain how the strength of intermolecular forces governs a substance's state and its physical properties.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/833/L6bQtWaElk_J.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/74T2opX_Hi7_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/833/74T2opX_Hi7_.jpg</video:thumbnail_loc>

            <video:title>Temperature and state changes</video:title>

            <video:description><![CDATA[
This lesson defines phase transitions (melting, boiling, etc.) and the associated thermal changes. We explain how temperature determines whether a substance's kinetic energy is sufficient to overcome intermolecular forces, resulting in a change of state.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/833/74T2opX_Hi7_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O_NdyuQNJCOg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/830/O_NdyuQNJCOg.jpg</video:thumbnail_loc>

            <video:title>Dispersion and dipole forces</video:title>

            <video:description><![CDATA[
This lesson covers the two main types of van der Waals forces: London dispersion forces, which exist in all molecules, and dipole-dipole forces, which exist only in polar molecules.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/830/O_NdyuQNJCOg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aVDHDij_eMxF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/830/aVDHDij_eMxF.jpg</video:thumbnail_loc>

            <video:title>Hydrogen bonding</video:title>

            <video:description><![CDATA[
This lesson defines hydrogen bonding as an especially strong type of dipole-dipole interaction that occurs when hydrogen is bonded to a highly electronegative atom (N, O, or F).  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/830/aVDHDij_eMxF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_F1_vdLt2n3s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/_F1_vdLt2n3s.jpg</video:thumbnail_loc>

            <video:title>Properties of gases</video:title>

            <video:description><![CDATA[
This lesson introduces Boyle's Law and Charles's Law, the foundational empirical relationships for gases. We explain the inverse relationship between pressure and volume (Boyle's) and the direct relationship between volume and absolute temperature (Charles's). Master the proportionality and corresponding mathematical forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/_F1_vdLt2n3s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_HBbNHRXOr21</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/832/_HBbNHRXOr21.jpg</video:thumbnail_loc>

            <video:title>Welcome and postulates</video:title>

            <video:description><![CDATA[
Welcome to the course; this lesson establishes the course roadmap. We introduce the Kinetic Theory of Matter by defining its core postulates which link the microscopic motion of particles to the macroscopic properties of gases. This theory forms the basis for all subsequent discussions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/832/_HBbNHRXOr21.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/II5T_H_Y_UzR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/219/II5T_H_Y_UzR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on images of linear maps. Solved: Let T:R^3\to IR^3 be defined by T(a,b,c)=(a-b+c,2a+b-c,-a-2b+2c). Determine the range and its dimension. Write out two vectors in range(T) and two vectors not in range(T). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/219/II5T_H_Y_UzR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/motTSPuv3L1B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/motTSPuv3L1B.jpg</video:thumbnail_loc>

            <video:title>Shifts and reflections</video:title>

            <video:description><![CDATA[
Apply transformation rules to modify base graphs without plotting new points. Adding constants shifts the curve vertically or horizontally, and multiplying by negative one reflects the shape across the coordinate axes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/motTSPuv3L1B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1gjHzBjQKkL3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/1gjHzBjQKkL3.jpg</video:thumbnail_loc>

            <video:title>Cubic model (2)</video:title>

            <video:description><![CDATA[
Bulk cubes have low surface area. Why does this limit their chemical reactivity compared to nano forms? See the ratio analysis here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/1gjHzBjQKkL3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ctDkcOuK8Zbn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/845/ctDkcOuK8Zbn.jpg</video:thumbnail_loc>

            <video:title>Ionic equations</video:title>

            <video:description><![CDATA[
This lesson defines and contrasts molecular, total ionic, and net ionic equations for reactions in aqueous solution. You will learn the rules for identifying strong electrolytes that dissociate into spectator ions, enabling the accurate derivation of the net ionic equation which represents only the chemically relevant species. Mastering this is crucial for understanding reaction mechanisms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/845/ctDkcOuK8Zbn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oSD_NB3csNth</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/851/oSD_NB3csNth.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a brief overview of the course, outlining the key topics of the equilibrium constant, Le Chatelier's principle, and acid-base chemistry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/851/oSD_NB3csNth.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_mRGifi80Gc7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/_mRGifi80Gc7.jpg</video:thumbnail_loc>

            <video:title>Empirical and molecular formulae</video:title>

            <video:description><![CDATA[
This lesson formally defines the empirical and molecular formulae. We establish the difference between the simplest whole-number ratio and the actual composition required for compound identification.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/_mRGifi80Gc7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rHmpy0aZn4js</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/rHmpy0aZn4js.jpg</video:thumbnail_loc>

            <video:title>Chemical formulae (3)</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates the full two-step process: determining the empirical formula from elemental percentages, then using the given molecular mass to derive the final molecular formula. Solved: An organic compound on analysis was found to contain 54.5% C, 9.2% H, and the rest as oxygen. If the molecular weight of the compound is 44 g mol-1, what are the empirical and molecular formulae of the compound? (the percentage expressed by mass) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/rHmpy0aZn4js.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xZ3Kwm3wAZ9w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/843/xZ3Kwm3wAZ9w.jpg</video:thumbnail_loc>

            <video:title>Change in oxidation number</video:title>

            <video:description><![CDATA[
This lesson introduces the change in oxidation number method for balancing complex redox reactions. You will learn to assign oxidation numbers to identify the atoms that are oxidised and reduced, then use the change in these numbers to determine the precise stoichiometric ratio of reactants required for conservation of charge and mass. This method is an alternative to the half-reaction approach.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/843/xZ3Kwm3wAZ9w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jvrJQ7fnkC05</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/845/jvrJQ7fnkC05.jpg</video:thumbnail_loc>

            <video:title>Assigning oxidation numbers</video:title>

            <video:description><![CDATA[
This lesson presents the full set of rules for the unambiguous assignment of oxidation numbers to elements in compounds or ions. You will learn the hierarchy of rules governing common elements like oxygen, hydrogen, and halogens, and how to use the sum of these values to determine the oxidation state of the central atom. Accurate assignment is the first mandatory step for balancing all redox equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/845/jvrJQ7fnkC05.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JGh1qtw9s9o9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/JGh1qtw9s9o9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
Worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: When the athlete releases the shot, it is 1.82 m above the ground and its initial velocity is v_o = 13.6 m/s. Determine the horizontal distance the shot travels from the point of release to the point where it hits the ground. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/JGh1qtw9s9o9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742213275750.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/YhUgox3cvaz_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/YhUgox3cvaz_.jpg</video:thumbnail_loc>

            <video:title>A composite shape</video:title>

            <video:description><![CDATA[
Find the centre of mass of a composite shape by treating the removed section as negative mass. This walkthrough demonstrates how to calculate the final coordinates by subtracting the moments of the smaller square from the original full square. Solved: A uniform square metal plate has sides of length 12 \, cm. A smaller square section with sides of 4 \, cm is cut out from the top-right corner of the plate. If the bottom-left corner of the original plate is at the origin (0,0), find the coordinates of the centre of mass of the remaining L-shaped plate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/YhUgox3cvaz_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/g2vzAQ1GCe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1067/g2vzAQ1GCe.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Electrons control every chemical reaction. Why do atoms bond in specific ways? Get the roadmap for this course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1067/g2vzAQ1GCe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qjqUKHL28j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/qjqUKHL28j.jpg</video:thumbnail_loc>

            <video:title>Exponential and logarithmic functions</video:title>

            <video:description><![CDATA[
Exponential graphs show rapid growth or decay, and logarithmic graphs are the inverse. Use horizontal and vertical asymptotes to sketch these curves accurately on the axes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/qjqUKHL28j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/92QmTKuvtC-q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/92QmTKuvtC-q.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 0.8-kg collar travels with negligible friction on the vertical rod under the action of the constant force P=20N . If the collar starts from rest at A , determine its speed as it passes point B. The value of R=1.6m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/92QmTKuvtC-q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746784786250.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/FitOPthAt27O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/FitOPthAt27O.jpg</video:thumbnail_loc>

            <video:title>Effect of concentration</video:title>

            <video:description><![CDATA[
Govern the direction of equilibrium shifts by analysing variations in reactant and product concentrations. You will master the mechanical application of Le Chateliers principle to predict how the system counteracts the addition or removal of species to restore equilibrium.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/FitOPthAt27O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Cw_7XnsG3O8A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/Cw_7XnsG3O8A.jpg</video:thumbnail_loc>

            <video:title>Effect of pressure</video:title>

            <video:description><![CDATA[
Analyse how changes in total pressure or volume dictate the shift of gaseous equilibria towards the side with fewer or more moles. You will master the mechanical relationship between partial pressures and the stoichiometric coefficients required to restore equilibrium stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/Cw_7XnsG3O8A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DpuztwdBg_SI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/DpuztwdBg_SI.jpg</video:thumbnail_loc>

            <video:title>Effect of temperature</video:title>

            <video:description><![CDATA[
Master the mechanical shift of equilibrium in response to temperature changes by identifying reactions as exothermic or endothermic. You will command the use of heat as a reactant or product to predict directional shifts and changes in the equilibrium constant.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/DpuztwdBg_SI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5ao1XEkyVH6r</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/5ao1XEkyVH6r.jpg</video:thumbnail_loc>

            <video:title>Entropy of phase transitions</video:title>

            <video:description><![CDATA[
This lesson explains how to calculate entropy changes during phase transitions using the enthalpy of fusion or vaporisation. You will learn to use the formula relating heat exchange to temperature at the melting and boiling points. This method allows for precise numerical determination of disorder changes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/5ao1XEkyVH6r.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5YaQ9PT4s2a4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/5YaQ9PT4s2a4.jpg</video:thumbnail_loc>

            <video:title>Free energy and spontaneity</video:title>

            <video:description><![CDATA[
Spontaneity depends on the balance between enthalpy and entropy changes. This lesson explains how a negative Gibbs free energy value confirms a reaction is feasible without external work. You will learn to use the sign of the free energy change to predict if a process occurs naturally.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/5YaQ9PT4s2a4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GLPUCzOUp8SA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/GLPUCzOUp8SA.jpg</video:thumbnail_loc>

            <video:title>Factors affecting free energy</video:title>

            <video:description><![CDATA[
This lesson explains how enthalpy and entropy changes interact to determine the sign of Gibbs free energy. You will learn to predict reaction spontaneity by comparing the magnitudes of heat energy released and disorder gained at specific temperatures.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/GLPUCzOUp8SA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sd5zAVNXH8wn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/Sd5zAVNXH8wn.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Gibbs free energy combines enthalpy and entropy to determine if a reaction is spontaneous. This lesson defines the function and explains why a negative change signifies a feasible process. You will learn to use this single value to predict chemical stability and reaction direction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/Sd5zAVNXH8wn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I0zvW438KbBV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/861/I0zvW438KbBV.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson introduces chemical kinetics as the study of how fast reactions happen and the paths they take. You will see how rates differ from equilibrium and why controlling speed is vital in industry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/861/I0zvW438KbBV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Skj4kN_AvyMD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/862/Skj4kN_AvyMD.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Reaction rate is the change in concentration of reactants or products over time. This lesson defines this fundamental concept and then distinguishes between average speed over a period and the exact instantaneous rate at a specific moment.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/862/Skj4kN_AvyMD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Bbh0gn_fBE51</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/Bbh0gn_fBE51.jpg</video:thumbnail_loc>

            <video:title>Predicting entropy change</video:title>

            <video:description><![CDATA[
Entropy change depends on the physical state and number of moles of substances. This lesson explains why gases have higher entropy than liquids or solids and how to predict if a reaction increases disorder. You will learn to determine the sign of entropy change by comparing reactant and product states.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/Bbh0gn_fBE51.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z98i0huw0XVR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/Z98i0huw0XVR.jpg</video:thumbnail_loc>

            <video:title>Second-order reactions</video:title>

            <video:description><![CDATA[
Calculate reaction time and concentration using the second-order integrated rate law. This walkthrough shows how to find rate constants from graphs of 1/[A] versus time. Apply these methods to solve kinetics problems with speed and accuracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/Z98i0huw0XVR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qkdILOGvSfpS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/qkdILOGvSfpS.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson explains the equilibrium between a solid salt and its dissolved ions in a saturated solution. You will learn to define the solubility product constant and understand its role in predicting if a substance will dissolve or form a precipitate.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/qkdILOGvSfpS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hPPmqbAirMT6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/hPPmqbAirMT6.jpg</video:thumbnail_loc>

            <video:title>Solubility product</video:title>

            <video:description><![CDATA[
This lesson defines the solubility product constant and explains how to write its equilibrium expression for sparingly soluble salts. You will learn to use this constant to calculate ion concentrations in a saturated solution and determine the mathematical relationship between Ksp and molarity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/hPPmqbAirMT6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rDg_QWodSzzh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/856/rDg_QWodSzzh.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a brief overview of the course, outlining the key topics of enthalpy, entropy, and Gibbs free energy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/856/rDg_QWodSzzh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fKvfC9lvdrE7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/fKvfC9lvdrE7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: The 60 g balancing weight is attached to the rim of a car wheel. When the car travels at the constant speed v_o, the path of A is the curate cycloid x = v_ot - r sin \frac {v_ot}{R}y = R - r cos \frac {v_ot}{R}(a) Show that the acceleration of the weight has a constant magnitude.(b) Calculate the magnitude of the force acting between the weight and the wheel if v_o = 90km/h, R = 0.40 m, and r = 0.25 m(neglect gravitational acceleration) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/fKvfC9lvdrE7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744388245488.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gxJrMaV4J4lH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/865/gxJrMaV4J4lH.jpg</video:thumbnail_loc>

            <video:title>Arrhenius' equation</video:title>

            <video:description><![CDATA[
Use the Arrhenius equation to calculate how temperature changes affect the rate constant of a reaction. You will learn to relate activation energy and the frequency factor to reaction speed. Master this formula to predict chemical behaviour under different thermal conditions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/865/gxJrMaV4J4lH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kNnnIsADsEcE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/kNnnIsADsEcE.jpg</video:thumbnail_loc>

            <video:title>Half-life (2)</video:title>

            <video:description><![CDATA[
Compare half-life for zero, first, and second-order reactions. Determine rate constants and predict how changes in initial concentration affect reaction time. Master these worked examples to solve kinetics problems with speed and accuracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/kNnnIsADsEcE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H7oDh22FzI7t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/H7oDh22FzI7t.jpg</video:thumbnail_loc>

            <video:title>Half-life</video:title>

            <video:description><![CDATA[
Define half-life as the time required for reactant concentration to drop by half. This lesson derives half-life equations for zero, first, and second-order reactions. Use these results to calculate exactly how long a chemical process takes to complete.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/H7oDh22FzI7t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5_rHyOlw1xVn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/865/5_rHyOlw1xVn.jpg</video:thumbnail_loc>

            <video:title>Activation Energy calculation</video:title>

            <video:description><![CDATA[
Calculate activation energy using the two-point Arrhenius equation. This walkthrough demonstrates how to determine energy barriers in kilojoules per mole when temperature and rate constants change. Master these steps to predict how thermal changes impact chemical reaction speeds.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/865/5_rHyOlw1xVn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B5IH1nZj2_V4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/B5IH1nZj2_V4.jpg</video:thumbnail_loc>

            <video:title>Half-life (1)</video:title>

            <video:description><![CDATA[
Calculate half-life and rate constants for zero and first-order reactions. This walkthrough solves problems involving ammonia decomposition and pesticide decay. Use these methods to determine how much chemical remains after a specific time.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/B5IH1nZj2_V4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ce7EUb_d97RC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/Ce7EUb_d97RC.jpg</video:thumbnail_loc>

            <video:title>Second-order reactions</video:title>

            <video:description><![CDATA[
Second-order reactions depend on concentration squared. You will master the integrated rate law and learn to identify these reactions through linear graphs of one over concentration against time.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/Ce7EUb_d97RC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vmJoP58tttpy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/vmJoP58tttpy.jpg</video:thumbnail_loc>

            <video:title>First-order reactions</video:title>

            <video:description><![CDATA[
First-order reactions depend on one reactant concentration. You will master the integrated rate law formula and learn to identify these reactions using linear graphs of the natural log against time.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/vmJoP58tttpy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LlVdNBawi869</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/LlVdNBawi869.jpg</video:thumbnail_loc>

            <video:title>Equilibrium constants</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the equilibrium constant for a redox reaction using standard cell potential values. You will work through examples to relate the thermodynamics of a cell to its state of chemical equilibrium.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/LlVdNBawi869.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gc_S15j5FegU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/868/gc_S15j5FegU.jpg</video:thumbnail_loc>

            <video:title>Inert electrodes</video:title>

            <video:description><![CDATA[
This lesson explains the role of inert electrodes like platinum and graphite in galvanic cells where reactants are not solid metals. You will learn how these electrodes provide a surface for electron transfer without participating in the reaction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/868/gc_S15j5FegU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6Z71g5b5tUaH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/868/6Z71g5b5tUaH.jpg</video:thumbnail_loc>

            <video:title>Structure</video:title>

            <video:description><![CDATA[
This lesson explains the physical components of a galvanic cell, including the anode, cathode, and salt bridge. You will learn how these parts work together to convert spontaneous chemical reactions into electrical energy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/868/6Z71g5b5tUaH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FDC_ksp1bwez</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/868/FDC_ksp1bwez.jpg</video:thumbnail_loc>

            <video:title>Cell notation</video:title>

            <video:description><![CDATA[
This lesson explains the standard cell notation used to represent galvanic cells compactly. You will learn how to write the anode and cathode components, including the salt bridge, using standard chemical symbols.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/868/FDC_ksp1bwez.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SJ9aDY3SxtJe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/868/SJ9aDY3SxtJe.jpg</video:thumbnail_loc>

            <video:title>Cell reactions</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to derive the balanced overall chemical equation for a galvanic cell directly from its standard cell notation. You will work through examples to correctly separate anode and cathode reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/868/SJ9aDY3SxtJe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SUAuPuQG7V2z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/SUAuPuQG7V2z.jpg</video:thumbnail_loc>

            <video:title>Electrode potential</video:title>

            <video:description><![CDATA[
This lesson explains electrode potential as a measure of an element's tendency to gain electrons. You will learn how standard reduction potentials are determined and used to calculate the overall electromotive force of a cell.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/SUAuPuQG7V2z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gAdYyJ6HZYpC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/gAdYyJ6HZYpC.jpg</video:thumbnail_loc>

            <video:title>Standard cell potential (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the standard cell potential using reduction potential values. You will work through examples to identify electrodes and determine cell notation for spontaneous redox reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/gAdYyJ6HZYpC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wjne_JDk6wkt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/Wjne_JDk6wkt.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson defines electrolytic cells as systems using external electricity to drive non-spontaneous chemical reactions. You will learn the fundamental differences between these cells and galvanic cells.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/Wjne_JDk6wkt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GZwpdgBORKCR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/GZwpdgBORKCR.jpg</video:thumbnail_loc>

            <video:title>Mass deposited</video:title>

            <video:description><![CDATA[
Calculate the mass of metal deposited at the cathode using current and time. This lesson provides step-by-step solutions for practical problems involving copper and gold. It is the direct application of Faraday’s laws to quantitative electrolysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/GZwpdgBORKCR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jHY0Tj_UeiBh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/jHY0Tj_UeiBh.jpg</video:thumbnail_loc>

            <video:title>Stoichiometric values</video:title>

            <video:description><![CDATA[
Calculate the number of electrons, gas molecules, and oxidation states using Faraday’s laws and Avogadro’s number. This walkthrough relates electrical charge to chemical stoichiometry during electrolysis. Use these steps to solve quantitative problems involving current, time, and substance amount.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/jHY0Tj_UeiBh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lHhInqhp04Sa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/870/lHhInqhp04Sa.jpg</video:thumbnail_loc>

            <video:title>Current passed</video:title>

            <video:description><![CDATA[
Calculate mass, valency, and atomic mass for substances sharing the same current in series cells using Faraday's first and second laws. This walkthrough demonstrates how to compare chemical equivalents and identify unknown metals to solve multi-step electrolysis problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/870/lHhInqhp04Sa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CQ0T4z9sXGG7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/873/CQ0T4z9sXGG7.jpg</video:thumbnail_loc>

            <video:title>Types of radiation</video:title>

            <video:description><![CDATA[
Identify alpha, beta, and gamma radiation by their charge and ability to pass through materials. This lesson explains how each type of radiation is produced during nuclear decay and how they behave in an electric field.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/873/CQ0T4z9sXGG7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sg50A6Og92sU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/873/Sg50A6Og92sU.jpg</video:thumbnail_loc>

            <video:title>Balancing nuclear reactions</video:title>

            <video:description><![CDATA[
When a nucleus decays multiple times, tracking the changes becomes tricky. What happens to mass and atomic numbers after successive emissions? We solve three challenging problems step-by-step to show you the exact method.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/873/Sg50A6Og92sU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O3NXOy49uR2Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/873/O3NXOy49uR2Y.jpg</video:thumbnail_loc>

            <video:title>Nuclear stability</video:title>

            <video:description><![CDATA[
Some atomic nuclei last forever while others fall apart in seconds. What determines whether a nucleus stays stable or decays? This lesson reveals the hidden factors that control nuclear stability and predict which atoms will remain intact.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/873/O3NXOy49uR2Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cKLRmwpL2qwp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/cKLRmwpL2qwp.jpg</video:thumbnail_loc>

            <video:title>Internal motion</video:title>

            <video:description><![CDATA[
Calculate the shift of a plank on ice as a painter moves across it. This walkthrough uses the fact that the system's centre of mass remains stationary due to zero external horizontal force, allowing you to relate the painter's displacement to the plank's opposite movement. Solved: A 60 \, kg painter stands at one end of a 3.0 \, m long wooden plank (mass 40 \, kg) resting on a very smooth, icy surface. The painter walks from one end of the plank to the other to reach his tools. Calculate the distance the plank shifts in the opposite direction relative to the ice. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/cKLRmwpL2qwp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8aFxJ9MlSGi6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/673/8aFxJ9MlSGi6.jpg</video:thumbnail_loc>

            <video:title>Building your experience table</video:title>

            <video:description><![CDATA[
This lesson introduces the <table> element and its core children: <thead>, <tbody>, <tr>, <th>, and <td>. We will then use this knowledge to build a complete, semantically correct table to display your education or work experience.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/673/8aFxJ9MlSGi6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hiA94RgKb4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/hiA94RgKb4.jpg</video:thumbnail_loc>

            <video:title>Semicircles</video:title>

            <video:description><![CDATA[
Review worked examples to identify semicircle equations containing square roots. Extract the centre and radius directly from the formula, then use the positive or negative sign to sketch the upper or lower curve accurately. Solved: Sketch the graph of the function k(x) = \sqrt{81 - x^2} and state its domain. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/hiA94RgKb4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qqrvCHxkxY1N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/874/qqrvCHxkxY1N.jpg</video:thumbnail_loc>

            <video:title>Nuclear fusion</video:title>

            <video:description><![CDATA[
Light nuclei repel each other, yet they combine in the sun to produce massive energy. What force overcomes this natural resistance, and what specific conditions allow this fusion to occur?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/874/qqrvCHxkxY1N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U3avCIsqEBSk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/U3avCIsqEBSk.jpg</video:thumbnail_loc>

            <video:title>Triangular superposition</video:title>

            <video:description><![CDATA[
Charges at triangle corners exert forces at angles. How do you combine these perpendicular pulls and pushes to find the exact net force on one charge? Watch the video for the vector solution. Solved: Three point charges are fixed at the vertices of a right-angled frame. The charges are q_1 = +12.0 \text{ nC}, q_2 = -6.00 \text{ nC}, and q_3 = +10.0 \text{ nC}. The charges are arranged such that q_2 is at the right-angle vertex, with q_1 located 8.00 \text{ m} directly above it and q_3 located 6.00 \text{ m} to its right. Determine the magnitude and direction of the net electrostatic force acting on q_3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/U3avCIsqEBSk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ykzAwJQrtVHA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/874/ykzAwJQrtVHA.jpg</video:thumbnail_loc>

            <video:title>Nuclear fission</video:title>

            <video:description><![CDATA[
Heavy nuclei store dangerous energy within their core. What triggers them to split, and how does one break cause many others to follow? We reveal the process that turns a tiny particle into a massive energy source.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/874/ykzAwJQrtVHA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nTyVlcCI7QwI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/nTyVlcCI7QwI.jpg</video:thumbnail_loc>

            <video:title>Effects on basicity</video:title>

            <video:description><![CDATA[
Electron shifts change how molecules accept protons. Why do some groups boost basicity while others kill it? See the electronic rules at play.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/nTyVlcCI7QwI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YMSiVmJKu0H8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/875/YMSiVmJKu0H8.jpg</video:thumbnail_loc>

            <video:title>Uses of radioisotopes</video:title>

            <video:description><![CDATA[
Radioactive materials seem dangerous, yet they save lives daily. How can something that harms also heal, and what makes radioisotopes valuable in medicine, industry, and archaeology? The answer reveals why we depend on these unstable atoms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/875/YMSiVmJKu0H8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ykWR65r3ZpCz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/ykWR65r3ZpCz.jpg</video:thumbnail_loc>

            <video:title>Verifying set equality</video:title>

            <video:description><![CDATA[
A worked problem showing how to prove two sets are equal by demonstrating that each set is a subset of the other.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/ykWR65r3ZpCz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ak17QcyKe2X_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/Ak17QcyKe2X_.jpg</video:thumbnail_loc>

            <video:title>Power sets</video:title>

            <video:description><![CDATA[
A methodical walkthrough of how to list the objects of a power set is explained.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/Ak17QcyKe2X_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/segW5sJinf1Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/segW5sJinf1Z.jpg</video:thumbnail_loc>

            <video:title>Sets of numbers</video:title>

            <video:description><![CDATA[
Worked example involving sets of numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/segW5sJinf1Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Jbz2xhdu3YPK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/Jbz2xhdu3YPK.jpg</video:thumbnail_loc>

            <video:title>Solving two-set problems (1)</video:title>

            <video:description><![CDATA[
A step-by-step solution to a standard problem involving the cardinality of the union of two sets. It demonstrates the principle of inclusion-exclusion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/Jbz2xhdu3YPK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y7UuoMIK06gJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/Y7UuoMIK06gJ.jpg</video:thumbnail_loc>

            <video:title>Solving three-set problems (1)</video:title>

            <video:description><![CDATA[
A worked example solving a cardinality problem involving three intersecting sets, requiring systematic application of the inclusion-exclusion principle.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/Y7UuoMIK06gJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T0ezG5NXKCSG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/T0ezG5NXKCSG.jpg</video:thumbnail_loc>

            <video:title>What is a set?</video:title>

            <video:description><![CDATA[
Provides a precise definition of a mathematical set. The lesson covers the two essential methods for describing a set's elements: the roster form and set-builder notation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/T0ezG5NXKCSG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PY8mU26dOAZk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/876/PY8mU26dOAZk.jpg</video:thumbnail_loc>

            <video:title>Singleton, empty and universal sets</video:title>

            <video:description><![CDATA[
This lesson introduces three fundamental types of sets. The singleton set contains exactly one element. The empty set (or null set) contains no elements at all. The universal set includes all elements under consideration in a given context or problem. Understanding these special sets is essential, as they form the foundation for more advanced ideas in set theory.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/876/PY8mU26dOAZk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zP9hmjfKbmmW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/zP9hmjfKbmmW.jpg</video:thumbnail_loc>

            <video:title>Complements of sets</video:title>

            <video:description><![CDATA[
A practical walkthrough of calculating the complement of a set.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/zP9hmjfKbmmW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gcdOs_Rj4RX_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/gcdOs_Rj4RX_.jpg</video:thumbnail_loc>

            <video:title>Subsets and equality</video:title>

            <video:description><![CDATA[
This lesson explains the concept of a subset, where all elements of one set are contained within another. The distinction between a subset and a proper subset is clarified. Equality of sets are explained in terms of subsets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/gcdOs_Rj4RX_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gOwdkbSGWcTb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/gOwdkbSGWcTb.jpg</video:thumbnail_loc>

            <video:title>The union of sets</video:title>

            <video:description><![CDATA[
Defines the union of two or more sets as the set containing all elements from the original sets. It covers the notation and fundamental properties of the union operation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/gOwdkbSGWcTb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m_oZjkLjLsie</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/878/m_oZjkLjLsie.jpg</video:thumbnail_loc>

            <video:title>The intersection of sets</video:title>

            <video:description><![CDATA[
Defines the intersection of sets as the set containing only the elements common to all original sets. Notation and properties are detailed.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/878/m_oZjkLjLsie.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hHHy3yEaV_ox</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/877/hHHy3yEaV_ox.jpg</video:thumbnail_loc>

            <video:title>The power set</video:title>

            <video:description><![CDATA[
Introduces the power set of a given set A as the set of all possible subsets of A. The notation and its relationship to cardinality are covered.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/877/hHHy3yEaV_ox.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/r7SQJm6jTuxd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/r7SQJm6jTuxd.jpg</video:thumbnail_loc>

            <video:title>Solving three-set problems (2)</video:title>

            <video:description><![CDATA[
A worked example solving a cardinality problem involving three intersecting sets, requiring systematic application of the inclusion-exclusion principle.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/r7SQJm6jTuxd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Qt2DPuSwTPRb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/882/Qt2DPuSwTPRb.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
A direct statement on the course's purpose and structure. This lesson explains the importance of mathematical progressions in modelling patterns of growth, decay, and summation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/882/Qt2DPuSwTPRb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y6PFxUrjv19K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/Y6PFxUrjv19K.jpg</video:thumbnail_loc>

            <video:title>Finding the nth term</video:title>

            <video:description><![CDATA[
A worked calculation to find a specific term in a GP given the first term, common ratio, and term number. This is a direct application of the nth term formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/Y6PFxUrjv19K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UhKozPjJtCPS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/UhKozPjJtCPS.jpg</video:thumbnail_loc>

            <video:title>Equation of a straight line</video:title>

            <video:description><![CDATA[
Vector (three-dimensional) equations of a straight line, and why y=mx+c no longer cuts it.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/UhKozPjJtCPS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b59MVnOQl1nx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/100/b59MVnOQl1nx.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of double integrals. Solved: Evaluate \int_{1}^{2} \int_{0}^{1} \\(x^2+y^2) \,dx\,dy 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/100/b59MVnOQl1nx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/g3hRVRYGUTnO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/g3hRVRYGUTnO.jpg</video:thumbnail_loc>

            <video:title>Finding the number of terms</video:title>

            <video:description><![CDATA[
A worked calculation to find the number of terms in a finite AP. This is a direct application of the last term formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/g3hRVRYGUTnO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_jieTSiivBsQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/882/_jieTSiivBsQ.jpg</video:thumbnail_loc>

            <video:title>Defining a series</video:title>

            <video:description><![CDATA[
Defines a series as the sum of the terms in a sequence. It differentiates between finite and infinite series, a critical distinction for later concepts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/882/_jieTSiivBsQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RtRPFt0DIC44</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/RtRPFt0DIC44.jpg</video:thumbnail_loc>

            <video:title>Sum to infinity</video:title>

            <video:description><![CDATA[
Introduces the concept of a convergent geometric series. It derives and applies the formula for the sum to infinity, a critical concept for calculus.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/RtRPFt0DIC44.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B0IjxrOcu6PS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/B0IjxrOcu6PS.jpg</video:thumbnail_loc>

            <video:title>The sum of n terms</video:title>

            <video:description><![CDATA[
Covers the derivation and application of the formula for the sum of the first n terms of an arithmetic series.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/B0IjxrOcu6PS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y2Y8GDwyXWqq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/y2Y8GDwyXWqq.jpg</video:thumbnail_loc>

            <video:title>Calculating the sum of a series</video:title>

            <video:description><![CDATA[
A step-by-step walkthrough of calculating the sum of a finite geometric series. This problem demonstrates the correct application of the GP sum formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/y2Y8GDwyXWqq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qgHYMNLsEhjx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/qgHYMNLsEhjx.jpg</video:thumbnail_loc>

            <video:title>The sum of n terms</video:title>

            <video:description><![CDATA[
Covers the derivation and application of the formula for the sum of the first n terms of a geometric series.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/qgHYMNLsEhjx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2B1w91_oOnYR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/409/2B1w91_oOnYR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on second-order ordinary differential equations - 2022/2023 final semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/409/2B1w91_oOnYR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jDyxTWXsWfDd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/jDyxTWXsWfDd.jpg</video:thumbnail_loc>

            <video:title>More problem involving sum of an AP</video:title>

            <video:description><![CDATA[
A problem requiring the use of the sum of an AP is considered and solved.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/jDyxTWXsWfDd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HmG8tOjLP3bM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/HmG8tOjLP3bM.jpg</video:thumbnail_loc>

            <video:title>Hybrid pattern</video:title>

            <video:description><![CDATA[
Spot a fraction that hides two different patterns. How do you split the numerator to solve both parts by sight? This walkthrough shows you how to separate and conquer. Solved: Obtain the integral \int \frac{x + 5}{x^{2} + 36} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/HmG8tOjLP3bM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n3FqMdIeO2Z5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Thumbnails/341/n3FqMdIeO2Z5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating centroids of composite areas using those of their component areas. Solved: Locate the centroid of the plane area shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MQ7fmvNaMu/Previews/341/n3FqMdIeO2Z5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1741551301383.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/voMuxG-zui0z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/401/voMuxG-zui0z.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on differentiability of single-variable functions - 2023/2024 mid-semester examination questions. Solved: Let the function f:x\in I\subset \mathbb{R} \to \mathbb{R} be defined by f{[x]}=\lambda^-4 , where \lambda\in \mathbb{R} and I is a closed interval. Then every point x \in I is 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/401/voMuxG-zui0z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3ZkAxvGzOfKA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/405/3ZkAxvGzOfKA.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on applications of partial derivatives - 2023/2024 mid-semester examination questions. Solved: Let P (-2,5) be a critical point of function f (x,y) . If f_xx(-2,5)=5 ,f_yy(-2,5)=10 and f_xy(-2,5)=-7 , determine the nature of P 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/405/3ZkAxvGzOfKA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KMt-6ZIKqG2M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/84/KMt-6ZIKqG2M.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on Newton's method of solution of equations in one variable. Solved: Perform four iterations of the Newton's method to find the smallest positive root of the equationf(x) = x^3 - 5x + 1 = 0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/84/KMt-6ZIKqG2M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eu5eY13J6oLH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/519/eu5eY13J6oLH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on orthogonal curvilinear coordinates - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/519/eu5eY13J6oLH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jRs110Vfe58Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/522/jRs110Vfe58Y.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on linear maps - solutions to 2022/2023 final semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/522/jRs110Vfe58Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XOZFY5sZzoJB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/520/XOZFY5sZzoJB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on complex numbers - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/520/XOZFY5sZzoJB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fp_8ty9zp9FT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/fp_8ty9zp9FT.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Alkanes are saturated hydrocarbons with only single carbon bonds. Why are they called paraffins and why do they resist most chemical attacks? This lesson defines their general formula, sp3 hybridisation, and inert nature precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/fp_8ty9zp9FT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BHctZ7ZcBWAh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/BHctZ7ZcBWAh.jpg</video:thumbnail_loc>

            <video:title>Motion of the centre of mass</video:title>

            <video:description><![CDATA[
Calculate the velocity vector of the centre of mass for two moving objects. This walkthrough demonstrates how to find the system's overall motion by calculating the weighted average of the individual velocity vectors based on their masses. Solved: Two remote-controlled toys are moving on a smooth floor. Toy 1 (1.5 \, kg) moves with a velocity of (4.0\hat{i} - 2.0\hat{j}) \, m/s, while Toy 2 (2.5 \, kg) moves at (2.0\hat{i} + 8.0\hat{j}) \, m/s. Find the resultant velocity vector of the system's centre of mass. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/BHctZ7ZcBWAh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_nh2COc7P5Y2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/_nh2COc7P5Y2.jpg</video:thumbnail_loc>

            <video:title>A ballistic pendulum</video:title>

            <video:description><![CDATA[
Calculate the firing speed of a pellet by combining momentum conservation and energy conservation. This walkthrough shows how to find the post-impact speed from the swing height and then use momentum balance to determine the pellet's initial velocity. Solved: A 15 \, g pellet is fired from an air rifle into a 2.5 \, kg sandbag hanging from a ceiling. The pellet gets embedded in the bag, causing it to swing upwards to a vertical height of 12 \, cm. Calculate the initial firing speed of the pellet. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/_nh2COc7P5Y2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5qaw8QZou1kR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Thumbnails/521/5qaw8QZou1kR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on linear vector spaces - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ryZQRQJIiJ/Previews/521/5qaw8QZou1kR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aQNvj-Gn5Fav</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Thumbnails/645/aQNvj-Gn5Fav.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector products - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Previews/645/aQNvj-Gn5Fav.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XDE-TLFd7bb8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Thumbnails/646/XDE-TLFd7bb8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector equations - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Previews/646/XDE-TLFd7bb8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JnyHXvqQMZst</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Thumbnails/644/JnyHXvqQMZst.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector algebra and geometry - solutions to 2023/2024 mid-semester examination questions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MqumQj2AMM/Previews/644/JnyHXvqQMZst.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rlHtFS-gy1ha</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/rlHtFS-gy1ha.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating line integrals in two and three dimensions. Solved: Evaluate \int_c f(r)dt, where f=(x^2+y^2+z^2)^2 and c is given by \vec{r}(t)=\cos t\vec{i} + \sin t\vec{j }+ 3t\vec{k} (0\le {t} \le {2\pi}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/rlHtFS-gy1ha.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zvHdG7vGJ2xN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/zvHdG7vGJ2xN.jpg</video:thumbnail_loc>

            <video:title>Rational functions</video:title>

            <video:description><![CDATA[
Rational functions are ratios of two polynomials that form split curves. Identify vertical asymptotes by finding where the denominator equals zero and locate horizontal asymptotes to define boundaries. Use these lines and key intercepts to sketch the branches accurately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/zvHdG7vGJ2xN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kqTH0P0Duk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/kqTH0P0Duk.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This course teaches you to calculate exact rates of change. You will master first principles and key rules like the chain rule. See the full roadmap here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/kqTH0P0Duk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jBukuhbiQD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/jBukuhbiQD.jpg</video:thumbnail_loc>

            <video:title>Derivative proofs (1)</video:title>

            <video:description><![CDATA[
The power rule is a shortcut. How does binomial expansion prove the derivative of x to the n? Watch to see the logic behind the formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/jBukuhbiQD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a_KiwiCkauFU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/a_KiwiCkauFU.jpg</video:thumbnail_loc>

            <video:title>System with varying mass</video:title>

            <video:description><![CDATA[
Calculate the thrust, acceleration, and final velocity of a drone with changing mass. This walkthrough applies the rocket equation to determine how constant fuel ejection produces force and increases speed as the total system mass decreases over time. Solved: A heavy-duty rescue drone has a total mass of 120 \, kg, which includes 80 \, kg is fuel. Its high-pressure thrusters eject fuel at a constant rate of 0.5 \, kg/s with a speed of 450 \, m/s relative to the drone. (a) Calculate the constant thrust force produced. (b) Determine the initial acceleration of the drone. (c) Calculate the velocity of the drone after 60 \, seconds of flight, assuming it starts from rest in a friction-free environment. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/a_KiwiCkauFU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IV4sz2C_vT7w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/925/IV4sz2C_vT7w.jpg</video:thumbnail_loc>

            <video:title>Discrete particles</video:title>

            <video:description><![CDATA[
Calculate the centre of mass for a system of three objects at different coordinates. This walkthrough shows how to find the weighted average of the x and y positions by multiplying each mass by its distance from the origin and dividing by the total system mass. Solved: Three heavy bags are placed on a warehouse floor. Bag A (5 \, kg) is at the origin (0,0), Bag B (10 \, kg) is at coordinates (4 \, m, 0), and Bag C (15 \, kg) is at (0, 6 \, m). Calculate the x and y coordinates of the centre of mass for this three-bag system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/925/IV4sz2C_vT7w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fm0_JOtUhu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/fm0_JOtUhu.jpg</video:thumbnail_loc>

            <video:title>Rational asymptotes</video:title>

            <video:description><![CDATA[
Find the lines that a graph approaches but never touches by analyzing the denominator and the ratio of leading coefficients. This identifies the vertical and horizontal boundaries. Solved: Identify the equations of the vertical and horizontal asymptotes for the rational function h(x) = \frac{x+11}{x-4}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/fm0_JOtUhu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KFMPBuYkod8Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/135/KFMPBuYkod8Z.jpg</video:thumbnail_loc>

            <video:title>Worked examples I</video:title>

            <video:description><![CDATA[
Worked examples on the polar, cylindrical and spherical coordinates. Solved: Change the equation x^2+y^2-z^2=25 into an equation in polar coordinates 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/135/KFMPBuYkod8Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LGADsgfWtxys</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/964/LGADsgfWtxys.jpg</video:thumbnail_loc>

            <video:title>Header layout</video:title>

            <video:description><![CDATA[
This is a practical lesson where we will use Flexbox to style our portfolio header, placing the logo on the left and the navigation links on the right.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/964/LGADsgfWtxys.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ytC0o3vGwg7l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/872/ytC0o3vGwg7l.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a brief overview of the course, outlining the key topics of radioactive disintegration, nuclear reactions, and the uses of radioisotopes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/872/ytC0o3vGwg7l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R0rR6EPwOZGY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/R0rR6EPwOZGY.jpg</video:thumbnail_loc>

            <video:title>Decomposing functions</video:title>

            <video:description><![CDATA[
Learn how to break down complex expressions into their simpler component functions. This process is the reverse of composition and is vital for solving difficult derivatives in later courses. You will identify the inner and outer parts of a function to simplify mathematical analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/R0rR6EPwOZGY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BscdZylfmQXo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/BscdZylfmQXo.jpg</video:thumbnail_loc>

            <video:title>Coupling with pendulums</video:title>

            <video:description><![CDATA[
Charged beads hang apart due to repulsion. How do you balance electric force, gravity, and tension to find the charge from the angle? Watch the video for the force diagram. Solved: Two identical small beads, each of mass 25.0 \text{ g}, are suspended from a common point using insulating strings 1.80 \text{ m} long. When they are given identical charges, they repel each other until each string makes an angle of 15.0^\circ with the vertical. Determine the magnitude of the charge on each bead. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/BscdZylfmQXo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fpFXSLct2mQE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/fpFXSLct2mQE.jpg</video:thumbnail_loc>

            <video:title>Arithmetic operations</video:title>

            <video:description><![CDATA[
Learn to add, subtract, multiply, and divide functions to create new expressions. You will also find the domain for these combined operations by identifying where the original functions overlap. This lesson shows you how to handle multiple mathematical relationships at once.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/fpFXSLct2mQE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bJO5cf1JnY3w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/bJO5cf1JnY3w.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion. Solved: After subjecting a car to wind-tunnel testing, the students estimate that the tangential component of the car's acceleration will be a_t = (0.6 - 0.002v^3) m/s^2, where v is the car's velocity in m/s. If the car starts from rest at A, what are its velocity and acceleration in terms of normal and tangential components when it reaches B? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/bJO5cf1JnY3w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742218830672.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nKUetzqyTS05</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/820/nKUetzqyTS05.jpg</video:thumbnail_loc>

            <video:title>Milikan's Oil drop experiment</video:title>

            <video:description><![CDATA[
This lesson details Millikan's Oil drop experiment, which established the elementary electric charge. By using Thomson's charge-to-mass ratio, this experiment allowed for the first accurate calculation of the electron's mass.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/820/nKUetzqyTS05.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7DtpaHacxpc0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/7DtpaHacxpc0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion. Solved: If the car passes A with a speed of 20 m/s and begins to increase its speed at a constant rate of 0.5m/s^2, determine the magnitude of the car's acceleration when s = 101.98 m and x = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/7DtpaHacxpc0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742219054869.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/u_A8i6E_g8kO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/u_A8i6E_g8kO.jpg</video:thumbnail_loc>

            <video:title>Constant acceleration (1)</video:title>

            <video:description><![CDATA[
This example covers 1D constant acceleration. We apply the standard kinematic equations. Observe how to identify variables and select the correct formula to solve for the unknown. Solved: A car moving with a speed of 90km/hr is brought to rest in 10s by the application of the brakes. How far did the car travel after the brakes were applied ? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/u_A8i6E_g8kO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HDcwoMpJXvgN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/HDcwoMpJXvgN.jpg</video:thumbnail_loc>

            <video:title>Notations</video:title>

            <video:description><![CDATA[
Maths uses many symbols for the same idea. Why do Leibniz, prime and operator notations all exist? Watch to learn when to use each.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/HDcwoMpJXvgN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1_usMT2A004L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/1_usMT2A004L.jpg</video:thumbnail_loc>

            <video:title>Constant acceleration</video:title>

            <video:description><![CDATA[
This lesson focuses on the special case of constant acceleration. We will derive the standard set of algebraic kinematic equations that govern this type of motion. These equations are the essential tools for solving a wide class of mechanics problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/1_usMT2A004L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2j5atPJOPD8n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/969/2j5atPJOPD8n.jpg</video:thumbnail_loc>

            <video:title>What is Physics?</video:title>

            <video:description><![CDATA[
This lesson provides a precise definition of physics. It is the fundamental science of matter and energy, distinguished by its reliance on mathematical models and precise measurement to describe reality. This quantitative approach is the basis for all physical science and engineering.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/969/2j5atPJOPD8n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b0_qcxtWFPCU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/b0_qcxtWFPCU.jpg</video:thumbnail_loc>

            <video:title>Solving two-set problems (2)</video:title>

            <video:description><![CDATA[
A step-by-step solution to a standard problem involving the cardinality of the union of two sets. It demonstrates the principle of inclusion-exclusion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/b0_qcxtWFPCU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tGJOVUPctUJk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/tGJOVUPctUJk.jpg</video:thumbnail_loc>

            <video:title>Representation of three sets</video:title>

            <video:description><![CDATA[
This lesson details the standard construction for a three-set Venn diagram. We will identify and define five unique regions created by their intersection. Mastery of this model is required for solving complex cardinality problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/tGJOVUPctUJk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7xe1Gp2Ng9md</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/694/7xe1Gp2Ng9md.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video provides a worked example for converting from one number base to another. You will learn the crucial two-step process: converting to base 10 first, then converting the result to the final base.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/694/7xe1Gp2Ng9md.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YXZQsgLKatBQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/820/YXZQsgLKatBQ.jpg</video:thumbnail_loc>

            <video:title>Shortcomings of Dalton's theory</video:title>

            <video:description><![CDATA[
Dalton's theory was foundational but flawed. This lesson identifies its critical shortcomings, namely the divisibility of atoms and the existence of isotopes. Understanding these failures is necessary to trace the progression to modern atomic models.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/820/YXZQsgLKatBQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vwQg_Zmak_5f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/vwQg_Zmak_5f.jpg</video:thumbnail_loc>

            <video:title>Types of salts</video:title>

            <video:description><![CDATA[
This lesson classifies salts as acidic, basic, or neutral based on the strength of the parent acid and base. You will learn how the cation and anion interactions with water determine the final pH of the solution. Mastering these categories is essential for predicting the outcome of neutralisation reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/vwQg_Zmak_5f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UXC3k66nCVo4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/UXC3k66nCVo4.jpg</video:thumbnail_loc>

            <video:title>Proving De Morgan's laws</video:title>

            <video:description><![CDATA[
This lesson covers De Morgan's Laws, using Venn diagrams for visual proof. Master this graphical method to confirm abstract set identities and verify the results of complement and intersection/union operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/UXC3k66nCVo4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_Cfp0_FLSooB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/879/_Cfp0_FLSooB.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson defines the Venn diagram as the standard tool for visually representing sets and their relationships. We will establish the fundamental conventions required to translate abstract set notation into a clear graphical format for analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/879/_Cfp0_FLSooB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oUleivOBEruY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Thumbnails/881/oUleivOBEruY.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
A concise review of the key definitions, notations, and operations covered in the course. This lesson ensures all foundational material has been consolidated.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MiMbNvuaAF/Previews/881/oUleivOBEruY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rAIoS0ocrb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/rAIoS0ocrb.jpg</video:thumbnail_loc>

            <video:title>Acid-base strength</video:title>

            <video:description><![CDATA[
Electron pull controls reactivity. How does chlorine position tune acid strength, and why does fluorine weaken basicity in nitrogen compounds? Watch to master both trends. Solved: (1) Arrange the following in increasing order of acid strength:(a) 2-chlorobutanoic acid(b) 3-chlorobutanoic acid(c) 4-chlorobutanoic acid(d) butanoic acid(2) Which is a stronger base: CH_3NH_2 and NF_3? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/rAIoS0ocrb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hseCeQmm2kgG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/hseCeQmm2kgG.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
The derivative comes from first principles. How does the Newton quotient become exact as the interval shrinks to zero? Watch to see the limit in action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/hseCeQmm2kgG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eMx_eqez_0tZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/eMx_eqez_0tZ.jpg</video:thumbnail_loc>

            <video:title>Conducting sphere</video:title>

            <video:description><![CDATA[
Conducting spheres maintain constant potential throughout their interior. Why does the value inside equal the surface potential rather than zero? We calculate the potential for points on and within the sphere. Solved: A hollow conducting metal sphere has a radius of 12.0 \text{ cm} and carries a net positive charge of 40.0 \text{ nC}. Taking the electric potential to be zero at infinity, determine: (i) the electric potential at the surface of the sphere, and (ii) the electric potential at a point 8.0 \text{ cm} from the centre. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/eMx_eqez_0tZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a4Y-myLaF13s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/317/a4Y-myLaF13s.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a rigid body under the action of forces in space. Solved: An opening in a floor is covered by a 1\times1.2-m sheet of plywood with a mass 18kg. The sheet is hinged at A and B and is maintained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction (a) at A, (b) at B, (c) at C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/317/a4Y-myLaF13s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738677515768.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Qs2Nn581J8Jg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/978/Qs2Nn581J8Jg.jpg</video:thumbnail_loc>

            <video:title>Energy levels</video:title>

            <video:description><![CDATA[
This lesson explains how Bohr's model of quantized energy levels accounts for the hydrogen emission spectrum. We will demonstrate how electron transitions between these discrete energy levels produce the specific lines observed, and define the principal quantum number, n.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/978/Qs2Nn581J8Jg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SvfIjN5qxDsL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/SvfIjN5qxDsL.jpg</video:thumbnail_loc>

            <video:title>Examples of ionic bonds (2)</video:title>

            <video:description><![CDATA[
This second lesson reinforces ionic bond formation via electron transfer. We demonstrate bond formation for Calcium chloride (CaCl2) and Lithium oxide (Li2O). Master how to balance the number of atoms to achieve a neutral compound.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/SvfIjN5qxDsL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QpPwk47nSJQp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/baSCjoC949/Thumbnails/936/QpPwk47nSJQp.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Master the four-stage operational workflow of attending university lectures, watching UniDrills lessons for clarity, solving practice problems for mastery, and asking instructors for support. This lesson explains how to implement a systematic approach to ensure clarity and excellent result.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/baSCjoC949/Previews/936/QpPwk47nSJQp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AeLGrazU7sVd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/978/AeLGrazU7sVd.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson reviews the critical failures of Rutherford's classical atomic model, specifically its inability to account for atomic stability and line spectra. We establish the context for Bohr's revolutionary quantum hypothesis, which directly addresses these shortcomings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/978/AeLGrazU7sVd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wx16dtLYjHOg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/wx16dtLYjHOg.jpg</video:thumbnail_loc>

            <video:title>Inverses of compositions</video:title>

            <video:description><![CDATA[
Learn how to find the inverse of combined functions by reversing the order of the original operations. You will master the socks-and-shoes rule to decompose and invert multi-step processes accurately. This lesson ensures you can solve complex equations involving nested inverse relationships.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/wx16dtLYjHOg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I7Y5QhtQD3xW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/I7Y5QhtQD3xW.jpg</video:thumbnail_loc>

            <video:title>Instantaneous variables</video:title>

            <video:description><![CDATA[
Apply calculus to find the instantaneous angular velocity and acceleration of a grinding plate. This walkthrough shows how to differentiate the angular position equation with respect to time to get exact spin rates.  Use these steps to solve for variable rotation. Solved: The angular position of a heavy grinding plate in a local mill is described by the equation \theta = 4.0 + 2.5t + 1.2t^2, where \theta is in radians and t is in seconds. Calculate the instantaneous angular velocity of the plate at t = 3.0 \text{ s} and its constant angular acceleration. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/I7Y5QhtQD3xW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q8K8hHv7gu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/Q8K8hHv7gu.jpg</video:thumbnail_loc>

            <video:title>Trigonometric properties</video:title>

            <video:description><![CDATA[
Extract the amplitude and period from a sine function's equation to describe its wave motion. This lesson shows how coefficients dictate the height and width of the graph. Solved: Determine the amplitude and the period of the wave defined by g(x) = 12 \sin(7x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/Q8K8hHv7gu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mpkiIhIP1Nu3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/mpkiIhIP1Nu3.jpg</video:thumbnail_loc>

            <video:title>Atomic and ionic radii</video:title>

            <video:description><![CDATA[
This lesson defines atomic and ionic radii, explaining the trends across periods and down groups. We will justify these size changes using the concepts of effective nuclear charge and electron shielding.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/mpkiIhIP1Nu3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SWxsLsquBk7x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/SWxsLsquBk7x.jpg</video:thumbnail_loc>

            <video:title>Calculating scalar products</video:title>

            <video:description><![CDATA[
This is a practical session on calculating the scalar product. We will solve problems using both the component method and the angular formula. Examples will include finding the angle between two known vectors, a key application of the dot product. Solved: 5. A vector of magnitude 10 units and another vector of magnitude 6.0 units differ in directions by 60^{\circ}. Find their scalar product. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/SWxsLsquBk7x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GZoQ64v4E35O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/974/GZoQ64v4E35O.jpg</video:thumbnail_loc>

            <video:title>Summary and lookahead</video:title>

            <video:description><![CDATA[
We consolidate the course toolkit: dimensional analysis, vector algebra, and vector calculus. We then show how these tools are immediately applied to mechanics. This summary verifies your readiness for the next course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/974/GZoQ64v4E35O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C5VRfI8sSeZg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/C5VRfI8sSeZg.jpg</video:thumbnail_loc>

            <video:title>Motion under gravity (1)</video:title>

            <video:description><![CDATA[
This example applies 1D constant acceleration to vertical motion. We use the standard kinematic equations, setting acceleration to -g. Watch how to correctly establish the coordinate system and sign conventions. Solved: A ball is thrown vertically upward from the ground with an initial speed of 15.0m/s. How high will the ball rise? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/C5VRfI8sSeZg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cJXV6P7h0nKf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/965/cJXV6P7h0nKf.jpg</video:thumbnail_loc>

            <video:title>Interactivity with pseudo-classes</video:title>

            <video:description><![CDATA[
A static site lacks professional polish. This lesson introduces the :hover pseudo-class and transition property to add smooth, interactive feedback to buttons and cards, making the user interface feel responsive and professional.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/965/cJXV6P7h0nKf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lWkboWVZYmE0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/lWkboWVZYmE0.jpg</video:thumbnail_loc>

            <video:title>Motion under gravity (2)</video:title>

            <video:description><![CDATA[
A further example of 1D motion under gravity. We apply the standard kinematic equations, reinforcing the use of a = -g and correct sign conventions. Solved: A stone is thrown vertically upward from the top of a building 30.0m high with a speed of 12.0m/s. How long will it take for the stone to reach the ground? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/lWkboWVZYmE0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IWuzxkcubbun</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/IWuzxkcubbun.jpg</video:thumbnail_loc>

            <video:title>Electronic configuration</video:title>

            <video:description><![CDATA[
This lesson explains how electrons occupy orbitals using the Aufbau principle, Pauli exclusion, and Hund???s rule to determine the electronic configuration of any element.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/IWuzxkcubbun.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X5UssvsEnR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/X5UssvsEnR.jpg</video:thumbnail_loc>

            <video:title>Composite functions</video:title>

            <video:description><![CDATA[
Master how to calculate a composite function by substituting one linear expression into a quadratic equation. You will learn the correct order of operations to expand and simplify the resulting expression. This walkthrough provides the exact steps needed to solve nested functions accurately. Solved: Given the functions f(x) = x^{2} + 5 and g(x) = 3x - 2, evaluate the composite function result for (f \circ g)(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/X5UssvsEnR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uLBBjpUzX_76</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/uLBBjpUzX_76.jpg</video:thumbnail_loc>

            <video:title>Coupling with springs</video:title>

            <video:description><![CDATA[
Electric pull stretches the spring until forces balance. How do you equate Coulomb force to Hooke's law using the final separation distance to find the spring constant? Watch the video for the equilibrium setup. Solved: A small block with a charge of +3.50 \mu\text{C} rests on a smooth horizontal floor and is attached to a spring. When a second charge of -9.00 \mu\text{C} is held fixed at a distance from it, the block is pulled toward the fixed charge, stretching the spring by 10.0 \text{ mm}. At this equilibrium position, the final separation between the two charges is 14.0 \text{ cm}. Calculate the spring constant k of the spring. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/uLBBjpUzX_76.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OHtGTuLMGSJC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/OHtGTuLMGSJC.jpg</video:thumbnail_loc>

            <video:title>Linear inverse</video:title>

            <video:description><![CDATA[
Learn to derive the inverse of a linear function by swapping variables and solving for the new output. You will master the algebraic steps to isolate the variable and verify your result. This walkthrough shows you how to turn a multiplication and addition process into a subtraction and division. Solved: Determine the formula for the inverse function f^{-1}(x) given the linear function f(x) = 5x + 8. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/OHtGTuLMGSJC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/akLkT6zK5XK6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/967/akLkT6zK5XK6.jpg</video:thumbnail_loc>

            <video:title>What you built</video:title>

            <video:description><![CDATA[
This lesson provides a final review of the complete portfolio project. We will trace the journey from an unstyled HTML document to a fully responsive webpage, reinforcing the core layout, styling, and positioning techniques you have mastered.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/967/akLkT6zK5XK6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZmgoRuuAlE9P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/928/ZmgoRuuAlE9P.jpg</video:thumbnail_loc>

            <video:title>Total linear acceleration</video:title>

            <video:description><![CDATA[
Calculate tangential and radial acceleration for a grinding wheel spinning at constant acceleration.  This walkthrough shows how to find the total linear acceleration of a point on a rotating edge. Solved: A heavy grinding wheel in a metal workshop has a radius of 0.40 \text{ m}. It starts from rest and accelerates at a constant rate of 3.0 \text{ rad/s}^2. For a point on the outer edge of the wheel, calculate the tangential acceleration and the radial (centripetal) acceleration at t = 4.0 \text{ s}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/928/ZmgoRuuAlE9P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0T_5mbPWpc5x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/971/0T_5mbPWpc5x.jpg</video:thumbnail_loc>

            <video:title>Length measurement</video:title>

            <video:description><![CDATA[
Length is defined and its SI unit, the metre, is established. We cover the correct use of standard measuring instruments, including vernier calipers and micrometers, to ensure experimental accuracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/971/0T_5mbPWpc5x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q7cpFmsuTFQR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/Q7cpFmsuTFQR.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Electrons do not sit still; they shift. Why does one group pull density while another pushes it? See how these invisible moves dictate reactivity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/Q7cpFmsuTFQR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iqRcWmF3aJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/iqRcWmF3aJ.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity (1)</video:title>

            <video:description><![CDATA[
Equal-degree rational functions have a fixed limit at infinity. How do you find the value of the limit without expanding every term? Watch the ratio of the leading coefficients give the answer. Solved: Evaluate \lim_{x \to \infty} \frac{9x^2 + 4x - 7}{3x^2 - 2x + 1}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/iqRcWmF3aJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aVFejbyxOcZn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/aVFejbyxOcZn.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson introduces uniform circular motion, defining it as motion at a constant speed along a circular path. We establish that while speed is constant, the continuous change in the direction of the velocity vector necessitates acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/aVFejbyxOcZn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SjWA19HLJM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/SjWA19HLJM.jpg</video:thumbnail_loc>

            <video:title>Superposition principle</video:title>

            <video:description><![CDATA[
Every nearby charge exerts an independent force on any single point. How do you add these directional vectors using x and y components to find the exact net force? Watch the video to see the complete breakdown.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/SjWA19HLJM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fPsB_fsuF8Dc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/fPsB_fsuF8Dc.jpg</video:thumbnail_loc>

            <video:title>Finding the nth term of an AP</video:title>

            <video:description><![CDATA[
This practical lesson demonstrates how to apply the formula for the nth term of an Arithmetic Progression (AP). We work through a complete example, solving for the first term, common difference, and a specific term.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/fPsB_fsuF8Dc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Jl13XswH3Nn3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/Jl13XswH3Nn3.jpg</video:thumbnail_loc>

            <video:title>Calculating density</video:title>

            <video:description><![CDATA[
This lesson derives the density equation from the Ideal Gas Law. We explain how pressure and temperature affect gas density, and how the molar mass of a gas is directly related to its density. Master this critical derivation for engineering applications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/Jl13XswH3Nn3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LgAZxEpq1bq3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/135/LgAZxEpq1bq3.jpg</video:thumbnail_loc>

            <video:title>Worked examples III</video:title>

            <video:description><![CDATA[
More worked examples on the polar, cylindrical and spherical coordinates. Solved: The spherical coordinates of some position is given by(1, \frac{\pi}{6},\frac{\pi}{6}). Find the rectangular coordinates(x,y,z) of the point. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/135/LgAZxEpq1bq3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0LJ2HYZKhuJ_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/837/0LJ2HYZKhuJ_.jpg</video:thumbnail_loc>

            <video:title>Relative atomic mass</video:title>

            <video:description><![CDATA[
This lesson defines Relative Atomic Mass as the mass of an atom relative to the carbon-12 standard. We explain the contribution of isotopes to the weighted average atomic mass of an element. Master this concept to accurately use the periodic table for mass calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/837/0LJ2HYZKhuJ_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pk8sD_1hBA3d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/Pk8sD_1hBA3d.jpg</video:thumbnail_loc>

            <video:title>Speed, velocity and acceleration</video:title>

            <video:description><![CDATA[
This lesson establishes the calculus-based relationships between the key kinematic quantities in one dimension. We formally define instantaneous velocity as the derivative of position, and acceleration as the derivative of velocity. Speed is the magnitude of the velocity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/Pk8sD_1hBA3d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GMLmocTvhhDm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/967/GMLmocTvhhDm.jpg</video:thumbnail_loc>

            <video:title>Your next step</video:title>

            <video:description><![CDATA[
This lesson provides a clear roadmap for your continued development. You will receive specific project ideas for immediate practice, an introduction to advanced CSS topics like Grid and animations, and a look ahead to the next course on JavaScript.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/967/GMLmocTvhhDm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tomqM2ldRx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/tomqM2ldRx.jpg</video:thumbnail_loc>

            <video:title>Antiderivatives</video:title>

            <video:description><![CDATA[
Every derivative hides its origin. How do you recover the full function when constants vanish during differentiation? We define the antiderivative and fix the notation to capture every possible solution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/tomqM2ldRx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S8ZCJzoGJLtr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/908/S8ZCJzoGJLtr.jpg</video:thumbnail_loc>

            <video:title>Speed and velocity (2)</video:title>

            <video:description><![CDATA[
This lesson moves beyond averages to define instantaneous velocity ??? the rate of change of position at a specific moment. We will introduce this concept formally as the derivative of position with respect to time. Instantaneous speed is the magnitude of this resultant vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/908/S8ZCJzoGJLtr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NxkcO7RRIuEi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/971/NxkcO7RRIuEi.jpg</video:thumbnail_loc>

            <video:title>Mass measurement</video:title>

            <video:description><![CDATA[
This lesson covers the practical methods for measuring mass. We demonstrate the correct use of laboratory instruments, such as the beam balance and electronic balance, to obtain accurate results.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/971/NxkcO7RRIuEi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gLUjl30Ynb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/gLUjl30Ynb.jpg</video:thumbnail_loc>

            <video:title>Reciprocal patterns</video:title>

            <video:description><![CDATA[
Reciprocal functions test your algebra. How do you simplify complex fractions in the limit definition? Watch to master the cancellation steps. Solved: Find the gradient of the curve f(x) = \frac{1}{x+5} at the point where x = 1 using the method of first principles. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/gLUjl30Ynb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0NfVXf6WBcBT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/0NfVXf6WBcBT.jpg</video:thumbnail_loc>

            <video:title>Mixed quadratic and rational systems (2)</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of simultaneous systems where reciprocal terms intersect with the difference of two squares. You will master the mechanical substitution of linear factors into fractional equations to reduce the system into solvable forms and determine precise coordinate sets. Solved: 6. Solve the equations\frac{x}{y} + \frac{y}{x} = \frac{10}{3}x^2 - y^2 = 8 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/0NfVXf6WBcBT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X1wQ9e94IjdJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/X1wQ9e94IjdJ.jpg</video:thumbnail_loc>

            <video:title>Position, distance and displacement</video:title>

            <video:description><![CDATA[
This lesson formally defines position along a single coordinate axis. It establishes one-dimensional displacement as a vector quantity, reinforcing the critical distinction between this signed value and the total distance travelled.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/X1wQ9e94IjdJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NGfpgMtwaHzH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/NGfpgMtwaHzH.jpg</video:thumbnail_loc>

            <video:title>Vector components</video:title>

            <video:description><![CDATA[
This lesson covers the critical technique of resolving a vector into its perpendicular components using trigonometry. Mastering this process is the non-negotiable prerequisite for performing analytical vector algebra, particularly addition and subtraction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/NGfpgMtwaHzH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aI_quwDFkPEs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/aI_quwDFkPEs.jpg</video:thumbnail_loc>

            <video:title>Definitions</video:title>

            <video:description><![CDATA[
This lesson establishes the critical distinction between scalar and vector quantities. We define scalars by magnitude alone and vectors by both magnitude and direction, providing clear, contrasting examples. This classification is non-negotiable for correct physical analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/aI_quwDFkPEs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PFhebDwKQ7WF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/PFhebDwKQ7WF.jpg</video:thumbnail_loc>

            <video:title>Differentiating vectors</video:title>

            <video:description><![CDATA[
To analyse how vector quantities change with time, we must apply calculus. This lesson covers the differentiation of a vector function with respect to a scalar variable, a process performed on each component. This is the formal method for deriving velocity from position.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/PFhebDwKQ7WF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y_nWGcrOmTT6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/Y_nWGcrOmTT6.jpg</video:thumbnail_loc>

            <video:title>Vector products (1)</video:title>

            <video:description><![CDATA[
This lesson introduces the first method of vector multiplication: the scalar or dot product. We define this operation, which yields a scalar quantity, and cover the methods for its calculation using both vector components and the angle between them.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/Y_nWGcrOmTT6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/njqpqSFJqNqP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/908/njqpqSFJqNqP.jpg</video:thumbnail_loc>

            <video:title>Acceleration</video:title>

            <video:description><![CDATA[
This lesson defines acceleration, the vector quantity describing the rate of change of velocity. We will establish both average and instantaneous acceleration, with the latter being the derivative of velocity with respect to time. An object accelerates if its speed or direction of motion changes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/908/njqpqSFJqNqP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UBSfS_383pFA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/UBSfS_383pFA.jpg</video:thumbnail_loc>

            <video:title>The geometric mean</video:title>

            <video:description><![CDATA[
Defines the geometric mean of two numbers and its relationship to a Geometric Progression. This lesson also covers the insertion of multiple geometric means.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/UBSfS_383pFA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xcn_Y2xn0SCc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/xcn_Y2xn0SCc.jpg</video:thumbnail_loc>

            <video:title>Inverse of a composition</video:title>

            <video:description><![CDATA[
Master how to calculate the inverse of a composition by finding individual inverse functions first. You will apply the specific rule of reversing the order of operations to derive the final formula accurately. This walkthrough ensures you understand the relationship between nested functions. Solved: Determine the formula for the inverse of the composition (f \circ g)^{-1}(x) given the functions f(x) = 8x and g(x) = x + 15. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/xcn_Y2xn0SCc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LnW2iTQnYy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/LnW2iTQnYy.jpg</video:thumbnail_loc>

            <video:title>Steam distillation</video:title>

            <video:description><![CDATA[
Knowing vapour pressures at a given temporature, how do you verify boiling and calculate the mass of eugenol co-distilled with water? Watch to solve it step by step. Solved: In a steam distillation of clove oil at 99.0°C, the vapour pressure of water is 733 mmHg and the vapour pressure of eugenol is 27 mmHg. Given that:M_{eugenol} = 164.20 \text{ g mol}^{-1}1. Verify that the mixture boils at 99°C under these conditions2. Calculate the mass ratio of eugenol/water in the distillate3. If 50 cm³ of water is collected in the distillate, what mass of eugenol is co-distilled? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/LnW2iTQnYy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OCmiXtpXuFzf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/908/OCmiXtpXuFzf.jpg</video:thumbnail_loc>

            <video:title>Position, distance and displacement</video:title>

            <video:description><![CDATA[
This lesson defines the foundational quantities of location and movement. We will establish an object's position, and critically distinguish between the total distance travelled (a scalar) and its overall displacement (a vector). This distinction is non-negotiable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/908/OCmiXtpXuFzf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Nb5vl9GVgaKt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/Nb5vl9GVgaKt.jpg</video:thumbnail_loc>

            <video:title>Volume laws</video:title>

            <video:description><![CDATA[
This lesson introduces Avogadro's Law and Gay-Lussac's Law. We establish the direct proportionality between volume and moles, and between pressure and absolute temperature, respectively, under constant conditions. Master these fundamental empirical relationships for solving gas state problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/Nb5vl9GVgaKt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B6a_tOKpKH3Q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/B6a_tOKpKH3Q.jpg</video:thumbnail_loc>

            <video:title>Vector products (2)</video:title>

            <video:description><![CDATA[
This lesson introduces the vector (cross) product, an operation that yields a new vector perpendicular to the original two. We will cover the calculation of the resultant vector's magnitude and the use of the right-hand rule to determine its direction, a process essential for analysing torque.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/B6a_tOKpKH3Q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ek8v00gMXnnn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/ek8v00gMXnnn.jpg</video:thumbnail_loc>

            <video:title>Free-fall acceleration</video:title>

            <video:description><![CDATA[
This lesson examines motion under the sole influence of gravity. We define free-fall acceleration as a constant value near the Earth's surface. The standard kinematic equations are then directly applied to solve problems involving vertical motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/ek8v00gMXnnn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4zXYRuL9HmRx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/971/4zXYRuL9HmRx.jpg</video:thumbnail_loc>

            <video:title>Length</video:title>

            <video:description><![CDATA[
This lesson establishes the formal definition of length as a fundamental base quantity. We define its standard SI unit, the metre, and its significance within the international system of units.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/971/4zXYRuL9HmRx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PGVcsYPhW9vE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/PGVcsYPhW9vE.jpg</video:thumbnail_loc>

            <video:title>Vector addition</video:title>

            <video:description><![CDATA[
Vectors do not add like scalars. This lesson covers the formal methods for vector addition, from the graphical head-to-tail rule for visualisation to the precise analytical method of adding components. Mastering this is essential for calculating any resultant vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/PGVcsYPhW9vE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TZVrNYjlS4Q6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/TZVrNYjlS4Q6.jpg</video:thumbnail_loc>

            <video:title>Definition and the nth term formula</video:title>

            <video:description><![CDATA[
Derives and explains the formula for finding the value of any term in a GP. This is the primary tool for analysing geometric sequences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/TZVrNYjlS4Q6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z1l9ihrrzCET</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/845/Z1l9ihrrzCET.jpg</video:thumbnail_loc>

            <video:title>Oxidizing and reducing agents</video:title>

            <video:description><![CDATA[
This lesson focuses on identifying the roles of the oxidizing and reducing agents in any redox reaction. You will learn the reciprocal relationship between the species that is oxidised and the species that causes reduction, and vice versa. Clearly identifying these agents is necessary for understanding the direction and potential of electrochemical cells.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/845/Z1l9ihrrzCET.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EuEklpkXmP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/EuEklpkXmP.jpg</video:thumbnail_loc>

            <video:title>Square-root patterns</video:title>

            <video:description><![CDATA[
Roots complicate the limit definition. How do you remove the square root to find velocity? Watch to learn the conjugate trick. Solved: A motorcycle's position is given by s(t) = \sqrt{5t+1} metres. Derive the expression for its instantaneous velocity at any time t > -1/5 using first principles. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/EuEklpkXmP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yNZeYPKB14</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/yNZeYPKB14.jpg</video:thumbnail_loc>

            <video:title>Null potential point</video:title>

            <video:description><![CDATA[
Opposite charges create a point of zero potential. Where exactly do the positive and negative contributions cancel out on the axis? We solve the algebraic equation to find this null point. Solved: A positive point charge of +18.0 \text{ nC} is fixed at the origin, while a second point charge of -45.0 \text{ nC} is fixed on the x-axis at x = 2.10 \text{ m}. Find the coordinate on the x-axis between the two charges where the resultant electric potential is exactly zero. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/yNZeYPKB14.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VWUPlcbiO6t7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/979/VWUPlcbiO6t7.jpg</video:thumbnail_loc>

            <video:title>De Broglie???s Theory</video:title>

            <video:description><![CDATA[
This lesson explains de Broglie???s proposal that all matter exhibits wave properties. It introduces the relation ?? = h/mv and shows how this idea connects particle motion to quantised electron states.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/979/VWUPlcbiO6t7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/55G_ckL2HfkQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/55G_ckL2HfkQ.jpg</video:thumbnail_loc>

            <video:title>Unit vectors</video:title>

            <video:description><![CDATA[
This lesson introduces unit vectors ??? dimensionless vectors with a magnitude of one, used solely to specify direction. We will define the standard basis vectors, $\hat{i}$, $\hat{j}$, and $\hat{k}$, and use them to construct a concise and efficient notation for all vector algebra.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/55G_ckL2HfkQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fBP2Se2xa_fY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/675/fBP2Se2xa_fY.jpg</video:thumbnail_loc>

            <video:title>What is JavaScript?</video:title>

            <video:description><![CDATA[
HTML is the skeleton and CSS is the style; JavaScript is the brain that adds behaviour. This lesson defines JavaScript's role as the language of interactivity on the web, making pages responsive and dynamic.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/675/fBP2Se2xa_fY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4hrSuNxFX7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/4hrSuNxFX7.jpg</video:thumbnail_loc>

            <video:title>Decomposing functions</video:title>

            <video:description><![CDATA[
Learn to break down a complex engine pressure formula into three basic parts. You will identify the inner linear part, the middle power operation, and the final multiplication constant. This walkthrough teaches you to separate nested layers to simplify future calculus calculations. Solved: A mechanical engineering student is calculating the pressure in a car engine. The pressure is given by the function h(x) = 5(3x - 2)^6. Decompose this expression into three basic component functions a(x), b(x), and c(x) such that h(x) = c[b(a(x))]. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/4hrSuNxFX7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s97u8ZHVWhHb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/s97u8ZHVWhHb.jpg</video:thumbnail_loc>

            <video:title>Position and displacement vectors</video:title>

            <video:description><![CDATA[
This lesson generalises the concept of position to two and three dimensions using the position vector. We define this vector by its components and establish the displacement vector as the change in an object's position.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/s97u8ZHVWhHb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vyzTgTehvMkD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/vyzTgTehvMkD.jpg</video:thumbnail_loc>

            <video:title>Solving for the first term and ratio</video:title>

            <video:description><![CDATA[
A problem requiring the solution of simultaneous equations to find the first term and common ratio of a GP when two other terms are given.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/vyzTgTehvMkD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R3XT6rd56cSx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/R3XT6rd56cSx.jpg</video:thumbnail_loc>

            <video:title>Molecular geometry</video:title>

            <video:description><![CDATA[
Molecular shape depends on hybridisation. How do sp3, sp2, and sp states determine if a molecule is linear or tetrahedral? See the link between orbitals and geometry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/R3XT6rd56cSx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c_CaHC9bsfSL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/c_CaHC9bsfSL.jpg</video:thumbnail_loc>

            <video:title>Differentiability and continuity</video:title>

            <video:description><![CDATA[
Smooth curves allow differentiation; sharp corners break it. Can a function be continuous yet fail to have a gradient? Watch to see why continuity is necessary but not sufficient.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/c_CaHC9bsfSL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_8yxffid61h4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/_8yxffid61h4.jpg</video:thumbnail_loc>

            <video:title>Last term and sum of a finite AP</video:title>

            <video:description><![CDATA[
Master the core formulae for Arithmetic Progressions. This lesson defines the last term  and the  sum of terms for a finite AP, providing essential tools for linear analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/_8yxffid61h4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eEWj1pb_Mueq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/eEWj1pb_Mueq.jpg</video:thumbnail_loc>

            <video:title>Sub-atomic particles</video:title>

            <video:description><![CDATA[
This lesson defines the fundamental properties of the three subatomic particles. We will detail the relative mass and charge of the proton, neutron, and electron. A firm command of these values is required for all subsequent atomic calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/eEWj1pb_Mueq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F_9HiKiIEKWC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/F_9HiKiIEKWC.jpg</video:thumbnail_loc>

            <video:title>Hydrolysis of salts (2)</video:title>

            <video:description><![CDATA[
This lesson covers advanced hydrolysis problems involving salts of weak acids and weak bases. You will learn to calculate the degree of hydrolysis and the resulting pH by applying the relationship between Kh, Ka, and Kb. Master these complex equilibrium calculations to ensure high precision. Solved: Determine the pH of a solution containing 0.15 M potassium benzoate (K_a \text{ of C}_6\text{H}_5\text{COOH} = 6.5 \times 10^{-5}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/F_9HiKiIEKWC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kmbzt5uFyhyn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/kmbzt5uFyhyn.jpg</video:thumbnail_loc>

            <video:title>Resolving vectors (2)</video:title>

            <video:description><![CDATA[
This lesson is a focused problem walkthrough. We apply trigonometry to resolve another vector into its perpendicular components. Master the calculation steps; this skill is required. Solved: 2. A force vector \vec{F} of magnitude 50N is directed 35^{\circ} west of south. Find its x- and y- components. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/kmbzt5uFyhyn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7maTSOtaWAYD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/7maTSOtaWAYD.jpg</video:thumbnail_loc>

            <video:title>Chromatography</video:title>

            <video:description><![CDATA[
Given solvent and spot distances, how do you calculate Rf values and rank polarity on silica gel? Watch to solve and interpret like a pro. Solved: Separate a mixture of 2 components using TLC. If the solvent front moves a distance of 8.0 cm, component A moves a distance of 2.4 cm and B a distance of 6.8 cm. Calculate the retention factor of A and B and comment on their relative polarity if silica gel is used as the adsorbent. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/7maTSOtaWAYD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hpISoRC6UrHz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/hpISoRC6UrHz.jpg</video:thumbnail_loc>

            <video:title>Isotopy</video:title>

            <video:description><![CDATA[
This lesson defines isotopy, where atoms of the same element possess different numbers of neutrons. We will examine how this affects mass number whilst the atomic number remains constant, using key examples like the isotopes of hydrogen and carbon.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/hpISoRC6UrHz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a2IglgF_SvTY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/a2IglgF_SvTY.jpg</video:thumbnail_loc>

            <video:title>Types</video:title>

            <video:description><![CDATA[
Covalent bonds come in different strengths. What distinguishes a single sigma bond from double or triple pi bonds? See the types that define molecular stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/a2IglgF_SvTY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w_IZjhzY7S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/w_IZjhzY7S.jpg</video:thumbnail_loc>

            <video:title>Quadratic patterns</video:title>

            <video:description><![CDATA[
First principles handle any curve. How do you simplify the algebra for a quadratic function? Watch to see the limit calculation. Solved: Find the gradient of the curve y = 4x^2 + 5 at the point where x = 1.2 using the method of first principles. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/w_IZjhzY7S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/boDOvVaOn4We</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/boDOvVaOn4We.jpg</video:thumbnail_loc>

            <video:title>Multiple-angle patterns</video:title>

            <video:description><![CDATA[
Compound angles test your trig limits. How do you handle the inner coefficient in cos 2x? Watch to see the identity application. Solved: Derive the derivative of the function f(x) = \cos 2x from first principles. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/boDOvVaOn4We.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IoZMwdMVldQF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/970/IoZMwdMVldQF.jpg</video:thumbnail_loc>

            <video:title>The fundamental quantities</video:title>

            <video:description><![CDATA[
This lesson identifies the seven fundamental quantities that form the irreducible basis of the SI system. We will define each one in turn. Immediate recall of this complete set is a non-negotiable requirement for any work in the physical sciences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/970/IoZMwdMVldQF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zql4LBsMv9Ks</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/970/Zql4LBsMv9Ks.jpg</video:thumbnail_loc>

            <video:title>Notations and prefixes</video:title>

            <video:description><![CDATA[
Physical measurements span vast orders of magnitude. This lesson presents the standard methods for managing this scale: scientific notation (standard form) and SI prefixes. Correct application of these conventions is mandatory for all technical work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/970/Zql4LBsMv9Ks.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AuDHQxbos04w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/971/AuDHQxbos04w.jpg</video:thumbnail_loc>

            <video:title>Mass</video:title>

            <video:description><![CDATA[
This lesson defines mass as the measure of inertia, a fundamental quantity distinct from weight. We establish its formal definition and its SI base unit, the kilogram (kg).  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/971/AuDHQxbos04w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7qiK4yMY_Flz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/970/7qiK4yMY_Flz.jpg</video:thumbnail_loc>

            <video:title>Physical quantities</video:title>

            <video:description><![CDATA[
This lesson defines a physical quantity: any property that can be quantified by measurement. It establishes that every quantity consists of a numerical magnitude and a unit. This two-part structure is the fundamental basis for all quantitative science.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/970/7qiK4yMY_Flz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Fm8aLxtoJVWq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/Fm8aLxtoJVWq.jpg</video:thumbnail_loc>

            <video:title>Fundamental quantum numbers</video:title>

            <video:description><![CDATA[
This lesson introduces Schr??dinger???s equation as the foundation of atomic structure. It explains how its solutions give the principal and azimuthal quantum numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/Fm8aLxtoJVWq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qaaVsRKdSFhi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/676/qaaVsRKdSFhi.jpg</video:thumbnail_loc>

            <video:title>Basic operators</video:title>

            <video:description><![CDATA[
This lesson covers the basic operators for performing calculations and making comparisons. We will explore arithmetic operators for math and comparison operators for evaluating logical statements.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/676/qaaVsRKdSFhi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qDsxzqXmxZIC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/820/qDsxzqXmxZIC.jpg</video:thumbnail_loc>

            <video:title>Shortcomings of Thomson's model</video:title>

            <video:description><![CDATA[
This lesson examines the failure of Thomson's 'plum pudding' model. The model was invalidated by Rutherford's gold foil experiment, as it could not explain the large-angle scattering of alpha particles and some other concept.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/820/qDsxzqXmxZIC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5XF0DX7j_7N5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/5XF0DX7j_7N5.jpg</video:thumbnail_loc>

            <video:title>Fundamental laws</video:title>

            <video:description><![CDATA[
Learn the rules for limits involving addition, subtraction, multiplication, and division. These laws allow you to break down complex expressions into simple parts for quick and accurate evaluation. You will also master constant multiple and power rules to solve various problems with precision.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/5XF0DX7j_7N5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sLxZeifBgc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/sLxZeifBgc.jpg</video:thumbnail_loc>

            <video:title>Reciprocals and radicals</video:title>

            <video:description><![CDATA[
Fractions and roots look tricky in calculus. How do you rewrite reciprocals and radicals as powers to use the standard rule? Watch to see the simple conversion trick.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/sLxZeifBgc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/niW87v4HV_Ng</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/niW87v4HV_Ng.jpg</video:thumbnail_loc>

            <video:title>Polarity scale</video:title>

            <video:description><![CDATA[
Bond polarity varies by strength. How do you rank bonds from nonpolar to ionic using electronegativity? See the scale that measures electron pull.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/niW87v4HV_Ng.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NVoBWkJOQARX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1072/NVoBWkJOQARX.jpg</video:thumbnail_loc>

            <video:title>Empirical and molecular formula (3)</video:title>

            <video:description><![CDATA[
Elemental analysis gives percentage composition and molar mass of an organic acid. How do you convert these values into the correct molecular formula? This worked example shows the exact calculation steps to solve this problem accurately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1072/NVoBWkJOQARX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0yXdL2aPLZI_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/0yXdL2aPLZI_.jpg</video:thumbnail_loc>

            <video:title>Adding vectors (2)</video:title>

            <video:description><![CDATA[
This problem applies the component method to vector addition. We resolve multiple vectors, sum their x and y components, and then calculate the final resultant vector. Master this standard calculation; it is essential.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/0yXdL2aPLZI_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YcMyHeLkIOc2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/YcMyHeLkIOc2.jpg</video:thumbnail_loc>

            <video:title>Calculating vector products (2)</video:title>

            <video:description><![CDATA[
We execute another vector (cross) product calculation. This problem applies the determinant method and also demonstrates calculator verification. Master this core procedure. Solved: 8. Find \vec{A} \times \vec{B} given that \vec{A} = 3\underline{i} + \underline{j} - 2\underline{k} and \vec{B} = 2\underline{i} - 4\underline{j} + 3\underline{k}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/YcMyHeLkIOc2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aYMce6Fdaofk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/aYMce6Fdaofk.jpg</video:thumbnail_loc>

            <video:title>Velocity vectors</video:title>

            <video:description><![CDATA[
This lesson defines the average velocity vector and the instantaneous velocity vector. The instantaneous velocity is always tangent to the particle's path, and its magnitude is the particle's speed.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/aYMce6Fdaofk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mCURiQXBbz_F</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/mCURiQXBbz_F.jpg</video:thumbnail_loc>

            <video:title>Formal charges</video:title>

            <video:description><![CDATA[
Learn to calculate formal charge for each atom. This tool is essential for evaluating competing Lewis structures - such as those for Phosgene (COCl2). We apply rules to select the most stable structure - which is the one that minimises formal charge.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/mCURiQXBbz_F.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Uyw0OAjglOMB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/Uyw0OAjglOMB.jpg</video:thumbnail_loc>

            <video:title>Examples of ionic bonds (1)</video:title>

            <video:description><![CDATA[
This lesson reviews the formation of simple ionic compounds via electron transfer. We demonstrate bond formation for Sodium chloride (NaCl), Calcium chloride (CaCl2), and Lithium oxide (Li2O). Focus on calculating the correct number of electrons transferred to achieve stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/Uyw0OAjglOMB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JfkXvjtnh_dB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/JfkXvjtnh_dB.jpg</video:thumbnail_loc>

            <video:title>Exceptions to the octet rule</video:title>

            <video:description><![CDATA[
The octet rule is not absolute. This lesson details its three exceptions - incomplete octets, odd-electron species, and expanded octets. We examine Nitrogen monoxide (NO) and Boron trifluoride (BF3) to master the odd-electron and incomplete octet cases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/JfkXvjtnh_dB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TKhfjTflN0Hw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/TKhfjTflN0Hw.jpg</video:thumbnail_loc>

            <video:title>Angular acceleration</video:title>

            <video:description><![CDATA[
Calculate the rate of change in angular speed for blender blades using the acceleration formula. You will convert RPM to radians per second before finding the final acceleration value. This step-by-step walkthrough shows how to solve for objects speeding up their spin. Solved: The blades of an electric blender speed up from 1500 \text{ rev/min} to 4500 \text{ rev/min} in 10 \text{ seconds}. Calculate the average angular acceleration of the blades in \text{rad/s}^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/TKhfjTflN0Hw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wa3kBolyupLW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/829/wa3kBolyupLW.jpg</video:thumbnail_loc>

            <video:title>Examples (2)</video:title>

            <video:description><![CDATA[
This second lesson reinforces hybridization theory - focusing on molecules with expanded octets. We determine the hybridization of Boron trichloride (BCl3), Phosphorus pentachloride (PCl5), and Sulphur hexafluoride (SF6). Master identifying hybrid orbitals including those that use d-orbitals (sp3d and sp3d2).  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/829/wa3kBolyupLW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sMcSthdaDlID</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/sMcSthdaDlID.jpg</video:thumbnail_loc>

            <video:title>Examples using formal charges (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates the practical application of formal charge. We review examples using the Chlorite ion (ClO2-) and Sulfuric acid (H2SO4). Master the rules for selecting the most plausible Lewis structure by minimising formal charges.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/sMcSthdaDlID.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Eh9QNEjYDFjL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/Eh9QNEjYDFjL.jpg</video:thumbnail_loc>

            <video:title>Solvent extraction formula</video:title>

            <video:description><![CDATA[
Stop guessing extraction yields. How does the general formula prove that multiple small washes beat one large one? Watch to master the calculation for any number of steps. Solved: Generally, q^n = \left\{ \frac{V_{aq}}{K_D \cdot V_{org} + V_{aq}} \right\}^nApply this eq² to the previous example. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/Eh9QNEjYDFjL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lnBYUO4iA49X</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/lnBYUO4iA49X.jpg</video:thumbnail_loc>

            <video:title>Shapes of orbitals</video:title>

            <video:description><![CDATA[
This lesson describes the spatial shapes of s, p, d, and f orbitals. It explains how quantum numbers determine these forms and their significance in atomic structure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/lnBYUO4iA49X.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9VtoR6_WonPs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/886/9VtoR6_WonPs.jpg</video:thumbnail_loc>

            <video:title>Summary of progressions</video:title>

            <video:description><![CDATA[
A concise review of the key definitions, properties, and formulas for Arithmetic, Geometric, and Harmonic Progressions. This lesson ensures all material has been consolidated.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/886/9VtoR6_WonPs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uKPZ1_Uk3XiK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/uKPZ1_Uk3XiK.jpg</video:thumbnail_loc>

            <video:title>Examples using formal charges (2)</video:title>

            <video:description><![CDATA[
This lesson applies formal charge rules to structures with expanded octets. We use Phosphorus pentachloride (PCl5), Sulfur hexafluoride (SF6), and Sulfur tetrafluoride (SF4). Master how minimising formal charge determines the most plausible structure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/uKPZ1_Uk3XiK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tkAUHNisUb3o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/tkAUHNisUb3o.jpg</video:thumbnail_loc>

            <video:title>Properties of ionic compounds</video:title>

            <video:description><![CDATA[
This lesson details the physical properties of ionic compounds. We explain how strong electrostatic forces cause high melting points, brittleness, and electrical conductivity when molten or in solution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/tkAUHNisUb3o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/q0UXKgFbU7Er</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/q0UXKgFbU7Er.jpg</video:thumbnail_loc>

            <video:title>Angular acceleration</video:title>

            <video:description><![CDATA[
Angular acceleration measures the rate at which a spinning object changes its speed or direction of rotation. Calculate this using the change in angular velocity over time, expressed in radians per second squared. This quantity is the rotational version of linear acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/q0UXKgFbU7Er.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wt_izUH9qGGy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/wt_izUH9qGGy.jpg</video:thumbnail_loc>

            <video:title>Electronegativity</video:title>

            <video:description><![CDATA[
This lesson defines electronegativity: an atom's ability to attract shared electrons in a chemical bond. We will explain the periodic trends for this property, justifying them using effective nuclear charge and atomic size.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/wt_izUH9qGGy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/igp33wrFxGne</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/igp33wrFxGne.jpg</video:thumbnail_loc>

            <video:title>Angular displacement</video:title>

            <video:description><![CDATA[
Convert radians to degrees and revolutions using a circular saw example. This walkthrough demonstrates exact calculation steps for angular displacement. Proper unit conversion is the first step in solving any spinning problem. Solved: A circular saw blade in a carpentry workshop turns through an angle of 7.2 \text{ rad}. Calculate the number of degrees and the number of revolutions the blade has completed. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/igp33wrFxGne.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_SFDkLEi71jK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/_SFDkLEi71jK.jpg</video:thumbnail_loc>

            <video:title>Angular velocity</video:title>

            <video:description><![CDATA[
Convert revolutions per minute to radians per second using a grinding machine example. This calculation is vital for finding the true rate of spin in physics equations. Mastering this unit shift ensures your angular speed values are ready for standard formulas. Solved: A maize grinding machine at a local mill rotates at a steady rate of 1500 \text{ rev/min}. Calculate its angular velocity in \text{rad/s}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/_SFDkLEi71jK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V_T9JCKPcUvL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/972/V_T9JCKPcUvL.jpg</video:thumbnail_loc>

            <video:title>Homogeneity of equations</video:title>

            <video:description><![CDATA[
This lesson introduces the principle of dimensional homogeneity. This is the fundamental rule that for any physical equation to be valid, all its constituent terms must have the exact same dimensions. This concept is the basis for all dimensional checks.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/972/V_T9JCKPcUvL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VwSMYu3I3Quk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/VwSMYu3I3Quk.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity</video:title>

            <video:description><![CDATA[
Evaluate how a function behaves as the input increases or decreases without limit. You will master the rules for finding horizontal asymptotes and predicting end behaviour for polynomial and rational functions. This lesson explains how curves flatten out or grow as they move toward infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/VwSMYu3I3Quk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nRxTxEF03z_h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/927/nRxTxEF03z_h.jpg</video:thumbnail_loc>

            <video:title>Linear-angular relations</video:title>

            <video:description><![CDATA[
Calculate the angular speed of a grinding stone from its radius and tangential velocity. This walkthrough shows how to link straight-line movement to the rate of spin. Use this relation to solve for any part of a rotating machine. Solved: A grinding stone in a local market has a radius of 0.25 \text{ m}. If a point on its outer edge moves with a tangential speed of 2.5 \text{ m/s}, calculate the angular speed of the stone in \text{rad/s}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/927/nRxTxEF03z_h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1cGVtaELIMLi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/1cGVtaELIMLi.jpg</video:thumbnail_loc>

            <video:title>Two-variable inequality (1)</video:title>

            <video:description><![CDATA[
Solve a linear inequality with two variables by plotting the boundary line and shading the correct half-plane. You will learn to determine the solution region by testing a coordinate point and using solid or broken lines for inclusive or exclusive constraints. This is the basis for linear programming. Solved: 11. Graph the solution of the linear inequality3x - 2y \le 6 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/1cGVtaELIMLi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/geHmfc3bg6uS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/geHmfc3bg6uS.jpg</video:thumbnail_loc>

            <video:title>Adding vectors (1)</video:title>

            <video:description><![CDATA[
This lesson is a systematic application of the component method. We will resolve multiple vectors, sum their respective components, and then compute the final resultant vector's magnitude and direction. Solved: 3. Find the resultant of two forces 4N due East and 3N due North. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/geHmfc3bg6uS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hhn_2KEkA57C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/972/hhn_2KEkA57C.jpg</video:thumbnail_loc>

            <video:title>Dimensions</video:title>

            <video:description><![CDATA[
This lesson distinguishes the concept of a physical dimension from a unit. It establishes the fundamental dimensions ??? [M], [L], [T] ??? and demonstrates the method for deriving the dimensional formula for any quantity. This is the required first step for all analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/972/hhn_2KEkA57C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2sZXk98zflcp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/908/2sZXk98zflcp.jpg</video:thumbnail_loc>

            <video:title>Speed and velocity (1)</video:title>

            <video:description><![CDATA[
This lesson defines the rate of change of position. We will distinguish between average speed, a scalar quantity derived from total distance, and average velocity, a vector quantity derived from displacement. This distinction is fundamental to all subsequent analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/908/2sZXk98zflcp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/doFH_KgRRk0C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/doFH_KgRRk0C.jpg</video:thumbnail_loc>

            <video:title>Classification (1)</video:title>

            <video:description><![CDATA[
This lesson classifies elements as metals, non-metals, and metalloids. We will define the key physical and chemical properties that distinguish these classes and relate them to their positions on the periodic table.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/doFH_KgRRk0C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QIF6fYRtc47t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/QIF6fYRtc47t.jpg</video:thumbnail_loc>

            <video:title>Covalent bonds in heteronuclear molecules</video:title>

            <video:description><![CDATA[
This lesson covers covalent bonding between different atoms - heteronuclear molecules. We use Hydrogen fluoride (HF), Carbon dioxide (CO2), and Carbon monoxide (CO) to explain how differences in electronegativity lead to unequal electron sharing and polar bonds. Understand the resulting bond dipole moment.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/QIF6fYRtc47t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bw_NClGh0p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/bw_NClGh0p.jpg</video:thumbnail_loc>

            <video:title>Visual inspection</video:title>

            <video:description><![CDATA[
Learn to determine a limit visually by inspecting a graph with an open circle. You will track the output value as it approaches a gap from both sides to find the visual limit. This walkthrough shows that the limit exists at a hole even if the function is undefined there. Solved: A graph of a function shows a straight line with a slope of 1, defined by y = x + 7, but with an open circle at the point (5, 12). By inspecting the approach from both sides on the graph, determine \lim_{x \to 5} f(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/bw_NClGh0p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YQOhROLNd2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/YQOhROLNd2.jpg</video:thumbnail_loc>

            <video:title>Formal charge</video:title>

            <video:description><![CDATA[
Atoms in molecules carry hidden charges. How do you calculate formal charge to find the most stable structure? See the math that predicts molecular reality.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/YQOhROLNd2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cm5Ff0JUY4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/cm5Ff0JUY4.jpg</video:thumbnail_loc>

            <video:title>Parametric differentiation</video:title>

            <video:description><![CDATA[
Some curves depend on a third variable. How do you find the gradient when x and y are both defined by time? See how to link them for the answer.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/cm5Ff0JUY4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/toruaQ1pUR76</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/toruaQ1pUR76.jpg</video:thumbnail_loc>

            <video:title>Coordinate covalent bonds</video:title>

            <video:description><![CDATA[
This lesson defines the coordinate covalent bond. We use the Ammonium ion (NH4+) and the Hydronium ion (H3O+) to demonstrate bond formation where one atom supplies both shared electrons. Understand that the resulting bond is structurally identical to a standard covalent bond.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/toruaQ1pUR76.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AaxoaKZ8VoHY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/AaxoaKZ8VoHY.jpg</video:thumbnail_loc>

            <video:title>One-sided absolute values</video:title>

            <video:description><![CDATA[
Solve inequalities where the absolute value is on one side by splitting the expression into two distinct cases. You will learn to isolate the variable using case-based logic and represent the combined solution set on a number line. This walkthrough ensures precision when handling distance-based constraints. Solved: 9. Solve the inequality \left| \frac{3x-2}{4} \right| \le 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/AaxoaKZ8VoHY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JY5cS0Elg09h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/JY5cS0Elg09h.jpg</video:thumbnail_loc>

            <video:title>Polar covalent bonds</video:title>

            <video:description><![CDATA[
This lesson defines the polar covalent bond. We link differences in atomic electronegativity to unequal electron sharing - which creates a bond dipole. Bonds analysed include H-F, P-H, H-O, and C-Cl. Understand how bond polarity lies between pure covalent and ionic bonding.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/JY5cS0Elg09h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lQ_ByRZgbV2s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/lQ_ByRZgbV2s.jpg</video:thumbnail_loc>

            <video:title>Equations of motion (2)</video:title>

            <video:description><![CDATA[
This lesson isolates the vertical component of projectile motion. We establish that this motion proceeds under constant downward acceleration due to gravity. The three standard kinematic equations are derived and explained for use in this axis. Master these relationships to calculate maximum height and time of flight.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/lQ_ByRZgbV2s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/swzBzKNzbhik</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/828/swzBzKNzbhik.jpg</video:thumbnail_loc>

            <video:title>Examples (2)</video:title>

            <video:description><![CDATA[
This second lesson provides advanced VSEPR examples involving six or more electron domains. We determine the geometry of Xenon difluoride (XeF2), Sulphur hexafluoride (SF6), Bromine pentafluoride (BrF5), and Xenon tetrafluoride (XeF4). Master the prediction of complex geometries with multiple lone pairs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/828/swzBzKNzbhik.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fWkTC67tHjiu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/824/fWkTC67tHjiu.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
This lesson provides a final, high-level summary of the course. We will connect the evolution of atomic theory to the quantum model and reinforce the direct link between electronic configuration and periodic properties.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/824/fWkTC67tHjiu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pb_RRilrTNkA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/Pb_RRilrTNkA.jpg</video:thumbnail_loc>

            <video:title>Average velocity (2)</video:title>

            <video:description><![CDATA[
A further example applying the average velocity definition. We reinforce the vector subtraction to find displacement, then divide by the time interval. Master the calculation. Solved: A plane flies 483 km east from city A to city B in 45.0 min, and then 966 km south from city B to city C in 1.50 hr. For the total trip, find(a) the magnitude,(b) the directionof the plane's average velocity. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/Pb_RRilrTNkA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ixw7Ru9_P1l2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/928/ixw7Ru9_P1l2.jpg</video:thumbnail_loc>

            <video:title>Basic kinematics</video:title>

            <video:description><![CDATA[
Calculate angular displacement and final velocity for a processing shaft using rotational kinematics.  This walkthrough shows how to apply standard formulas when an object is already spinning and accelerating steadily. Use these steps to solve motion problems. Solved: A heavy shaft in a cassava processing machine rotates with a constant angular acceleration of 4.5 \text{ rad/s}^2. At the start of an observation (t = 0), the shaft is already spinning at 1.2 \text{ rad/s}. Calculate the angular displacement of the shaft and its final angular speed after 6.0 \text{ seconds}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/928/ixw7Ru9_P1l2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UfWn4bCwxv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/UfWn4bCwxv.jpg</video:thumbnail_loc>

            <video:title>Transcendental product</video:title>

            <video:description><![CDATA[
Mixing algebra with trigonometry requires care. How do you apply the product rule to to obtain the derivative? Watch the steps unfold. Solved: Determine the derivative of the function y = x^3 \cos x with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/UfWn4bCwxv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RO7HhjUiVm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/RO7HhjUiVm.jpg</video:thumbnail_loc>

            <video:title>Logarithmic differentiation</video:title>

            <video:description><![CDATA[
Standard rules fail when variables sit in both base and exponent. How do you differentiate complex products or variable powers? Learn the log trick to simplify and solve it.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/RO7HhjUiVm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v0G7CAm9bJFa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/850/v0G7CAm9bJFa.jpg</video:thumbnail_loc>

            <video:title>Summary and practice questions</video:title>

            <video:description><![CDATA[
This lesson reviews all core concentration units, dilution principles, and solution-phase stoichiometry. You will solve comprehensive practice questions that integrate these concepts to validate your analytical accuracy. Mastering these problems confirms your readiness for advanced volumetric analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/850/v0G7CAm9bJFa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xipI_j8gaHyU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/xipI_j8gaHyU.jpg</video:thumbnail_loc>

            <video:title>The arithmetic mean</video:title>

            <video:description><![CDATA[
Defines the arithmetic mean of two numbers and its relationship to an Arithmetic Progression. This lesson also covers the insertion of multiple arithmetic means.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/xipI_j8gaHyU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oSdJx74rtdOA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/831/oSdJx74rtdOA.jpg</video:thumbnail_loc>

            <video:title>Practice questions</video:title>

            <video:description><![CDATA[
This lesson features comprehensive practice questions covering all course topics: Lewis structures, VSEPR geometry, hybridisation, and intermolecular forces. Use this session to test your mastery of the connection between electronic structure and molecular properties.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/831/oSdJx74rtdOA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wH__EOf9CqPp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/677/wH__EOf9CqPp.jpg</video:thumbnail_loc>

            <video:title>Submitting the form</video:title>

            <video:description><![CDATA[
This lesson makes your contact form fully functional. You will learn to use a third-party service to handle submissions and apply JavaScript for client-side validation, ensuring the form works as a live, professional component.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/677/wH__EOf9CqPp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BtqFxEMpRt4G</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/BtqFxEMpRt4G.jpg</video:thumbnail_loc>

            <video:title>Worked examples III</video:title>

            <video:description><![CDATA[
More worked examples on classification of quadric surfaces by eigenvalue inspection and / or variable substitution. Solved: Given the quadric surface z^2=3x^2+4y^2-12 i)Obtain the symmetric coefficient matrix(SCM),find its rank, compute its eigenvalues and hence, predict the nature of the quadric surface.ii)Show that the normalized eigen vectors form the orthogonal diagonalizing matrixiii)Hence, classify the quadric surface using variable substitution approach 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/BtqFxEMpRt4G.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ItDsiVgrQMd8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/ItDsiVgrQMd8.jpg</video:thumbnail_loc>

            <video:title>Hydrogen bonding</video:title>

            <video:description><![CDATA[
This lesson defines hydrogen bonding - the strong intermolecular force. We explain its formation between hydrogen and N, O, or F. We contrast Water (H2O), Ethanol (C2H5OH), and Hydrogen fluoride (HF) with Hydrogen chloride (HCl) to establish the critical requirements.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/ItDsiVgrQMd8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rSIXL1ucVREs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/882/rSIXL1ucVREs.jpg</video:thumbnail_loc>

            <video:title>Defining a sequence</video:title>

            <video:description><![CDATA[
Formally defines a sequence as an ordered list of numbers. The lesson clarifies the concept of a term and the notation used to represent the general term of a sequence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/882/rSIXL1ucVREs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XeAh5XwdkCzl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/XeAh5XwdkCzl.jpg</video:thumbnail_loc>

            <video:title>Infinite limits</video:title>

            <video:description><![CDATA[
Learn to evaluate an infinite limit by approaching zero from the left and identifying the resulting vertical asymptote. You will see how the output increases without bound as the denominator gets smaller. This walkthrough shows you how to state the final equation for the asymptote accurately. Solved: Evaluate \lim_{x \to 0^-} \frac{12}{x^2} and state the equation of the vertical asymptote. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/XeAh5XwdkCzl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1w_PCAietlFX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1072/1w_PCAietlFX.jpg</video:thumbnail_loc>

            <video:title>Empirical and molecular formula (4)</video:title>

            <video:description><![CDATA[
Percentage composition and molar mass define an organic compound. How do you convert these analytical values into the correct molecular formula? This worked example demonstrates the precise calculation steps to solve this problem accurately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1072/1w_PCAietlFX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rm_lH3CfIFrN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/928/rm_lH3CfIFrN.jpg</video:thumbnail_loc>

            <video:title>Time to stop</video:title>

            <video:description><![CDATA[
Calculate how long a body takes to stop using the first rotational motion equation.  This walkthrough shows how to handle constant deceleration when a spinning machine loses power. Proper sign use is key to finding the correct time. Solved: A ceiling fan is spinning clockwise at 15.0 \text{ rad/s} when the power is turned off. Due to friction, it undergoes a constant angular deceleration of 0.60 \text{ rad/s}^2. Determine the time taken for the fan blades to come to a complete stop. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/928/rm_lH3CfIFrN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ntXtecR2uF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/ntXtecR2uF.jpg</video:thumbnail_loc>

            <video:title>Linear particle acceleration</video:title>

            <video:description><![CDATA[
Fields accelerate charged particles. How do you calculate the final speed of a proton in a uniform electric field? Watch to solve this linear acceleration problem. Solved: A proton is placed in a uniform electric field of magnitude 500\text{ N/C}. Calculate the speed of the proton after it has been accelerated from rest for 3.00 \times 10^{-7}\text{ s}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/ntXtecR2uF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5bk8QPVd0swd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/5bk8QPVd0swd.jpg</video:thumbnail_loc>

            <video:title>Chadwick's nuclear bombardment</video:title>

            <video:description><![CDATA[
This lesson details Chadwick's bombardment experiment, which provided the evidence for the neutron. By observing the neutral radiation from alpha particle bombardment of beryllium, he identified a new nuclear particle. This completed the proton-neutron atomic model.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/5bk8QPVd0swd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DqwIVOcUidKx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/DqwIVOcUidKx.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity</video:title>

            <video:description><![CDATA[
Learn to calculate the limit as a variable approaches infinity by identifying how terms with large denominators vanish. You will determine the horizontal asymptote by solving the remaining constant value. This walkthrough shows you how to predict long-term trends for rational expressions. Solved: Evaluate \lim_{x \to \infty} \left( \frac{8}{x} + 3 \right) and state the equation of the horizontal asymptote. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/DqwIVOcUidKx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X3KyUfVfIqhj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/X3KyUfVfIqhj.jpg</video:thumbnail_loc>

            <video:title>Rutherford's gold foil experiment</video:title>

            <video:description><![CDATA[
This lesson examines Rutherford's pivotal gold foil experiment. The surprising deflection of a few alpha particles at large angles invalidated the Thomson model. This observation was only explainable by concentrating the atom's mass and positive charge into a tiny nucleus.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/X3KyUfVfIqhj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iDLW2coEqGyH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/823/iDLW2coEqGyH.jpg</video:thumbnail_loc>

            <video:title>First ionisation energy</video:title>

            <video:description><![CDATA[
This lesson explains the periodic trend of first ionisation energy across periods and down groups. We will justify these variations using effective nuclear charge, electron shielding, and orbital stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/823/iDLW2coEqGyH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tP5rzUqqaVIv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/978/tP5rzUqqaVIv.jpg</video:thumbnail_loc>

            <video:title>Shortcomings</video:title>

            <video:description><![CDATA[
This lesson details the critical failures of the Bohr model, focusing on its inability to describe multi-electron atoms and its violation of the Heisenberg Uncertainty Principle. Understanding these shortcomings is essential to appreciate the necessity of the modern quantum mechanical model.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/978/tP5rzUqqaVIv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T48GrZ265Xio</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/820/T48GrZ265Xio.jpg</video:thumbnail_loc>

            <video:title>Laws of chemical combination</video:title>

            <video:description><![CDATA[
This lesson examines the laws governing mass relationships in chemical reactions. We cover conservation of mass, definite proportions, and multiple proportions. Understand these principles as the quantitative evidence for Dalton's atomic theory.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/820/T48GrZ265Xio.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DcDdf9A82c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/DcDdf9A82c.jpg</video:thumbnail_loc>

            <video:title>Logarithmic expansion</video:title>

            <video:description><![CDATA[
Complex fractions with powers are hard to differentiate. How do you use log laws to break them into simple sums before finding the derivative? Watch the expansion trick. Solved: Determine the derivative of the function w = \frac{(z+2)^2 \sqrt{z+5}}{(z-3)^4} with respect to z. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/DcDdf9A82c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8nQ5T5XsUWEi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Thumbnails/928/8nQ5T5XsUWEi.jpg</video:thumbnail_loc>

            <video:title>Revolutions without time</video:title>

            <video:description><![CDATA[
Calculate total revolutions for an accelerating object without using time. Use the third rotational kinematic equation to find angular displacement, then convert your final result from radians to revolutions. This method is the fastest way to solve motion problems where time is unknown. Solved: The rear tyre of a motorcycle accelerates from an angular speed of 6.0 \text{ rad/s} to 28.0 \text{ rad/s} with a constant angular acceleration of 4.0 \text{ rad/s}^2. Calculate the total number of revolutions the tyre completes during this period. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/x7iN4teAEW/Previews/928/8nQ5T5XsUWEi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HiEvdrmnbFW6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/HiEvdrmnbFW6.jpg</video:thumbnail_loc>

            <video:title>Calculating molar solubility</video:title>

            <video:description><![CDATA[
This lesson provides worked examples for calculating molar solubility from a given solubility product constant. You will learn to set up equilibrium expressions for various salts, such as chromium iodate, and solve for the unknown concentration of a saturated solution at 25 degrees Celsius. Solved: Example 1:Chromium iodate has the solubility product, K_{sp} value of 5.0 \times 10^{-6} at 25??C. Estimate the molar solubility of this salt at 25??C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/HiEvdrmnbFW6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BmmznzTDRdVI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/BmmznzTDRdVI.jpg</video:thumbnail_loc>

            <video:title>Common-ion effect (2)</video:title>

            <video:description><![CDATA[
This lesson covers calculating the molar solubility of silver bromide in a calcium bromide solution. You will learn to determine the initial concentration of the common bromide ion and use it in the equilibrium expression to solve for the reduced solubility of the silver salt. Solved: Example 2: What is the approximate molar solubility of silver bromide in a 0.10 M CaBr_2 solution, given that the K_{sp} for AgBr is 7.7 \times 10^{-13}? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/BmmznzTDRdVI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ukuRjK7o6VYk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1034/ukuRjK7o6VYk.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson explains how to arrange items when some are identical. You will learn the formula to remove duplicate patterns by dividing total permutations by the factorials of the repeated objects.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1034/ukuRjK7o6VYk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oHWn9MW_nlO9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/oHWn9MW_nlO9.jpg</video:thumbnail_loc>

            <video:title>Reciprocal ratios</video:title>

            <video:description><![CDATA[
Calculate the exact value of a primary ratio from a given reciprocal ratio using Pythagoras’ theorem. This walkthrough demonstrates how to sketch a triangle from a ratio to find missing sides and secondary functions. It is a critical skill for simplifying algebraic trigonometric expressions. Solved: Given that \csc \beta = \frac{17}{8}, where \beta is an acute angle, find the exact value of \cos \beta. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/oHWn9MW_nlO9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bjHLMdLWgHEg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/bjHLMdLWgHEg.jpg</video:thumbnail_loc>

            <video:title>Analysis of the trajectory (1)</video:title>

            <video:description><![CDATA[
This lesson derives the equation for the parabolic trajectory of a projectile. We combine the time-dependent horizontal and vertical equations to express y as a function of x. Master this derivation to prove that projectile motion is fundamentally parabolic.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/bjHLMdLWgHEg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5xkFYE0sG7e2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/5xkFYE0sG7e2.jpg</video:thumbnail_loc>

            <video:title>Field and weight balance</video:title>

            <video:description><![CDATA[
Electric force can balance weight. How do you find the field magnitude and direction to hold a charged object stationary? Watch to solve this equilibrium problem. Solved: A tiny bead with a mass of 6.50\text{ g} and a charge of -30.0 \mu\text{C} is held stationary in mid-air by a uniform vertical electric field. Determine the magnitude and direction (upward or downward) of this electric field. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/5xkFYE0sG7e2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SBLBrhTGP2Vc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/SBLBrhTGP2Vc.jpg</video:thumbnail_loc>

            <video:title>Relations</video:title>

            <video:description><![CDATA[
This lesson explains how to pair elements from two sets to form a relation using ordered pairs. You will learn to identify the domain and range and represent these links using arrow diagrams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/SBLBrhTGP2Vc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3qi8iEvjoUP2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/3qi8iEvjoUP2.jpg</video:thumbnail_loc>

            <video:title>Solution of weak bases</video:title>

            <video:description><![CDATA[
This lesson explains the partial ionisation of weak bases and the use of the base dissociation constant, Kb, to measure equilibrium strength. You will learn to formulate equilibrium expressions and calculate hydroxide ion concentrations. These steps are essential for determining the pH of basic solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/3qi8iEvjoUP2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P1qTlurexbu5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/678/P1qTlurexbu5.jpg</video:thumbnail_loc>

            <video:title>Looping with forEach</video:title>

            <video:description><![CDATA[
This lesson introduces iteration, the process of performing an action on every item in an array. You will learn the forEach method, a simple and readable way to loop through data collections without a complex setup.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/678/P1qTlurexbu5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8fkXmZ7jo_Fu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/8fkXmZ7jo_Fu.jpg</video:thumbnail_loc>

            <video:title>Use of LCM</video:title>

            <video:description><![CDATA[
Mixed radicals block standard substitution. How do you clear different root indices in one step? We use the LCM Power to rationalise the integrand. Solved: Evaluate the indefinite integral \int \frac{1}{x^{1/2} + x^{1/3}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/8fkXmZ7jo_Fu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kBtXUTV3UHdv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/883/kBtXUTV3UHdv.jpg</video:thumbnail_loc>

            <video:title>Definition and the nth term formula</video:title>

            <video:description><![CDATA[
Formally defines an Arithmetic Progression. It establishes the concept of the common difference added to each term to produce the next. Two main ingredients are essential in obtaining the nth of an arithmetic progression.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/883/kBtXUTV3UHdv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TaNWPn126uVb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/TaNWPn126uVb.jpg</video:thumbnail_loc>

            <video:title>Horizontal projectiles (2)</video:title>

            <video:description><![CDATA[
We analyse another case of a projectile launched horizontally from a height. With an initial vertical velocity of zero, the vertical analysis simplifies to free fall. We calculate the time of flight based solely on the drop height and determine the final horizontal displacement. Solved: 4. A stone is thrown horizontally with a speed of 15.0 \text{ m/s} from the top of a vertical cliff. It hits the ground after 3.0\text{s}. Calculate the magnitude and direction of its velocity just before it hits the ground. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/TaNWPn126uVb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2AzYy_kj23QJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/2AzYy_kj23QJ.jpg</video:thumbnail_loc>

            <video:title>Parabolic trajectory</video:title>

            <video:description><![CDATA[
Charges curve in uniform fields. How do you calculate the vertical deflection of an electron moving through parallel plates? Watch to solve this parabolic trajectory problem. Solved: An electron enters a region between two horizontal parallel plates with an initial horizontal speed of 4.00 \times 10^6 \text{ m/s}. The plates are 15.0 \text{ cm} long, and a uniform downward electric field of 300 \text{ N/C} exists between them. Calculate the vertical deflection of the electron as it exits the plates. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/2AzYy_kj23QJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vw5VYdNFw8y3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/Vw5VYdNFw8y3.jpg</video:thumbnail_loc>

            <video:title>Assembly work</video:title>

            <video:description><![CDATA[
System Energy requires summing every unique charge pair. How do you handle mixed signs in a triangular setup? We calculate the total assembly work for this configuration. Solved: Three charged particles are fixed at the corners of an equilateral triangle with sides of length 18.0 \text{ cm}. The charges are q_1 = +q, q_2 = -3q, and q_3 = +2q, where q = 250 \text{ nC}. Calculate the total electric potential energy stored in this system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/Vw5VYdNFw8y3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qfWNsAbnm9zT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/qfWNsAbnm9zT.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on vector equations with unknown vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/qfWNsAbnm9zT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U3XxKANGqVUo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/U3XxKANGqVUo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on vector equations with unknown vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/U3XxKANGqVUo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kESF5DuZlWHS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/kESF5DuZlWHS.jpg</video:thumbnail_loc>

            <video:title>Techniques</video:title>

            <video:description><![CDATA[
An overview of the solution techniques for vector equations with unknown vectors or unknown scalars.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/kESF5DuZlWHS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NYFbJSB6e2zl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/826/NYFbJSB6e2zl.jpg</video:thumbnail_loc>

            <video:title>Covalent bonds</video:title>

            <video:description><![CDATA[
This lesson defines the covalent bond as the sharing of electron pairs between non-metal atoms. We examine single, double, and triple bonds using Chlorine (Cl2), Disulfur (S2), and Nitrogen (N2). Master the concept of shared electrons creating molecular stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/826/NYFbJSB6e2zl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PXIZ8_NljlSL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/PXIZ8_NljlSL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on vector equations with unknown scalars.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/PXIZ8_NljlSL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/o_5mNxydkkFp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/o_5mNxydkkFp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
Worked examples on vector equations with unknown scalars.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/o_5mNxydkkFp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zyzEKkslRZTk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/223/zyzEKkslRZTk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on vector equations with unknown vectors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/223/zyzEKkslRZTk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XzKvdfhpT_oE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/XzKvdfhpT_oE.jpg</video:thumbnail_loc>

            <video:title>Motion parameters (2)</video:title>

            <video:description><![CDATA[
This complex worked example focuses on deriving centripetal acceleration from rotational frequency and radius. You will systematically convert the rotational rate from rpm to tangential speed before calculating the acceleration. Solving this multi-step problem confirms your quantitative mastery of uniform circular motion. Solved: 1. A racing car rounds a circular bend of radius 200\text{m}. If the car is moving at a constant speed of 144 \text{ km/hr}, what is its centripetal acceleration? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/XzKvdfhpT_oE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jsepvEMSZqHJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/jsepvEMSZqHJ.jpg</video:thumbnail_loc>

            <video:title>Motion parameters (1)</video:title>

            <video:description><![CDATA[
This worked example calculates the centripetal acceleration required for a racing car moving at a constant speed around a curve of known radius. The problem requires a necessary unit conversion from kilometres per hour to metres per second before computing the final acceleration value. Solving this establishes the direct relationship between speed, radius, and acceleration. Solved: 1. A racing car rounds a circular bend of radius 200\text{m}. If the car is moving at a constant speed of 144 \text{ km/hr}, what is its centripetal acceleration? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/jsepvEMSZqHJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/__nTVY16yGz1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/__nTVY16yGz1.jpg</video:thumbnail_loc>

            <video:title>Centripetal acceleration</video:title>

            <video:description><![CDATA[
This lesson introduces centripetal acceleration, the acceleration required to maintain uniform circular motion. We establish that it is constant in magnitude and directed radially inward.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/__nTVY16yGz1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1fjmHhtQyNmB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/1fjmHhtQyNmB.jpg</video:thumbnail_loc>

            <video:title>Uniform field relations</video:title>

            <video:description><![CDATA[
Uniform fields simplify potential to a linear drop. Why does voltage change at a constant rate here? We derive V equals Ed and show why equipotential surfaces form parallel planes perpendicular to the field.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/1fjmHhtQyNmB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aeJGcp9cILND</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/847/aeJGcp9cILND.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson introduces volumetric analysis as a critical application of stoichiometry for determining unknown solution concentrations. You will understand the course structure and the necessity of conducting reactions in the liquid phase to facilitate molecular contact and mimic biological systems. Mastery of these concepts is essential for all subsequent laboratory work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/847/aeJGcp9cILND.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HSbpccyeJcUa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/983/HSbpccyeJcUa.jpg</video:thumbnail_loc>

            <video:title>Mass concentration</video:title>

            <video:description><![CDATA[
This lesson defines mass concentration as the mass of a solute dissolved in a unit volume of solution, typically expressed in grams per litre. You will learn to calculate this value and interconvert it with molarity. Accurate determination of mass concentration is vital for reagent preparation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/983/HSbpccyeJcUa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m3Be1758Jj20</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/m3Be1758Jj20.jpg</video:thumbnail_loc>

            <video:title>Systems with product and linear constraints</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of non-linear simultaneous systems through subtraction and variable isolation. You will master the mechanical elimination of common algebraic products to reduce multi-variable constraints into solvable linear forms and determine precise coordinate pairs. Solved: 7. Solve the equationsxy - x = 4xy - y = 3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/m3Be1758Jj20.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BCU7cae6Za0P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/BCU7cae6Za0P.jpg</video:thumbnail_loc>

            <video:title>Simplifying expressions</video:title>

            <video:description><![CDATA[
Evaluate complex trigonometric fractions by substituting ratios derived from a given tangent value. Use Pythagoras’ theorem to find sine and cosine from a triangle sketch. This technique is essential for simplifying algebraic models in engineering and advanced mathematics. Solved: If \tan \alpha = \frac{5}{12}, calculate the exact value of \frac{2 \sin \alpha + 3 \cos \alpha}{4 \cos \alpha - \sin \alpha}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/BCU7cae6Za0P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xi3xNlagsw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/xi3xNlagsw.jpg</video:thumbnail_loc>

            <video:title>Polynomial gradients</video:title>

            <video:description><![CDATA[
Polynomials model real engineering systems. How do you find the exact rate of change for a multi-term function at a specific point? Watch the step-by-step calculation. Solved: If y = 2x^4 + 3x^3 - 5x^2 + 6x - 10, obtain an expression for dy/dx and calculate its value at x = 2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/xi3xNlagsw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tQdj9HvOmL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1076/tQdj9HvOmL.jpg</video:thumbnail_loc>

            <video:title>Nomenclature</video:title>

            <video:description><![CDATA[
Polyfunctional compounds contain multiple reactive groups that compete for naming dominance. How do you decide which group becomes the parent suffix and which gets demoted to a prefix? This lesson applies the IUPAC priority hierarchy to correctly assign principal and substituent roles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1076/tQdj9HvOmL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mz_LbPsvVAiA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/920/mz_LbPsvVAiA.jpg</video:thumbnail_loc>

            <video:title>Summary and next steps</video:title>

            <video:description><![CDATA[
Review Newton's three laws as the foundation of dynamics. This final summary bridges the gap between force-based analysis and the upcoming study of work and energy. Use these tools to prepare for more advanced mechanical problem-solving.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/920/mz_LbPsvVAiA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/43_YsRelXfyA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/43_YsRelXfyA.jpg</video:thumbnail_loc>

            <video:title>Precipitation</video:title>

            <video:description><![CDATA[
This lesson examines the formation of insoluble solids from aqueous reactants and the subsequent stoichiometric calculations required to predict precipitate mass. You will use molarity and balanced equations to determine limiting reagents and theoretical yields in precipitation reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/43_YsRelXfyA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jd5bb7VF0tvq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/jd5bb7VF0tvq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (20)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: A foldable tray for the paper supply of a photocopy machine is shown. The tray is supported by a single hinge at A and two slotted links ( one on each side of the tray). If the stack of paper weighs 20N and other weights may be neglected, determine the reaction at the hinge and at point B for one of the links. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/jd5bb7VF0tvq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736938512420.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/494AOM6uXSow</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/984/494AOM6uXSow.jpg</video:thumbnail_loc>

            <video:title>Standard solutions</video:title>

            <video:description><![CDATA[
This lesson defines primary and secondary standard solutions and the rigorous criteria for their preparation. You will identify high-purity stable compounds required for primary standards and understand the necessity of standardisation for secondary solutions to ensure analytical accuracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/984/494AOM6uXSow.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uiszdfEzcAHO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/984/uiszdfEzcAHO.jpg</video:thumbnail_loc>

            <video:title>Principles of dilution</video:title>

            <video:description><![CDATA[
This lesson establishes that the amount of solute remains constant during dilution while volume increases and concentration decreases. You will define the mathematical relationship between initial and final states and learn to apply the dilution equation for precise solution preparation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/984/uiszdfEzcAHO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6f_FFX6N7h7K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/983/6f_FFX6N7h7K.jpg</video:thumbnail_loc>

            <video:title>Molarity</video:title>

            <video:description><![CDATA[
This lesson rigorously defines molarity as the amount of solute in moles per unit volume of solution. You will learn the fundamental calculations required to determine molar concentration from mass and volume data. Mastery of this unit is mandatory for all quantitative volumetric analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/983/6f_FFX6N7h7K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J6grnPIjuxy3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/205/J6grnPIjuxy3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on representation, multiplication, division and powers of complex numbers in exponential form. Solved: 1.Prove that if z=re^{i\theta}, then \overline{z}=re^{-i\theta}2. Compute (1 + i)^{100} in exponential form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/205/J6grnPIjuxy3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UJE3_Cg2Ihcz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/UJE3_Cg2Ihcz.jpg</video:thumbnail_loc>

            <video:title>Boundary properties</video:title>

            <video:description><![CDATA[
Definite integrals obey strict boundary rules. How do reversed limits or split intervals affect the total? We define the core properties for manipulating integration limits.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/UJE3_Cg2Ihcz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iUHYusyEj6x9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/977/iUHYusyEj6x9.jpg</video:thumbnail_loc>

            <video:title>Relative velocity</video:title>

            <video:description><![CDATA[
This lesson introduces the fundamental equation of relative velocity. We will establish the subscript notation, which provides a systematic framework for relating the velocity of an object as measured in different inertial frames of reference.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/977/iUHYusyEj6x9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vhfwb35uuPmJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/vhfwb35uuPmJ.jpg</video:thumbnail_loc>

            <video:title>Normal force</video:title>

            <video:description><![CDATA[
This lesson defines the normal force as the perpendicular contact interaction exerted by a surface against an object. You will learn to calculate its magnitude by resolving force components for objects on horizontal and inclined surfaces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/vhfwb35uuPmJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J59dT2y7_SEu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/J59dT2y7_SEu.jpg</video:thumbnail_loc>

            <video:title>Neutralisation</video:title>

            <video:description><![CDATA[
This lesson defines neutralisation as the reaction between an acid and a base to produce a salt and water. You will master the stoichiometric requirements for achieving equivalence and learn to predict the resulting solution pH.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/J59dT2y7_SEu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zda_Fj8At5tQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/918/Zda_Fj8At5tQ.jpg</video:thumbnail_loc>

            <video:title>Fluid friction</video:title>

            <video:description><![CDATA[
Analyse the resistive drag forces acting on objects moving through liquid or gaseous media. You will master the mechanical dependence of fluid friction on object velocity, cross-sectional area, and medium viscosity to ensure accurate modelling of aerodynamic and hydrodynamic systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/918/Zda_Fj8At5tQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9CZb8oUBusRD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/9CZb8oUBusRD.jpg</video:thumbnail_loc>

            <video:title>Centripetal force</video:title>

            <video:description><![CDATA[
This lesson defines centripetal force as the net inward force required to maintain circular motion by continuously changing an object's velocity direction. You will learn to calculate this force using the product of mass and centripetal acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/9CZb8oUBusRD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xfpkdrsDNLaJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/xfpkdrsDNLaJ.jpg</video:thumbnail_loc>

            <video:title>Free-body diagrams</video:title>

            <video:description><![CDATA[
This lesson establishes the protocol for constructing free-body diagrams to isolate a body and represent all external forces as vectors. You will learn to translate physical interactions into coordinate systems to facilitate the application of Newton's laws.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/xfpkdrsDNLaJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DMreD3_fs8ic</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/916/DMreD3_fs8ic.jpg</video:thumbnail_loc>

            <video:title>Third law</video:title>

            <video:description><![CDATA[
This lesson defines Newton's third law, stating that forces always exist in equal and opposite action-reaction pairs between interacting bodies. You will learn to identify these pairs and understand why they never cancel out because they act on different objects.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/916/DMreD3_fs8ic.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b4_FxMSdA2Gl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/b4_FxMSdA2Gl.jpg</video:thumbnail_loc>

            <video:title>Complex numbers</video:title>

            <video:description><![CDATA[
Define the set of complex numbers as expressions combining real and imaginary components, denoted by the symbol C. You will identify the imaginary unit and establish the complex field as the superset encompassing all real numbers within the numerical hierarchy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/b4_FxMSdA2Gl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Es4kM_kpjCrM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/982/Es4kM_kpjCrM.jpg</video:thumbnail_loc>

            <video:title>Alkaline medium (2)</video:title>

            <video:description><![CDATA[
This lesson provides additional complex examples of balancing redox equations in basic medium, reinforcing the procedural steps. We focus on reactions where the conversion from acidic to basic medium requires careful charge checking. Completing these examples ensures robust mastery of the basic medium half-reaction technique. Solved: Example 2: Balance the reaction below in alkaline mediumAl_{(s)} + MnO_{4(aq)}^{-} \rightarrow MnO_{2(s)} + Al(OH)_{4(aq)}^{-} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/982/Es4kM_kpjCrM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I9tMJgA2YZRH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/I9tMJgA2YZRH.jpg</video:thumbnail_loc>

            <video:title>Auto-ionisation of water</video:title>

            <video:description><![CDATA[
This lesson explains how water molecules react with each other to form hydronium and hydroxide ions. You will define the ionic product of water, Kw, and understand its constant value at 25 degrees Celsius. This provides the mathematical basis for the entire pH scale.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/I9tMJgA2YZRH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tKlKtwRrD80L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/988/tKlKtwRrD80L.jpg</video:thumbnail_loc>

            <video:title>Integrated problem</video:title>

            <video:description><![CDATA[
Resolve a mixture analysis problem by applying conservation of mass and simultaneous equations to the combustion of propene and propane. You will calculate the percentage mass of the propane component by linking carbon dioxide and water yields to their respective molar sources. Solved: Example:A 3.50 g mixture of propene and propane is completely burned in excess oxygen. The combustion produces 8.80 g of CO2 and 4.05 g of H2O. Calculate the percentage by mass of propane in the mixture. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/988/tKlKtwRrD80L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dd32NQnCaIkT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/989/dd32NQnCaIkT.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson introduces the direct correlation between the mathematical form of the equilibrium constant and the balancing of a chemical equation. You will establish why specific stoichiometric coefficients dictate the numerical value of Kc and how inconsistencies in balancing lead to calculation errors.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/989/dd32NQnCaIkT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7n3MZvYglsTz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/988/7n3MZvYglsTz.jpg</video:thumbnail_loc>

            <video:title>Summary and practice problems</video:title>

            <video:description><![CDATA[
This final review consolidates mass conservation, ionic equation derivation, and redox balancing techniques into a unified stoichiometric framework. Use the provided high-level summary and practice problems to verify your computational accuracy and readiness for stoichiometry of solutions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/988/7n3MZvYglsTz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ak0QvS2_5eCa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/852/ak0QvS2_5eCa.jpg</video:thumbnail_loc>

            <video:title>Representations</video:title>

            <video:description><![CDATA[
This lesson visualises the transition to equilibrium using rate-time and concentration-time graphs. You will interpret how forward and reverse rates converge and identify the point where concentrations stabilise, providing a graphical basis for the law of mass action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/852/ak0QvS2_5eCa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Qz2CKDm2JtTz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/852/Qz2CKDm2JtTz.jpg</video:thumbnail_loc>

            <video:title>Quantitative description</video:title>

            <video:description><![CDATA[
Apply the law of mass action to derive the equilibrium constant expression (Kc) from balanced chemical equations. You will define the ratio of product-to-reactant concentrations and interpret the quantitative significance of the constant's magnitude in predicting reaction extent.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/852/Qz2CKDm2JtTz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_5FdmQ4PHDse</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/852/_5FdmQ4PHDse.jpg</video:thumbnail_loc>

            <video:title>Gaseous phase</video:title>

            <video:description><![CDATA[
This lesson introduces the equilibrium constant in terms of partial pressures (Kp) for gaseous systems. You will master the derivation of Kp expressions and apply the ideal gas law to establish the mathematical relationship between Kc and Kp based on the change in gaseous moles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/852/_5FdmQ4PHDse.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BCvhSnKAVMPr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/BCvhSnKAVMPr.jpg</video:thumbnail_loc>

            <video:title>Disjoint sets</video:title>

            <video:description><![CDATA[
Define disjoint sets as collections that share no common elements, resulting in an empty intersection. You will learn to identify these mutually exclusive groupings, a foundational requirement for partitioning data and calculating probabilities in discrete systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/BCvhSnKAVMPr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aITfZwcoFuGM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/852/aITfZwcoFuGM.jpg</video:thumbnail_loc>

            <video:title>Types</video:title>

            <video:description><![CDATA[
Distinguish between homogeneous and heterogeneous equilibria by examining phase distributions in reversible systems. You will learn to omit pure solids and liquids from equilibrium constant expressions to ensure accurate stoichiometric calculations for multi-phase reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/852/aITfZwcoFuGM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w_I4qxS9X9Zk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/w_I4qxS9X9Zk.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Examine the reflexive, antisymmetric, and transitive properties of set inclusion. You will master the formal axioms governing subset relationships to prove set equality through mutual inclusion and establish the logical hierarchy necessary for complex mathematical proofs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/w_I4qxS9X9Zk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zdaQupt_UBmF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/852/zdaQupt_UBmF.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson contrasts irreversible and reversible reactions to establish the concept of a dynamic system. You will examine the importance of chemical equilibrium in biological and industrial contexts, such as oxygen transport by haemoglobin and the synthesis of ammonia.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/852/zdaQupt_UBmF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UdoLliYyH3pt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/UdoLliYyH3pt.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Establish the formal mathematical definition of a set as a well-defined collection of distinct elements. You will examine the necessity of precision in categorisation to distinguish between valid mathematical sets and vague, subjective groupings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/UdoLliYyH3pt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yzjXc6KwpvCl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/yzjXc6KwpvCl.jpg</video:thumbnail_loc>

            <video:title>Differentiating an integral</video:title>

            <video:description><![CDATA[
The First Fundamental Theorem links integration and differentiation. How do you differentiate an integral with a variable upper limit? We apply the theorem to recover the original integrand directly. Solved: Determine the derivative G'(x) if the function is defined as G(x) = \int_{5}^{x} \sqrt{t^{4} + 9} \, dt. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/yzjXc6KwpvCl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8k6BXejfTTeF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/8k6BXejfTTeF.jpg</video:thumbnail_loc>

            <video:title>Membership notations</video:title>

            <video:description><![CDATA[
Apply the epsilon symbol and its negation to denote set membership and non-membership with mathematical precision. You will distinguish between elements and sets to ensure logical consistency when constructing algebraic expressions or proving set-theoretic arguments.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/8k6BXejfTTeF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GpZKznLYZcbZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/GpZKznLYZcbZ.jpg</video:thumbnail_loc>

            <video:title>Idempotent laws</video:title>

            <video:description><![CDATA[
Define the idempotent laws for union and intersection, stating that the operation of a set upon itself yields the original set. You will formalise the identities A union A equals A and A intersection A equals A, establishing the primary rules for simplifying redundant set expressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/GpZKznLYZcbZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7W3uy01WO1CZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/7W3uy01WO1CZ.jpg</video:thumbnail_loc>

            <video:title>Empty set</video:title>

            <video:description><![CDATA[
Define the empty set as the unique collection containing no elements and master its standard notation using the null symbol or empty braces. You will examine its foundational property as a subset of every set, a critical requirement for maintaining logical consistency in set algebra.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/7W3uy01WO1CZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_eVA1bxbgY8F</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/_eVA1bxbgY8F.jpg</video:thumbnail_loc>

            <video:title>Subsets</video:title>

            <video:description><![CDATA[
Establish the formal definition of subset inclusion, where every element of one set is contained within another. You will apply the standard inclusion symbol to denote this relationship, establishing the foundational logic required for verifying set hierarchies and proving set equality.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/_eVA1bxbgY8F.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c_B_ILXjTaQ8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/c_B_ILXjTaQ8.jpg</video:thumbnail_loc>

            <video:title>Irrational numbers</video:title>

            <video:description><![CDATA[
Define the set of irrational numbers as real numbers that cannot be expressed as simple fractions. You will identify key examples including non-repeating, infinite decimals and surds, establishing the complement of the rational set within the real number system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/c_B_ILXjTaQ8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ejUM9vrv2sIE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/ejUM9vrv2sIE.jpg</video:thumbnail_loc>

            <video:title>Natural numbers and integers</video:title>

            <video:description><![CDATA[
Define the set of natural numbers and integers while applying standard blackboard bold symbols for notation. You will examine the inclusion relationship between counting numbers and the set of all whole numbers, including negative values and zero.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/ejUM9vrv2sIE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eMpfBrjEZDor</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/eMpfBrjEZDor.jpg</video:thumbnail_loc>

            <video:title>Duality principle</video:title>

            <video:description><![CDATA[
Define the principle of duality, which states that every set identity remains valid when unions, intersections, and universal or empty sets are systematically interchanged. You will master the process of constructing dual statements, establishing the efficiency required to derive new theorems without additional proof.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/eMpfBrjEZDor.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/POLBYmbTdqJI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/POLBYmbTdqJI.jpg</video:thumbnail_loc>

            <video:title>Complements</video:title>

            <video:description><![CDATA[
Map absolute and relative complements within the universal set using spatial shading. You will identify the exterior regions of specific sets to represent logical negation, establishing the visual requirement for solving complex exclusion problems and verifying complement identities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/POLBYmbTdqJI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lM3gxwn15NFq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/lM3gxwn15NFq.jpg</video:thumbnail_loc>

            <video:title>Union and intersection</video:title>

            <video:description><![CDATA[
Master shaded representations of unions and intersections within two and three-set Venn diagrams. You will map the geometric regions corresponding to collective and shared memberships, establishing the spatial proof for basic algebraic operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/lM3gxwn15NFq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H4sBg_tjyhDz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/H4sBg_tjyhDz.jpg</video:thumbnail_loc>

            <video:title>Inclusion-exclusion principle</video:title>

            <video:description><![CDATA[
Define the Principle of Inclusion-Exclusion by systematically deriving the cardinality of unions for two and three sets. You will observe how subtracting intersections prevents the double-counting of elements, establishing the rigorous algebraic formula required for quantifying complex data overlaps.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/H4sBg_tjyhDz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hxqJ9vJH1Z_5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/hxqJ9vJH1Z_5.jpg</video:thumbnail_loc>

            <video:title>Involution law</video:title>

            <video:description><![CDATA[
Define the involution law, which states that the complement of a set's complement is the original set itself. You will master the symbolic negation of double complements, establishing the logical basis for simplifying complex algebraic expressions and restoring original data states in formal proofs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/hxqJ9vJH1Z_5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B8vv81LjGUYf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/B8vv81LjGUYf.jpg</video:thumbnail_loc>

            <video:title>De Morgan's laws</video:title>

            <video:description><![CDATA[
Define De Morgan's laws for the negation of unions and intersections. You will master the symbolic transformation where the complement of a union equals the intersection of complements, establishing the rigorous logic required to simplify complex boolean statements and set identities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/B8vv81LjGUYf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zkkBU_QdvRak</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/zkkBU_QdvRak.jpg</video:thumbnail_loc>

            <video:title>Distributive laws</video:title>

            <video:description><![CDATA[
Define the distributive laws governing the expansion of union over intersection and intersection over union. You will master the symbolic distribution of set operations across parentheses, establishing the core logic required to decompose and simplify complex multi-set identities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/zkkBU_QdvRak.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aAlQxXeoHDza</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/aAlQxXeoHDza.jpg</video:thumbnail_loc>

            <video:title>Identity laws</video:title>

            <video:description><![CDATA[
Define the identity laws governing the interaction of any set with the universal set and the empty set. You will master the symbolic reductions for unions and intersections involving these boundaries, establishing the primary identities required to eliminate null or universal terms from algebraic proofs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/aAlQxXeoHDza.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U3aEp4_C1h_K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/997/U3aEp4_C1h_K.jpg</video:thumbnail_loc>

            <video:title>Cardinality</video:title>

            <video:description><![CDATA[
Define the cardinality of Cartesian products by calculating the product of the individual set sizes. You will master the theorem stating that the size of a product set equals the individual cardinalities multiplied, establishing the quantitative framework for determining all possible ordered pairs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/997/U3aEp4_C1h_K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vpi7EO7MOy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/Vpi7EO7MOy.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Substitution reverses the Chain Rule to tame composite functions. How do you swap variables and balance the differential without leaving stray x terms behind? We map the exact steps to transform any complex integral into a standard form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/Vpi7EO7MOy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3s1YMr2rce32</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/3s1YMr2rce32.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: At the instant shown, \theta=60^\circ , and rod AB is subjected to a deceleration 16m/s^2 of when the velocity is 10m/s . Determine the angular velocity and angular acceleration of link CD at this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/3s1YMr2rce32.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744970626388.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vwqGH7Mtb12b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/vwqGH7Mtb12b.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: The Scotch - yoke mechanism converts rotational motion of the disk to oscillatory translation of the shaft. For given values of \theta ,\omega, \alpha, r, and d, determine the velocity and acceleration of point P of the shaft. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/vwqGH7Mtb12b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744972454700.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/_HHEQh_GrTLa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/_HHEQh_GrTLa.jpg</video:thumbnail_loc>

            <video:title>Definite integral</video:title>

            <video:description><![CDATA[
Definite integrals calculate exact numerical totals. How do you evaluate the area under a curve using antiderivatives? We apply the Second Fundamental Theorem to find the precise value. Solved: Determine the value of the definite integral: \int_{1}^{3} x^{2} dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/_HHEQh_GrTLa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y_MVw8j4jK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/Y_MVw8j4jK.jpg</video:thumbnail_loc>

            <video:title>Boundary transformation</video:title>

            <video:description><![CDATA[
Definite integrals require shifting boundaries when variables change. How do you map x-limits to u-values to avoid back-substitution errors? We transform the limits for direct evaluation in u-land.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/Y_MVw8j4jK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xeXYPHxYS1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/xeXYPHxYS1.jpg</video:thumbnail_loc>

            <video:title>Electric field lines</video:title>

            <video:description><![CDATA[
Electric fields are invisible. How do you map their direction and strength using simple lines? Watch to learn the rules for drawing and interpreting electric field lines.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/xeXYPHxYS1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ANSPoSoMnY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/ANSPoSoMnY.jpg</video:thumbnail_loc>

            <video:title>Negative power</video:title>

            <video:description><![CDATA[
Fractions in the denominator confuse many students. How do you apply the power rule to terms with negative indices? Watch to see the conversion and calculation. Solved: Determine the derivative of the function g(x) = \frac{12}{x^4} - \frac{5}{x^3} + 7 with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/ANSPoSoMnY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t0ySc_ntCH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1075/t0ySc_ntCH.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Alkanes form the parent chains for all organic nomenclature. How does removing one hydrogen atom systematically convert a stable alkane into a reactive alkyl substituent? This lesson establishes the direct naming link between saturated hydrocarbons and their corresponding side-chains.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1075/t0ySc_ntCH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dlOzp54O73Ux</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/dlOzp54O73Ux.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Define the inequality symbols and the principle that x is less than y if their difference is negative. You will learn to visualize relative size on the number line by identifying smaller values to the left and larger values to the right. This establishes the basic notation for all subsequent operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/dlOzp54O73Ux.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DjzTE3RENkGu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/219/DjzTE3RENkGu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on images of linear maps. Solved: Show that a linear map IR\to IR^2 defined by T\left( \begin{array}{ccc} x_1\\ x_2 \end{array} \right)=\left( \begin{array}{ccc}a & 0\\ 0 & b \end{array} \right) \left( \begin{array}{ccc} x_1\\ x_2 \end{array} \right) transform the circle x^2_1+x^2_2=1 into the ellipse \frac{y^2_1}{a^2}+\frac{y^2_2}{b^2}=1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/219/DjzTE3RENkGu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aObKi0f_8pMW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/212/aObKi0f_8pMW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on linear dependence and independence of vectors in a vector space. Solved: Determine whether or not these vectors are linearly independent(a) u=(1,2,-3),v=(4,5,-6)(b) u=(1,-3),v=(-2,6)(c) u=4t^2-3t+4,v=4t^2-3t-12(d) u=\left[ \begin{array}{ccc} 1 & 3&-4 \\ 5 & 0 & -1\ \end{array} \right],u=\left[ \begin{array}{ccc} -4 & -12&-16\\ -20 & 0 & 4\ \end{array} \right](e)u=(1,1,1),v=(1,2,3),w=(2,-1,1) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/212/aObKi0f_8pMW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2e7xGMVup-1X</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/197/2e7xGMVup-1X.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the Laplacian of scalar and vector fields in orthogonal curvilinear coordinates. Solved: Obtain the Laplacian of r in the cylindrical polar coordinate system (r,\theta,z) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/197/2e7xGMVup-1X.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hv2b_hlaNV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1060/hv2b_hlaNV.jpg</video:thumbnail_loc>

            <video:title>Electronic configuration</video:title>

            <video:description><![CDATA[
Carbon has six electrons. How do they arrange themselves before bonding starts? See the ground state layout that makes hybridisation possible.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1060/hv2b_hlaNV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GI2isAvFyV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/GI2isAvFyV.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Atoms stick together to form molecules. What forces hold carbon atoms in stable structures? See the basics of covalent bonding here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/GI2isAvFyV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vZRcORXLsc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/vZRcORXLsc.jpg</video:thumbnail_loc>

            <video:title>Polarity</video:title>

            <video:description><![CDATA[
Unequal electron sharing creates charge separation. How do you determine if a bond is polar or nonpolar? See the logic behind molecular polarity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/vZRcORXLsc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tWilYAb9cJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/tWilYAb9cJ.jpg</video:thumbnail_loc>

            <video:title>Representation of structures</video:title>

            <video:description><![CDATA[
Complex molecules need clear drawings. How do condensed and skeletal formulas simplify carbon structures? See the shorthand that saves time and space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/tWilYAb9cJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uXeDo0Y5SX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/uXeDo0Y5SX.jpg</video:thumbnail_loc>

            <video:title>Electronegativity</video:title>

            <video:description><![CDATA[
Atoms pull shared electrons with different strength. How does electronegativity create polar bonds in organic molecules? See the force that drives chemical reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/uXeDo0Y5SX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eoD4nQ89RtMY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/215/eoD4nQ89RtMY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on bases and dimensions of the sum and intersection of two subspaces of a vector space. Solved: Let P(t) be the vector space of the polynomials in t over \mathbb{R}. Suppose u and w are vector subspaces of P(t) generated by {t^3+4t^2-t+3, t^3+5t^2+5, 3t^3+10t^2-5t+5 } and {t^3+4t^2+6, t^3+2t^2-t+5, 2t^3+2t^2-3t+9} respectively. Find a basis and dimension for (a) u(b) w(c) u + w(d) u\cap w 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/215/eoD4nQ89RtMY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kgTPgLZkVJeS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/kgTPgLZkVJeS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Is the vector differential operator \nabla from the space V of all scalar functions into the space W of all vector functions linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/kgTPgLZkVJeS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Bfamp_q2Ga23</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/Bfamp_q2Ga23.jpg</video:thumbnail_loc>

            <video:title>Factorisation (1)</video:title>

            <video:description><![CDATA[
Execute the systematic factorisation of quadratic expressions using the grouping method and the difference of two squares. You will master the mechanical identification of common factors and product-sum pairs to decompose second-degree polynomials with precision. Solved: 5. Factorise P(x) = x^3 - 6x^2 + 11x - 6 completely. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/Bfamp_q2Ga23.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MHIDoUds3AAJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/MHIDoUds3AAJ.jpg</video:thumbnail_loc>

            <video:title>Symmetric equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of fourth-degree symmetric equations by dividing through by the central term and applying variable substitution. You will master the mechanical reduction of reciprocal coefficients into solvable quadratic forms to ensure absolute algebraic precision. Solved: 7. Solve the equation x^4 + 2x^3 - 6x^2 + 2x + 1 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/MHIDoUds3AAJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lTabOVpjhJu5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/lTabOVpjhJu5.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Master the systematic workflow for variable isolation by clearing fractions, grouping like terms, and applying inverse operations. This procedure ensures algebraic consistency and maintains equality throughout the transformation process.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/lTabOVpjhJu5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vkguaZm3btBI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/vkguaZm3btBI.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Master the systematic workflow for solving mixed systems by isolating a variable in the linear equation and substituting it into the non-linear expression. This procedure reduces multi-variable systems to a single solvable polynomial, ensuring precise identification of all intersection points.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/vkguaZm3btBI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jKtjZvF5DfYR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/jKtjZvF5DfYR.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Define polynomials as algebraic expressions with non-negative integer exponents and real coefficients. You will master identifying the degree and leading term of a polynomial, establishing the structural foundation for division and factorisation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/jKtjZvF5DfYR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IlUsvk9mJhHU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/IlUsvk9mJhHU.jpg</video:thumbnail_loc>

            <video:title>Real numbers</video:title>

            <video:description><![CDATA[
Define real numbers as the complete set encompassing all rational and irrational values on the continuous number line. You will master the structural hierarchy of the real number system, establishing the absolute precision required for all subsequent algebraic operations and functional analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/IlUsvk9mJhHU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SVIZ7GYCxLCh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1003/SVIZ7GYCxLCh.jpg</video:thumbnail_loc>

            <video:title>Factor theorem</video:title>

            <video:description><![CDATA[
Apply the Factor Theorem to identify binomial factors of higher-degree polynomials by verifying where the remainder equals zero. You will master the logical link between polynomial roots and linear factors, establishing the basis for complete expression factorisation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1003/SVIZ7GYCxLCh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HG_aD4azepW1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/100/HG_aD4azepW1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on evaluation of double integrals - involving change of variables. Solved: Evaluate \iint_R \\y \,dx\,dy , where R is the semicircular region D bounded by x^2 + y^2 = 1 and x^2 + y^2 = 4 as shown below 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/100/HG_aD4azepW1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747319201859.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/wC-a9Cgf7xI9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/wC-a9Cgf7xI9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Is T: M_{22} \to \mathbb{R} defined by T(A) = det(A) linear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/wC-a9Cgf7xI9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PMijTy7Na6Tp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/81/PMijTy7Na6Tp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on homogeneous functions and Euler's theorem. Solved: Let W be a homogeneous function of degree n. Show that x^2\frac{\partial ^2W}{\partial x^2}+2xy\frac{\partial ^2W}{\partial x\partial y}+y^2\frac{\partial ^2W}{\partial y^2}=n(n-1)W. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/81/PMijTy7Na6Tp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/178MlPNWiGdR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/220/178MlPNWiGdR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on matrix representations of linear maps. Solved: Let T:P_1\to P_2 be defined by T(a+bx)=ax+(\frac{b}{2})x^2. Give P_1 and P_2 the standard bases B=[1,x], and B^1=[1,x,x^2] respectively. Find the matrix representation of T with respect to the bases. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/220/178MlPNWiGdR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oPlNKtzeSAhD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/221/oPlNKtzeSAhD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the transition matrix between two bases of a vector space. Solved: Let T:IR^3\to IR^3 be the map defined by T(x,y,z)=(x+2y-z,-z,2x+y-3z).(a) Write down the matrix associated with T with respect to the standard bases in the domain and co-domain. (b) By calculating the relevant transition matrix, find the matrix associated with T with respect to the basis [(-1,0,0),(-1,-1,0),(-1,-1,-1)] in both domain and co-domain. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/221/oPlNKtzeSAhD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KDoya3_pZDUq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/213/KDoya3_pZDUq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on basis and dimension of vector spaces. Solved: Determine whether or not the following vectors form a basis for \mathbb{R^3}:(a) (1, 1,1), (1, 2, 3), (2, -1, 1)(b) (1, 0, -1), (1, -1, 1)(c) (2, 1, 3), (3, 2, 1), (1, 1, 1), (3, 2, 0)(d) (1, 1, 2), (1, 2, 5), (5, 3, 4) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/213/KDoya3_pZDUq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mkPCd67wHqDQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/mkPCd67wHqDQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: The force F acts on the bracket within the octant shown. If the magnitude of the x and z components of F are F_x=300N and F_z=600N, respectively, and \beta=60^\circ, determine the magnitude of F and its y component. Also, find the coordinate direction angles \alpha and \gamma. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/mkPCd67wHqDQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739788558055.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/c3Co1DA5dN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1062/c3Co1DA5dN.jpg</video:thumbnail_loc>

            <video:title>Hybrid orbitals</video:title>

            <video:description><![CDATA[
Atomic orbitals mix to form new shapes. How do s and p orbitals combine to create sp3, sp2, or sp hybrids? See the geometry that defines molecular structure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1062/c3Co1DA5dN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NOqAV9MM4p5_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/NOqAV9MM4p5_.jpg</video:thumbnail_loc>

            <video:title>Single linear inequality</video:title>

            <video:description><![CDATA[
Follow a step-by-step calculation to isolate the variable in a single linear inequality. You will apply the sign-reversal rule when multiplying or dividing by negative coefficients and represent the final solution on a number line. This walkthrough reinforces the mechanics of basic constraints. Solved: 1. Solve the inequality 5 - 2x > 9. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/NOqAV9MM4p5_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3erGsrCNKDSj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/3erGsrCNKDSj.jpg</video:thumbnail_loc>

            <video:title>Simplifying logarithms (1)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for simplifying logarithmic expressions by applying the power and inverse laws. You will learn to resolve terms where the logarithm is an exponent by using the relationship between bases to reduce complex expressions to a single value. Solved: 1. Simplify 5^{-3 \log_5 2}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/3erGsrCNKDSj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s5wK1YfQC_kg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/s5wK1YfQC_kg.jpg</video:thumbnail_loc>

            <video:title>Distinct linear factors (1)</video:title>

            <video:description><![CDATA[
Decompose rational expressions with unique linear denominators into separate partial fractions. Learn to determine unknown constants by substituting roots that eliminate terms. This walkthrough demonstrates the core technique for simplifying complex fractions before integration. Solved: 1. Resolve the following into partial fractions:\frac{x+7}{x^2-x-2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/s5wK1YfQC_kg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9muFEpvyMkRY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/9muFEpvyMkRY.jpg</video:thumbnail_loc>

            <video:title>Distinct linear factors (2)</video:title>

            <video:description><![CDATA[
Resolve more complex rational expressions with distinct linear denominators by applying the equating coefficients methods. This walkthrough shows how to calculate multiple unknown constants accurately to split a single fraction into its constituent parts for easier analysis. Solved: 2. Resolve \frac{4x-2}{(x-3)(x+1)} into partial fractions. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/9muFEpvyMkRY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4oBSuaI13W1M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/4oBSuaI13W1M.jpg</video:thumbnail_loc>

            <video:title>Repeated linear factors</video:title>

            <video:description><![CDATA[
Decompose fractions where the denominator contains repeated linear terms by setting up increasing powers of the factor. This walkthrough demonstrates how to solve for all constants using substitution and equating coefficients. Mastery of this setup is vital for correct algebraic expansion. Solved: 3. Resolve \frac{x^2-3x+1}{(x-2)^2(x+1)} into partial fractions. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/4oBSuaI13W1M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1gQl6oziolrT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1008/1gQl6oziolrT.jpg</video:thumbnail_loc>

            <video:title>Simplifying indices (1)</video:title>

            <video:description><![CDATA[
Execute the systematic reduction of complex exponential expressions using the product and quotient laws. You will master the mechanical steps to simplify multi-term indices with common bases through a rigorous calculation walkthrough. Solved: 1. Simplify \frac{3^a - 3^{a+1}}{4 \times 3^a - 3^a}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1008/1gQl6oziolrT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/skRwVRjDl2Ml</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1008/skRwVRjDl2Ml.jpg</video:thumbnail_loc>

            <video:title>Rules of indices</video:title>

            <video:description><![CDATA[
Master the three fundamental laws of indices governing the multiplication, division, and exponentiation of powers with common bases. You will execute the mechanical application of the product, quotient, and power rules to simplify exponential expressions with absolute precision.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1008/skRwVRjDl2Ml.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n_3FV8UvKv75</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1008/n_3FV8UvKv75.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Define indices as the representation of repeated multiplication through base and exponent notation. You will master the fundamental identity of powers and establish the technical definitions required to apply the core laws of indices to complex algebraic expressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1008/n_3FV8UvKv75.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QqGJwV3F22FX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/QqGJwV3F22FX.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Understand the systematic workflow for decomposing rational expressions by first checking for improper fractions. Learn to categorise denominators into linear, repeated, or quadratic factors to apply the correct algebraic template. This overview establishes the logic used in all calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/QqGJwV3F22FX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3rJtaaO_bzqm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/3rJtaaO_bzqm.jpg</video:thumbnail_loc>

            <video:title>Gasoline</video:title>

            <video:description><![CDATA[
Gasoline efficiency depends on resistance to engine knocking during combustion. How does the octane rating quantify this resistance and why do branched alkanes perform better than straight chains? This lesson defines octane number, explains pyrolysis, and links structure to fuel quality precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/3rJtaaO_bzqm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/26loN_7hDbef</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/26loN_7hDbef.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Define logarithms as the inverse of exponential operations and master the conversion between index and logarithmic forms. You will establish the technical relationship between base, exponent, and power to resolve equations where the unknown is an exponent.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/26loN_7hDbef.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RSFb1FHK889_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/RSFb1FHK889_.jpg</video:thumbnail_loc>

            <video:title>Product and quotient laws</video:title>

            <video:description><![CDATA[
This lesson explains the product and quotient laws for combining and separating logarithms. You will learn to simplify logarithmic expressions by converting multiplication into addition and division into subtraction, provided the bases are identical.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/RSFb1FHK889_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wtqMrCkJjZP0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/wtqMrCkJjZP0.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson outlines the systematic approach to solving equations where the variable is an exponent. You will learn to evaluate whether to equate bases directly or apply logarithms to both sides to isolate the unknown index for a precise solution.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/wtqMrCkJjZP0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nmAtpO7nA3a6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1012/nmAtpO7nA3a6.jpg</video:thumbnail_loc>

            <video:title>Definitions</video:title>

            <video:description><![CDATA[
This lesson defines a sequence as an ordered list of numbers and a series as the sum of those terms. You will learn to use subscript notation for general terms and distinguish between finite and infinite structures.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1012/nmAtpO7nA3a6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pfPgLoyHMbU5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1012/pfPgLoyHMbU5.jpg</video:thumbnail_loc>

            <video:title>Notations and terms</video:title>

            <video:description><![CDATA[
This lesson establishes the formal notation for sequence terms and general formulae using subscripts. You will learn to identify individual terms and express entire sequences through algebraic rules.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1012/pfPgLoyHMbU5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_wx2KF_C4NlR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/_wx2KF_C4NlR.jpg</video:thumbnail_loc>

            <video:title>Explicit formulae</video:title>

            <video:description><![CDATA[
An explicit formula defines any term in a sequence directly as a function of its Position N. This lesson explains how to calculate specific term values by substituting the term number into the general rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/_wx2KF_C4NlR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YpF9bNEyvg3P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/YpF9bNEyvg3P.jpg</video:thumbnail_loc>

            <video:title>Sigma notation</video:title>

            <video:description><![CDATA[
Sigma notation uses the Greek letter sigma to represent the compact sum of a sequence. This lesson explains how to interpret the upper and lower limits of summation and the general term formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/YpF9bNEyvg3P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t7Qgrmi12c69</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/t7Qgrmi12c69.jpg</video:thumbnail_loc>

            <video:title>Finding the general term</video:title>

            <video:description><![CDATA[
This lesson explains how to derive a general formula for the nth term by identifying patterns in a given set of numbers. You will learn to relate term values to their positions to create an explicit rule for any sequence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/t7Qgrmi12c69.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tN2g7iHHsS_T</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/tN2g7iHHsS_T.jpg</video:thumbnail_loc>

            <video:title>Common and natural logarithms</video:title>

            <video:description><![CDATA[
This lesson distinguishes between common logarithms in base 10 and natural logarithms in base e. You will learn the specific notation for each and understand why these two bases are the standard for scientific calculations and modelling growth or decay.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/tN2g7iHHsS_T.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4QixHPPnMsMl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1012/4QixHPPnMsMl.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides an overview of the course structure and the importance of discrete patterns in mathematical analysis. You will understand the roadmap for mastering arithmetic and geometric progressions, including their practical applications in finance and computing.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1012/4QixHPPnMsMl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/614PXLsCVM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1063/614PXLsCVM.jpg</video:thumbnail_loc>

            <video:title>Diamond</video:title>

            <video:description><![CDATA[
Pure carbon, extreme hardness. How does the tetrahedral sp3 network of diamond create such strength? See the structure-property link here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1063/614PXLsCVM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZvflUgcQL1uj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/ZvflUgcQL1uj.jpg</video:thumbnail_loc>

            <video:title>Algebraic properties (1)</video:title>

            <video:description><![CDATA[
Master the core rules for manipulating inequalities, specifically how addition and subtraction leave the sign unchanged while multiplication or division by negative values reverses the direction. You will learn to maintain algebraic balance and apply these properties to isolate variables accurately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/ZvflUgcQL1uj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/peCsnL32j6Yo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/peCsnL32j6Yo.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson defines the core objectives of the course and the role of set theory as the foundational language of modern mathematics. You will examine how rigorous set notation and logical structures underpin advanced computational systems and engineering models.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/peCsnL32j6Yo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gFomZC1Iqz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1063/gFomZC1Iqz.jpg</video:thumbnail_loc>

            <video:title>Amorphous carbon</video:title>

            <video:description><![CDATA[
Not all carbon is neat crystal. Why do soot and charcoal lack long-range order yet serve vital roles in purification and pigments? Watch to decode the messy structure of amorphous allotropes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1063/gFomZC1Iqz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_1AafmGNR0tN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/_1AafmGNR0tN.jpg</video:thumbnail_loc>

            <video:title>Definition and general term</video:title>

            <video:description><![CDATA[
A geometric progression is a sequence where each term is found by multiplying the previous one by a constant common ratio. This lesson defines the general term formula using the first term and common ratio to calculate any specific value.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/_1AafmGNR0tN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/12N7PzfGIIJt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/12N7PzfGIIJt.jpg</video:thumbnail_loc>

            <video:title>Expanding series (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step expansion of an alternating geometric series using sigma notation. You will master substituting integer values from the lower to the upper limit to calculate the precise total sum of the terms. Solved: 2. Expand the series \sum_{r=1}^{3} (-1)^{r+1} \cdot 2^r. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/12N7PzfGIIJt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tDphI5Do6RiP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/tDphI5Do6RiP.jpg</video:thumbnail_loc>

            <video:title>Definition and general term</video:title>

            <video:description><![CDATA[
An arithmetic progression is a sequence where each term increases or decreases by a constant common difference. This lesson defines the nth term formula using the first term and common difference to calculate any value in the progression.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/tDphI5Do6RiP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zSGyWXixmexO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/zSGyWXixmexO.jpg</video:thumbnail_loc>

            <video:title>Arithmetic-geometric progressions</video:title>

            <video:description><![CDATA[
Arithmetic-geometric progressions are formed by multiplying the corresponding terms of an arithmetic and a geometric sequence. This lesson defines their general term and explains how to identify this hybrid pattern in complex discrete data.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/zSGyWXixmexO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zXl70TlXRRWU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/zXl70TlXRRWU.jpg</video:thumbnail_loc>

            <video:title>Calculating rth terms</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates calculating terms within a geometric progression using the general term formula. You will master applying the first term and common ratio to find any numbered term or determine the exact position of a given value. Solved: 2. In the geometric progression 2, 10, 50, \dots, which term is equal to 1,250? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/zXl70TlXRRWU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KzSTf4Xs1cl_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/KzSTf4Xs1cl_.jpg</video:thumbnail_loc>

            <video:title>Convergence and sum to infinity</video:title>

            <video:description><![CDATA[
An infinite geometric series converges to a finite limit only if its common ratio is between negative one and one. This lesson defines the conditions for convergence and provides the formula for calculating the sum to infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/KzSTf4Xs1cl_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3_BQij9kElU1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/3_BQij9kElU1.jpg</video:thumbnail_loc>

            <video:title>Recurring decimals as series</video:title>

            <video:description><![CDATA[
Recurring decimals are infinite geometric series with a common ratio less than one. This lesson shows how to expand these decimals into series and use the sum to infinity formula to convert them into exact rational fractions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/3_BQij9kElU1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VK9q3fJeZrDV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/916/VK9q3fJeZrDV.jpg</video:thumbnail_loc>

            <video:title>First law</video:title>

            <video:description><![CDATA[
This lesson defines Newton's first law of motion and the concept of inertia. You will identify that objects maintain a constant velocity unless acted upon by a non-zero net force, establishing the requirement for inertial frames of reference in dynamic analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/916/VK9q3fJeZrDV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I9286ZnjoxSo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/790/I9286ZnjoxSo.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Establish your operational framework for CHM 101 by aligning your study objectives with the NUC CCMAS syllabus requirements. This orientation ensures technical compliance with Nigerian University standards while optimizing your use of the student-led learning system for maximum academic efficiency.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/790/I9286ZnjoxSo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IfqgNlA3ONEn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/IfqgNlA3ONEn.jpg</video:thumbnail_loc>

            <video:title>Equality and equivalence</video:title>

            <video:description><![CDATA[
Distinguish between identical sets and those sharing only the same cardinality. This lesson explains the criteria for set equality where elements must match exactly and set equivalence where only the total count is identical.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/IfqgNlA3ONEn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KEi3_O7Vf4xj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/KEi3_O7Vf4xj.jpg</video:thumbnail_loc>

            <video:title>Logical symbols</video:title>

            <video:description><![CDATA[
Master the formal shorthand for set membership and logical quantification. You will execute the technical use of symbols for exists, for all, such that, and implication to construct rigorous mathematical statements.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/KEi3_O7Vf4xj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R1WJ9nXjJyI9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/790/R1WJ9nXjJyI9.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Master the four-stage operational workflow of attending university lectures, watching UniDrills lessons for clarity, solving practice problems for mastery, and asking instructors for support. This lesson explains how to implement a systematic approach to ensure clarity and excellent result.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/790/R1WJ9nXjJyI9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MKbuY_9BiMku</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mqcR3AmTzO/Thumbnails/990/MKbuY_9BiMku.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Master the four-stage operational workflow of attending university lectures, watching UniDrills lessons for clarity, solving practice problems for mastery, and asking instructors for support. This lesson explains how to implement a systematic approach to ensure clarity and excellent result.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mqcR3AmTzO/Previews/990/MKbuY_9BiMku.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S_LUjsf7qCk8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/S_LUjsf7qCk8.jpg</video:thumbnail_loc>

            <video:title>Specifying sets</video:title>

            <video:description><![CDATA[
Master the two primary methods for defining sets: the roster method for listing elements explicitly and set-builder notation for specifying characteristic properties. You will learn to use symbolic logic to represent collections efficiently, ensuring clarity in both finite and infinite contexts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/S_LUjsf7qCk8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7UNaBN8rT7fG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/991/7UNaBN8rT7fG.jpg</video:thumbnail_loc>

            <video:title>Cardinality</video:title>

            <video:description><![CDATA[
Define cardinality as the measure of a set's size and master the notation for counting distinct elements. You will differentiate between finite and infinite collections, establishing the quantitative baseline required for subset calculations and power set analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/991/7UNaBN8rT7fG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x3J7FMEDL9Pp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/x3J7FMEDL9Pp.jpg</video:thumbnail_loc>

            <video:title>Power set</video:title>

            <video:description><![CDATA[
Define the power set as the collection of all possible subsets of a given set, including the empty set and the set itself. You will calculate power set cardinality using the formula 2 raised to the power of n and examine its role in combinatorial analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/x3J7FMEDL9Pp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZFGzAvxSL7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/ZFGzAvxSL7.jpg</video:thumbnail_loc>

            <video:title>Resonance structures</video:title>

            <video:description><![CDATA[
Some molecules defy single structures. How do you map electron delocalisation when one diagram fails? Watch to master resonance hybrids. Solved:  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/ZFGzAvxSL7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jxw3E9vGMj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1064/jxw3E9vGMj.jpg</video:thumbnail_loc>

            <video:title>Fullerenes</video:title>

            <video:description><![CDATA[
Carbon can form hollow cages. How do these closed structures differ from flat graphite sheets? Watch to see the shape of buckminsterfullerene.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1064/jxw3E9vGMj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SRsSG9d9dWE_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/916/SRsSG9d9dWE_.jpg</video:thumbnail_loc>

            <video:title>Mass and inertia</video:title>

            <video:description><![CDATA[
This lesson defines mass as the quantitative measure of inertia, the inherent resistance of an object to changes in its state of motion. You will understand how greater mass dictates a larger force requirement to achieve acceleration, establishing the physical basis for Newton's first law.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/916/SRsSG9d9dWE_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fM2nGv86wNIy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/916/fM2nGv86wNIy.jpg</video:thumbnail_loc>

            <video:title>Second law</video:title>

            <video:description><![CDATA[
This lesson defines Newton's second law as the quantitative relationship where net force equals mass multiplied by acceleration. You will learn to apply the vector form of this equation to determine the motion of a particle subjected to multiple external forces.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/916/fM2nGv86wNIy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SKFAHI0Ak3D6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/SKFAHI0Ak3D6.jpg</video:thumbnail_loc>

            <video:title>Universal set</video:title>

            <video:description><![CDATA[
Define the universal set as the comprehensive collection containing all objects under consideration in a specific context. You will learn to denote this boundary using the symbol U, establishing the necessary domain for performing complements and identifying relative subsets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/SKFAHI0Ak3D6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_3vZpc_WOljP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/915/_3vZpc_WOljP.jpg</video:thumbnail_loc>

            <video:title>Force vectors</video:title>

            <video:description><![CDATA[
This lesson treats force as a vector quantity possessing both magnitude and direction. You will learn to represent forces using arrows and apply vector addition to determine the resultant net force acting on a system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/915/_3vZpc_WOljP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NEkm5P3g5PrM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/NEkm5P3g5PrM.jpg</video:thumbnail_loc>

            <video:title>Proper subsets</video:title>

            <video:description><![CDATA[
Define a proper subset as a collection contained within another set that is not identical to the parent set. You will apply the specific notation for proper inclusion and identify the logical requirement that the parent set must contain at least one element not present in the subset.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/NEkm5P3g5PrM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B7cxh5Ae_LPi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/992/B7cxh5Ae_LPi.jpg</video:thumbnail_loc>

            <video:title>Identifying set relationships</video:title>

            <video:description><![CDATA[
Execute the systematic identification of subset and proper subset relations through a rigorous problem walkthrough. You will master the mechanical verification of set inclusion and mutual equality to ensure absolute accuracy in categorising discrete data collections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/992/B7cxh5Ae_LPi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T161ZJOGDLRn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/916/T161ZJOGDLRn.jpg</video:thumbnail_loc>

            <video:title>Force and mass</video:title>

            <video:description><![CDATA[
This lesson formalises the inverse relationship between mass and acceleration for a constant applied force. You will understand how mass acts as the quantitative measure of inertia and why the Newton is defined by the acceleration of a standard kilogram.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/916/T161ZJOGDLRn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VIpss57Zhj_Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/VIpss57Zhj_Y.jpg</video:thumbnail_loc>

            <video:title>Infinite sets and countability</video:title>

            <video:description><![CDATA[
Distinguish between countably and uncountably infinite sets by comparing the cardinality of integers to that of the real number system. You will apply Cantor's diagonal argument to prove that the size of the real continuum exceeds the countability of natural numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/VIpss57Zhj_Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/__0o8ePlbYd4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/__0o8ePlbYd4.jpg</video:thumbnail_loc>

            <video:title>Rational numbers</video:title>

            <video:description><![CDATA[
Define the set of rational numbers as quotients of integers with non-zero denominators. You will apply set-builder notation to formalise this collection and distinguish between terminating and recurring decimals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/__0o8ePlbYd4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uOtENFF96O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/uOtENFF96O.jpg</video:thumbnail_loc>

            <video:title>Nanochemistry</video:title>

            <video:description><![CDATA[
Matter behaves differently at the nanoscale. Why do properties shift from classical physics to quantum effects as size shrinks? Watch to bridge the gap between macro and nano worlds.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/uOtENFF96O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q_pjVx78Yg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/Q_pjVx78Yg.jpg</video:thumbnail_loc>

            <video:title>Graphene</video:title>

            <video:description><![CDATA[
Graphene is a single layer of carbon atoms. How does this flat hexagonal lattice allow electrons to move like relativistic particles? Watch to understand its extreme mobility.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/Q_pjVx78Yg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EYTg_dsswQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/EYTg_dsswQ.jpg</video:thumbnail_loc>

            <video:title>Carbon nanotubes</video:title>

            <video:description><![CDATA[
Carbon nanotubes are rolled graphene sheets. How does this cylindrical shape create tensile strength far greater than steel? Watch to see the structure behind the power.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/EYTg_dsswQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_3zecnt8OCnk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/_3zecnt8OCnk.jpg</video:thumbnail_loc>

            <video:title>Special number sets</video:title>

            <video:description><![CDATA[
Define notation for positive and negative subsets of integers and real numbers using superscript plus and minus symbols. You will distinguish between strictly positive collections and those including zero, establishing the precise domains required for specifying inequalities and functional constraints.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/_3zecnt8OCnk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NUIQ_Bi_GNAZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/NUIQ_Bi_GNAZ.jpg</video:thumbnail_loc>

            <video:title>Intersection</video:title>

            <video:description><![CDATA[
Define the intersection of sets as the collection of elements common to all participating sets. You will apply the intersection symbol and set-builder notation to formalise this operation, establishing the logical basis for identifying shared data across multiple criteria.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/NUIQ_Bi_GNAZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y4u9FrEYteLW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/y4u9FrEYteLW.jpg</video:thumbnail_loc>

            <video:title>Basic operations</video:title>

            <video:description><![CDATA[
Execute the systematic calculation of set unions, intersections, and differences through a rigorous problem walkthrough. You will master the mechanical application of operation rules to resolve complex data collections and identify disjoint relationships with absolute precision.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/y4u9FrEYteLW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RGONtlsVhcN_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1023/RGONtlsVhcN_.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson explains how to use balanced chemical equations to calculate the amounts of reactants and products. You will learn to use molar ratios to predict theoretical yields and identify the limiting reagent needed for any chemical reaction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1023/RGONtlsVhcN_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JRQ65IgX4V0N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/JRQ65IgX4V0N.jpg</video:thumbnail_loc>

            <video:title>Combined operations</video:title>

            <video:description><![CDATA[
Execute the systematic evaluation of multi-stage set expressions involving unions, intersections, and complements. You will master the order of operations and algebraic simplification required to resolve complex data groupings through rigorous calculation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/JRQ65IgX4V0N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fSYDJz_a08Zg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/fSYDJz_a08Zg.jpg</video:thumbnail_loc>

            <video:title>Complement</video:title>

            <video:description><![CDATA[
Define the complement of a set as the collection of all elements in the universal set that are not members of the given set. You will distinguish between absolute and relative complements, establishing the logical negation required for complex set algebra and data exclusion operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/fSYDJz_a08Zg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_QHMz_BeZY7N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/_QHMz_BeZY7N.jpg</video:thumbnail_loc>

            <video:title>Spring force</video:title>

            <video:description><![CDATA[
This lesson defines the restorative spring force using Hooke's Law. You will resolve the linear relationship between force, the spring constant, and displacement from equilibrium to solve for restorative magnitudes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/_QHMz_BeZY7N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pCJVedVHe_iM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/pCJVedVHe_iM.jpg</video:thumbnail_loc>

            <video:title>Tension</video:title>

            <video:description><![CDATA[
This lesson defines tension as the pulling force transmitted through a string, rope, or cable. You will learn to represent tension vectors in multi-body systems and apply Newton's laws to solve for unknown forces in coupled configurations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/pCJVedVHe_iM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qwM4c3vcxKRM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/qwM4c3vcxKRM.jpg</video:thumbnail_loc>

            <video:title>Gravity and weight</video:title>

            <video:description><![CDATA[
This lesson distinguishes between mass as an intrinsic property and weight as the gravitational force exerted on a body. You will apply the second law to define weight as the product of mass and the acceleration of free fall.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/qwM4c3vcxKRM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lJI8HKjIDVC9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/lJI8HKjIDVC9.jpg</video:thumbnail_loc>

            <video:title>Difference</video:title>

            <video:description><![CDATA[
Define the set difference as the collection of elements belonging to one set but not another. You will apply the minus or backslash notation to execute this operation, establishing the logical basis for data subtraction and isolating unique elements within overlapping collections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/lJI8HKjIDVC9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IpPeaXyHyXMn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/IpPeaXyHyXMn.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (3)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/IpPeaXyHyXMn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rO8Huxsg6mKA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/rO8Huxsg6mKA.jpg</video:thumbnail_loc>

            <video:title>Union</video:title>

            <video:description><![CDATA[
Define the union of sets as the total collection of elements belonging to at least one of the participating sets. You will apply the standard union symbol and set-builder notation to formalise this operation, establishing the logical basis for combining data aggregates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/rO8Huxsg6mKA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dxEAM5dBptxr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/dxEAM5dBptxr.jpg</video:thumbnail_loc>

            <video:title>Complement laws</video:title>

            <video:description><![CDATA[
Define the complement laws governing the union and intersection of a set with its own complement. You will master the symbolic identities leading to the universal set and the empty set, establishing the logical boundaries necessary for simplifying complex algebraic expressions and proving set identities.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/dxEAM5dBptxr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cYt4JSYj060O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/cYt4JSYj060O.jpg</video:thumbnail_loc>

            <video:title>Simplifying set expressions (2)</video:title>

            <video:description><![CDATA[
Execute advanced simplification of set expressions by synthesising De Morgans laws with absorption and complement identities. You will master the mechanical reduction of complex symbolic strings through a rigorous step-by-step walkthrough to reach minimal logical forms. Solved: 2. Simplify (A \cap B)' \cup B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/cYt4JSYj060O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aczFRwEKLT_f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/aczFRwEKLT_f.jpg</video:thumbnail_loc>

            <video:title>Element-wise proofs (1)</video:title>

            <video:description><![CDATA[
Execute the formal verification of set identities through a rigorous element-wise walkthrough. You will master the double-inclusion method by tracking arbitrary elements across unions and intersections to construct watertight logical proofs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/aczFRwEKLT_f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Thi4y_hGp7f_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/Thi4y_hGp7f_.jpg</video:thumbnail_loc>

            <video:title>Element-wise proofs (2)</video:title>

            <video:description><![CDATA[
Execute formal verification of a set difference identity through a rigorous element-wise walkthrough. You will master the logical resolution of negated operations and complex nesting to establish absolute mathematical equivalence between distinct set expressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/Thi4y_hGp7f_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sB_sGNiGfqK4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/918/sB_sGNiGfqK4.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Establish the fundamental classification of resistive forces by distinguishing between sliding, rolling, and fluid friction. You will master the mechanical criteria for each regime to ensure accurate identification of the specific contact or drag interactions acting within a dynamic system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/918/sB_sGNiGfqK4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3ed5mqhK1c4c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/918/3ed5mqhK1c4c.jpg</video:thumbnail_loc>

            <video:title>Rolling friction</video:title>

            <video:description><![CDATA[
Analyse the mechanical resistance encountered when a circular object rolls over a surface due to interfacial deformation. You will master the use of the coefficient of rolling friction to calculate energy losses in transport and engineering systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/918/3ed5mqhK1c4c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2zPUGJcZGNbv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/918/2zPUGJcZGNbv.jpg</video:thumbnail_loc>

            <video:title>Sliding friction</video:title>

            <video:description><![CDATA[
Distinguish between static and kinetic friction thresholds to determine the initiation and maintenance of sliding motion. You must master the mechanical application of coefficients of friction and normal forces to quantify these resistive interactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/918/2zPUGJcZGNbv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KwBSYM_cGC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/KwBSYM_cGC.jpg</video:thumbnail_loc>

            <video:title>Fractional power</video:title>

            <video:description><![CDATA[
Roots and fractional powers follow the same rule. How do you handle fractions in the exponent when finding the gradient? Watch to see the power rule in action. Solved: Find the gradient function for h(x) = 8x^{1/2} + 4x^{5/2} - 6x^{-1/2}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/KwBSYM_cGC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WETF2oytXP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1065/WETF2oytXP.jpg</video:thumbnail_loc>

            <video:title>Principles of nanochemistry</video:title>

            <video:description><![CDATA[
Size changes properties. Why do high surface area, quantum confinement, and defects alter reactivity? Watch to master the core principles of nanochemistry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1065/WETF2oytXP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LyAc3SbuqN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1074/LyAc3SbuqN.jpg</video:thumbnail_loc>

            <video:title>Major functional groups</video:title>

            <video:description><![CDATA[
Functional groups dictate the reactivity and classification of organic molecules. How do you distinguish a carbonyl in an aldehyde from one in a ketone based solely on structural position? This lesson maps every major functional group class to its defining bond arrangement and IUPAC category.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1074/LyAc3SbuqN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F_X0SoBekxaT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/F_X0SoBekxaT.jpg</video:thumbnail_loc>

            <video:title>Commutative laws</video:title>

            <video:description><![CDATA[
Define the commutative laws for union and intersection, stating that the order of sets in an operation does not affect the outcome. You will master the equivalence of A union B and B Union A, establishing the symmetry required for simplifying complex set equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/F_X0SoBekxaT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LH85IDYUBDw2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/LH85IDYUBDw2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: A rectangular plate is supported by three cables, knowing that the tension in cable AC is 60N, determine the weight of the plate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/LH85IDYUBDw2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739877166881.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/FO3oV2duZU8x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/107/FO3oV2duZU8x.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the divergence of vector fields and some Laplacian. Solved: Given r=\sqrt{x^2+y^2+z^2} =\|\mathbf{r}\|,\vec{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/107/FO3oV2duZU8x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8uwotVaUY00U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/83/8uwotVaUY00U.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the bisection method of solution of equations in one variable. Solved: Given the equation f(x) = x^3 + 4x^2 - 10 = 0,(i) show that f(x) has a root in the interval [1, 2],(ii) use the bisection method to determine the number of iterations necessary to solve the equation with an accuracy of 10^{-3},(iii) obtain the approximate solution given by the 5th iteration. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/83/8uwotVaUY00U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/903l1rraJZtp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/83/903l1rraJZtp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the bisection method of solution of equations in one variable. Solved: Use the bisection method to find solutions accurate to within 10^{-2} for the equation2xcos(2x) - (x + 1)^2 = 0 for -3 \leq x \leq -2; [-3, -2] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/83/903l1rraJZtp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Vsvxmk4KvAt6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/14/Vsvxmk4KvAt6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the vector product of two vectors and its implications. Solved: 1.If a=(3, -5, 1) and b=(0, 2, -4), Find a\times b.2.Find the unit vectors perpendicular to both a=3i+j-2k and b=2i-3j-k. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/14/Vsvxmk4KvAt6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/njFDkBgAoKKN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/njFDkBgAoKKN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n\to \infty} \frac{3n+2}{2n-5} =\frac{3}{2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/njFDkBgAoKKN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UvbfZ0RCGc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/UvbfZ0RCGc.jpg</video:thumbnail_loc>

            <video:title>Linear constraint</video:title>

            <video:description><![CDATA[
Linear brackets demand a precise differential balance. How do you handle the coefficient when swapping variables? This walkthrough shows the exact scaling required for correct integration. Solved: Find \int (3x - 2)^{5} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/UvbfZ0RCGc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/y5DtIUu1Tl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/y5DtIUu1Tl.jpg</video:thumbnail_loc>

            <video:title>Mesomeric effect</video:title>

            <video:description><![CDATA[
Electrons do not just sit still; they delocalise. How does pi electron shift stabilise a molecule beyond simple induction? Watch to map the true flow of charge.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/y5DtIUu1Tl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e1PPCq2kwX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1068/e1PPCq2kwX.jpg</video:thumbnail_loc>

            <video:title>Inductive effect</video:title>

            <video:description><![CDATA[
Electron density shifts through sigma bonds. How do you sort groups into electron withdrawing or electron donating types? See the logic of the inductive effect.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1068/e1PPCq2kwX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EEMVIQ8nLH3c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/12/EEMVIQ8nLH3c.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on centroids and weighted means of a number of points. Solved: The centroid of a triangle OAB is denoted by G. If O is the origin and A and B have position vectors 4\underline{i}+3\underline{j} and 6\underline{i}-\underline{j} respectively. a) Find the position vector of Gb) Find the distance from the origin to the origin to the centroid. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/12/EEMVIQ8nLH3c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NvkJqlqFoenQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/10/NvkJqlqFoenQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on ratio division of a line and collinearity. Solved: A and B are points with position vectors i -\underline{j} +4\underline{k} and 7\underline{i}-\underline{j}-2\underline{k} respectively.a) Find the position vectors of points P and Q which divide ABi) internally in the ratio 5:1ii) externally in the ratio 3:2, respectively.b) Show that the points A,B & Q are collinear (i.e, lie on the same straight line) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/10/NvkJqlqFoenQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WuX_vECJht6-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/10/WuX_vECJht6-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on ratio division of a line and collinearity. Solved: If A, B, C are points with position vectors \vec{a},\vec{b} and \vec{c} respectively, and P and Q divide AC and AB internally in the ratios 2:1 and 1:3respectively, in what ratio does the point of intersection of BP and QC divide QC? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/10/WuX_vECJht6-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/medkWAx-Rvz4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/67/medkWAx-Rvz4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on proving the convergence of real sequences. Solved: Prove that \lim_{n \to \infty} (\sqrt{n+1} -\sqrt{n})=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/67/medkWAx-Rvz4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mwL_M_y7IF7h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/65/mwL_M_y7IF7h.jpg</video:thumbnail_loc>

            <video:title>Worked examples</video:title>

            <video:description><![CDATA[
Worked examples on sum of the terms of a progression. Solved: Evaluate 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+... 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/65/mwL_M_y7IF7h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OCvhh6FJYCnD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/OCvhh6FJYCnD.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on computing matrix inverses. Solved: Given A=\left[\begin{array}{ccc} 3& 0 & 2\\ 2 & 0 & -2\\ 0 & 1 & 1\end{array}\right], ComputeA^-1 using (a) it's adjoint (b) an augmented matrix 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/OCvhh6FJYCnD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5jHo8DGTkw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/5jHo8DGTkw.jpg</video:thumbnail_loc>

            <video:title>Solvent extraction</video:title>

            <video:description><![CDATA[
Solutes split between immiscible liquids. How does the partition coefficient dictate which layer holds your product? Watch to master solvent extraction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/5jHo8DGTkw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OrkppBTADp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/OrkppBTADp.jpg</video:thumbnail_loc>

            <video:title>Crystallisation and distillation</video:title>

            <video:description><![CDATA[
How do you separate liquids from solids or split miscible liquids by boiling point? Watch to master simple distillation, fractional distillation, and fractional crystallisation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/OrkppBTADp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hYRYWVYmyz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1069/hYRYWVYmyz.jpg</video:thumbnail_loc>

            <video:title>Chromatography</video:title>

            <video:description><![CDATA[
Solutes split between stationary and mobile phases. How does the Rf value in TLC reveal a compound’s affinity? Watch to decode separation by partitioning.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1069/hYRYWVYmyz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0_utG3GvQlVn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/110/0_utG3GvQlVn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on algebra of matrices. Solved: Given A=\begin{array}{ccc} 3 & 7 \\ 1 & -5 \ \end{array}, B=\begin{array}{ccc} -1 & 2 \\ 5 & 3 \\ \end{array}, C=\begin{array}{ccc} 0 \\ 8\\ \end{array}, find (a) A+B (b) 2B+A (c) A-B (d) B-3A (e) AB (f) BA (g) 2AC (h) BC. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/110/0_utG3GvQlVn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/G7FNsQDrS_vz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/G7FNsQDrS_vz.jpg</video:thumbnail_loc>

            <video:title>More worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on solutions of square systems of linear equations using Cramer's rule. Solved: Solve for x, y and z using Cramer's rule, given2x-8y+6z=2-3x+16y-5z=-7-3x+15y-9z=-12 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/G7FNsQDrS_vz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pNMEWTv-631T</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/113/pNMEWTv-631T.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating determinants by row and column operations. Solved: Evaluate the following determinants(a) \left|\begin{array}{ccc}2&5&4\\5&6&7\\8&9&1\end{array}\right| 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/113/pNMEWTv-631T.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/k1hSwQKAdq5x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/k1hSwQKAdq5x.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on transposes and properties of matrix transposes. Solved: Show that any square matrix A can be written as a sum of a symmetric and a skew-symmetric matrix. Hence or otherwise, express \left[\begin{array}{ccc}1& 3\\ 5& 6\end{array}\right] as a sum of a symmetric matrix and a skew-symmetric matrix 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/k1hSwQKAdq5x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XHi5PqgV4LIl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/XHi5PqgV4LIl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on gradients, directional derivatives and normals to surfaces. Solved: Given that r=\Vert\mathbf{r}\rVert =\sqrt{x^2+y^2+z^2},\vec{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k} ,evaluate (i)\nabla r 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/XHi5PqgV4LIl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pKgDri-cWSBC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/pKgDri-cWSBC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on gradients, directional derivatives and normals to surfaces. Solved: Given the scalar function v=xy^2-z^2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/pKgDri-cWSBC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D3ihaTb8ViZG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1397/D3ihaTb8ViZG.jpg</video:thumbnail_loc>

            <video:title>Reactions</video:title>

            <video:description><![CDATA[
The pi electrons of the double bond make alkenes nucleophilic and prone to electrophilic attack. How do halogenation, hydration, and addition of hydrogen halides proceed through carbocation intermediates? This lesson maps each electrophilic addition mechanism and distinguishes ionic from free-radical pathways precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1397/D3ihaTb8ViZG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wcgiG8AOZs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/wcgiG8AOZs.jpg</video:thumbnail_loc>

            <video:title>Carbon and hydrogen estimation</video:title>

            <video:description><![CDATA[
Every organic compound contains carbon and hydrogen, but measuring their exact mass percentages requires precise combustion analysis. How does burning a sample in copper oxide and absorbing the products in KOH reveal the true elemental composition? Watch to see the method explained step by step.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/wcgiG8AOZs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UdnXxL2oCx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1070/UdnXxL2oCx.jpg</video:thumbnail_loc>

            <video:title>Lassaigne test (1)</video:title>

            <video:description><![CDATA[
Organic bonds hide nitrogen, sulfur, and halogens. How does fusing with sodium metal break these bonds to reveal the elements? Watch to master the Lassaigne test preparation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1070/UdnXxL2oCx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hqdfWEuSh7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1070/hqdfWEuSh7.jpg</video:thumbnail_loc>

            <video:title>Carbon and hydrogen detection</video:title>

            <video:description><![CDATA[
Every organic compound holds carbon and hydrogen. How do you prove their presence using copper oxide, lime water, and anhydrous copper sulfate? Watch to spot the tell-tale signs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1070/hqdfWEuSh7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DZYLTZA4MB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/DZYLTZA4MB.jpg</video:thumbnail_loc>

            <video:title>Halogens and sulphur estimation</video:title>

            <video:description><![CDATA[
The Carius method estimates halogens and sulphur in organic compounds. How does heating with fuming nitric acid convert these elements into weighable precipitates? Watch to understand this sealed tube technique.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/DZYLTZA4MB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YqT8UG7j0r</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/YqT8UG7j0r.jpg</video:thumbnail_loc>

            <video:title>Nitrogen estimation (1)</video:title>

            <video:description><![CDATA[
Quantitative nitrogen estimation requires specific methods for different compounds. Why does the Kjeldahl method fail for azo and diazonium compounds? Watch to understand the scope of this technique.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/YqT8UG7j0r.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WaabESTmm245</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/WaabESTmm245.jpg</video:thumbnail_loc>

            <video:title>Quadratic inequality (2)</video:title>

            <video:description><![CDATA[
Follow a second walkthrough on quadratic inequalities to sharpen your factorisation and interval testing skills. You will determine the exact range of values that satisfy the expression and express the result using standard interval notation. This example reinforces accuracy in complex cases. Solved: 6. Find the values of x which satisfy2x^2 - 7x + 9 < x^2 - 2x + 3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/WaabESTmm245.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WwsrnZUqKhpk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/WwsrnZUqKhpk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on solving homogeneous linear ordinary differential equations with constant coefficients. Solved: Solve the following:\frac{d^2x}{dt^2} +\frac{dx}{dt} -6x=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/WwsrnZUqKhpk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tAkrJD0qfbJl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/tAkrJD0qfbJl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: The disk is originally rotating at \omega_0=8rad\s. If it is subjected to a constant angular acceleration of \alpha=6rad\s^2, determine the magnitudes of the velocity and the n and t components of acceleration of point B just after the wheel undergoes 2 revolutions. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/tAkrJD0qfbJl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743770162010.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dl8uoF1wd0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/leaJsMegUb/Thumbnails/1190/dl8uoF1wd0.jpg</video:thumbnail_loc>

            <video:title>Primary ratios</video:title>

            <video:description><![CDATA[
Define sine, cosine, and tangent using the sides of a right-angled triangle. These primary ratios relate angles to side lengths, forming the basis for all trigonometric calculations. Master these definitions to solve problems in geometry, structural analysis, and wave mechanics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/leaJsMegUb/Previews/1190/dl8uoF1wd0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xn8x0ezUFkfM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/xn8x0ezUFkfM.jpg</video:thumbnail_loc>

            <video:title>Algebraic split</video:title>

            <video:description><![CDATA[
Complex fractions block easy differentiation. How do you split a rational function into simple power terms to avoid the quotient rule? Watch the algebraic trick that simplifies the work. Solved: Find the derivative of y = \frac{(x+2)(x+3)}{x^3}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/xn8x0ezUFkfM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m70_JMtcVS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/m70_JMtcVS.jpg</video:thumbnail_loc>

            <video:title>Trigonometric parameters</video:title>

            <video:description><![CDATA[
Parametric equations define motion using time. How do you find the gradient when x and y are both trigonometric functions of t? Watch the simplification steps. Solved: A component in a car engine moves such that its position coordinates at time t are defined by x = 8(t - \sin t) and y = 8(1 - \cos t). Determine the expression for the gradient \frac{dy}{dx} in its simplest trigonometric form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/m70_JMtcVS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VhgZZuKOJ9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1072/VhgZZuKOJ9.jpg</video:thumbnail_loc>

            <video:title>Empirical and molecular formula (2)</video:title>

            <video:description><![CDATA[
Combustion Data hides the true atomic ratio. How do you derive an empirical formula from masses of carbon dioxide and water? Watch this walkthrough to master the conversion steps. Solved: An organic compound has the empirical formula CH_{2}O. If its measured molar mass is 180.18 \text{ g/mol}, determine its molecular formula. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1072/VhgZZuKOJ9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xemtFRPa2c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1072/xemtFRPa2c.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Raw data is useless without a formula. How do you turn percentage composition into an exact molecular identity? Watch to see the logic that connects mass to structure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1072/xemtFRPa2c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yiJ4g2LLeX3Q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/yiJ4g2LLeX3Q.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on particle rectilinear motion problems of the first kind. Solved: A particle moves along a straight line such that its position is defined by s=(2t^3+3t^2-12t-10)m. Determine the velocity, average velocity, and the average speed of the particle when t=3s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/yiJ4g2LLeX3Q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GzHXUxlH3pCP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/GzHXUxlH3pCP.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems. Solved: A particle is an experimental apparatus has a velocity given by v=k\sqrt{s} , where v is in millimeters per second, the position s is millimeters, and the constant k=0.2mm^\frac{1}{2}s^-1 . If the particle has a velocity v_0=3mm/s at t=0, determine the particle position , velocity, and acceleration as functions of time, and compute the time, position, and acceleration of the particle when the velocity reaches 15mm/s 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/GzHXUxlH3pCP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MFKfS4dZNDsu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/MFKfS4dZNDsu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems. Solved: A particle travels along a straight line with a velocity v=(12-3t^2)m/s , where t is in seconds . When t=1s , the particle is located 10m to the left of the origin . Determine the acceleration when t=4s, the displacement from t=0 to t=10s , and the distance the particle travels during this time period. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/MFKfS4dZNDsu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m10E7m9Ggd_a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/m10E7m9Ggd_a.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems. Solved: The cone falling with a speed v_0 strikes and penetrates the block if packing material. The acceleration of the cone impact is a=g-cy^2 , where c is a positive constant and y is the penetration distance . If the maximum penetration depth is observed to be y_m, determine the constant c. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/m10E7m9Ggd_a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746265296340.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/87V9D_mrtnmG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/87V9D_mrtnmG.jpg</video:thumbnail_loc>

            <video:title>Two-sided absolute values</video:title>

            <video:description><![CDATA[
Solve inequalities with absolute values on both sides by squaring both expressions or testing boundary cases. This walkthrough demonstrates how to eliminate the modulus bars and solve the resulting quadratic or linear relationship to find the final solution set. Precise case analysis is essential here. Solved: 10. Solve the inequality |x+2| > |2x-1|. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/87V9D_mrtnmG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PklWc9g5GU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1076/PklWc9g5GU.jpg</video:thumbnail_loc>

            <video:title>Priority list</video:title>

            <video:description><![CDATA[
Polyfunctional molecules contain multiple reactive groups that compete for naming dominance. Which functional group claims the parent suffix when a carboxylic acid and an alcohol exist in the same structure? This lesson establishes the strict IUPAC priority hierarchy to resolve such conflicts definitively.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1076/PklWc9g5GU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3yFgeU3fpH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1074/3yFgeU3fpH.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Functional groups define the behaviour of organic compounds. Why does a single atom arrangement determine whether a molecule is an alcohol or an alkane? This lesson explains how specific bonds classify organic substances and set their chemical properties.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1074/3yFgeU3fpH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NoX38l7_ib</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1075/NoX38l7_ib.jpg</video:thumbnail_loc>

            <video:title>Nomenclature</video:title>

            <video:description><![CDATA[
IUPAC nomenclature converts complex branched structures into unique, standard names. How do you correctly prioritise the parent chain and assign locants when multiple substituents compete for position? This lesson applies the four-step naming protocol to resolve ambiguity in alkane identification.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1075/NoX38l7_ib.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VxHPNpKjZA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1075/VxHPNpKjZA.jpg</video:thumbnail_loc>

            <video:title>Nomenclature</video:title>

            <video:description><![CDATA[
Branched alkanes with complex substituents like sec-butyl and isopropyl test the limits of standard naming rules. How do you correctly identify the true parent chain when a substituent itself contains branching? This walkthrough applies IUPAC priority rules to resolve the structure systematically.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1075/VxHPNpKjZA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X_fdaQrptN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1077/X_fdaQrptN.jpg</video:thumbnail_loc>

            <video:title>Aromatic compounds</video:title>

            <video:description><![CDATA[
Benzene forms the parent structure of all aromatic compounds. How do you correctly name substituted benzene derivatives under IUPAC rules? This lesson establishes the precise nomenclature for these stable ring systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1077/X_fdaQrptN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ILRcXeMdQ2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1077/ILRcXeMdQ2.jpg</video:thumbnail_loc>

            <video:title>Cyclic compounds</video:title>

            <video:description><![CDATA[
Cyclic compounds form rings without aromatic stability. How do you name saturated and unsaturated rings correctly under IUPAC rules? This lesson defines the exact nomenclature for these non-aromatic structures.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1077/ILRcXeMdQ2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/G4UMMcXN_LIR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/G4UMMcXN_LIR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: The angular velocity of the rotating disk is \omega=4\sqrt{t}, where t is in seconds. Find the angular displacement of the disk for the time interval t=0 to t=6s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/G4UMMcXN_LIR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743768023361.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/fI1SGITFUa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1077/fI1SGITFUa.jpg</video:thumbnail_loc>

            <video:title>Di-substituted aromatics</video:title>

            <video:description><![CDATA[
Two substituents on a benzene ring create positional isomers. How do you assign correct locants and distinguish ortho, meta, or Para arrangements? This lesson defines the exact IUPAC rules for naming di-substituted aromatics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1077/fI1SGITFUa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T5kCfI-VmiyQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/T5kCfI-VmiyQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: The elements of the mechanism for deployment of a spacecraft magnetometer boom are shown. Determine the angular velocity of the boom when the driving link OB crosses the y-axis with an angular velocity w_{OB} = 0.5 rad/sec if tan \theta = \frac 4 3 at this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/T5kCfI-VmiyQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744986216992.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/RfvExtHSqluL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/148/RfvExtHSqluL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on acceleration analysis of the motion of a rigid body undergoing general plane motion using the acceleration of a point relative to another point on the same rigid body. Solved: The ends of bar AB are confined to move along the paths shown . At a given instant, A has a velocity of 8ft/s and an acceleration of 3ft/s^2. Determine the angular velocity and angular acceleration of AB at this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/148/RfvExtHSqluL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1745152936776.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vEoi7YufrM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1078/vEoi7YufrM.jpg</video:thumbnail_loc>

            <video:title>Chain isomerism</video:title>

            <video:description><![CDATA[
Same molecular formula can hide different carbon skeletons. Why does branching lower boiling point despite identical atom counts? This lesson explains chain isomerism and links structural shape to physical properties like volatility.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1078/vEoi7YufrM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/atsp1339Gbr4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/atsp1339Gbr4.jpg</video:thumbnail_loc>

            <video:title>Fundamental theorem (2)</video:title>

            <video:description><![CDATA[
Definite integrals yield exact numerical totals. How do you compute this area without summing infinite rectangles? We apply the Second Fundamental Theorem to evaluate antiderivatives at the boundaries.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/atsp1339Gbr4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NWxGit9WSa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1078/NWxGit9WSa.jpg</video:thumbnail_loc>

            <video:title>Position and functional group</video:title>

            <video:description><![CDATA[
Same formula but different groups create distinct chemicals. How do you tell position isomers from functional group isomers? We clarify the structural shift that changes the compound class.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1078/NWxGit9WSa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fSziX1uQdq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/fSziX1uQdq.jpg</video:thumbnail_loc>

            <video:title>Differential balance</video:title>

            <video:description><![CDATA[
Composite functions hide their derivatives inside the integrand. How do you match the outside factor to the inner derivative? This walkthrough balances the differential for a clean substitution. Solved: Evaluate the indefinite integral \int x^{2} \sin(x^{3}) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/fSziX1uQdq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZWJq4FyJ5Ueo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/ZWJq4FyJ5Ueo.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (8)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/ZWJq4FyJ5Ueo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QUTIjt86VODA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/213/QUTIjt86VODA.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on basis and dimension of vector spaces. Solved: 1. Which of the following sets cannot form a basis for \mathbb{R^2}?(a) {(1,0), (0,1)}(b) {(1,3), (2,5)}(c) {(0,-2), (-2,0)}(d) {(10,6), (5,3)}2. Let {u,v} be a basis for \mathbb{R^2} over \mathbb{R}. Which of the following is true?(a) \alpha u + \beta v = 0 for any \alpha,\beta \epsilon\mathbb{R}(b) For any w \epsilon \mathbb{R^2} , there exist nonzero scalars, \alpha,\beta such that w = \alpha u + \beta v(c) u =\alpha v for some scalar \alpha(d) \alpha u + \beta v = 0 for nonzero scalars \alpha,\beta(e) None of the above. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/213/QUTIjt86VODA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gNuEbF9VcwQl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/9/gNuEbF9VcwQl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on vector components in two and three dimensions. Solved: Find w if vectors w\underline{i}+5\underline{j} and -2\underline{i}+6\underline{j} are parallel. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/9/gNuEbF9VcwQl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9cGHYwRsYxsb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/9cGHYwRsYxsb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: The force F = { 6i + 8j + 10k } N creates a moment about point O of M_O = { -14i + 8j + 2k } N . m. If the force passes through a point having an x coordinate of 1 m, determine the y and z coordinates of the point. Also, realizing that M_O = Fd, determine the perpendicular distance d from point O to the line of action of F. Note: The figure shows F and M_O in an arbitrary position. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/9cGHYwRsYxsb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738692380455.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/9T2T93B9sdwf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/278/9T2T93B9sdwf.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on stationary points of a function of two variables. Solved: A rectangular box, open at the top, is to have a volume of 32ft^3 . What must be the dimension so that the total surface is a minimum? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/278/9T2T93B9sdwf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VOenEQ3hsf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1079/VOenEQ3hsf.jpg</video:thumbnail_loc>

            <video:title>Cis and trans</video:title>

            <video:description><![CDATA[
Restricted rotation around double bonds locks substituents into fixed spatial positions. How do you correctly assign cis and trans labels when priority groups sit on the same or opposite sides? This lesson establishes the precise rules for geometric identification.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1079/VOenEQ3hsf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S8cVe8zt4g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1079/S8cVe8zt4g.jpg</video:thumbnail_loc>

            <video:title>E and Z system</video:title>

            <video:description><![CDATA[
Cis and trans labels fail when a double bond carries three or four different substituents. How do you assign unambiguous geometric descriptors using atomic priority rules? This lesson establishes the rigorous E and Z nomenclature system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1079/S8cVe8zt4g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SVkRkyyvkVHb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/SVkRkyyvkVHb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: Compute the magnitude of the moment M_O of the 250-lb force about the axis O-O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/SVkRkyyvkVHb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740297133604.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-MjUUpm2TG5h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/-MjUUpm2TG5h.jpg</video:thumbnail_loc>

            <video:title>Worked examples III</video:title>

            <video:description><![CDATA[
Worked examples on the equation of a hyperbola. Solved: 1 Sketch the parabolasy=2x^2 ; x=2y^22 Sketch the parabola y^2-4y-12x+40=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/-MjUUpm2TG5h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MlQzHNQbVg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/MlQzHNQbVg.jpg</video:thumbnail_loc>

            <video:title>Arithmetic operations</video:title>

            <video:description><![CDATA[
Solve a practical problem on combining functions for profit modelling by calculating the sum of two separate expressions. You will learn to find the final domain by identifying the intersection of individual input ranges. This walkthrough ensures you can handle restricted intervals accurately. Solved: Given the functions f(x) = \frac{1}{6-x} defined on the interval 0 \leq x < 6 and g(x) = x - 4 defined on the interval 0 < x \leq 8, determine the domain of the combined function h(x) = f(x) + 2g(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/MlQzHNQbVg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bdh6pVDadA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/bdh6pVDadA.jpg</video:thumbnail_loc>

            <video:title>Stereoisomer count</video:title>

            <video:description><![CDATA[
Molecules with multiple chiral centres produce complex stereoisomer sets. How do you calculate the exact count without drawing every structure? This lesson applies the 2^n rule to determine total stereoisomers accurately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/bdh6pVDadA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/86IILHWJ_b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/86IILHWJ_b.jpg</video:thumbnail_loc>

            <video:title>R and S system</video:title>

            <video:description><![CDATA[
Enantiomers share identical IUPAC names yet possess distinct biological effects. How do you assign unique descriptors to these mirror-image molecules? This lesson explains the R and S configuration system for precise stereochemical naming.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/86IILHWJ_b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Lie5yIB6cX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/Lie5yIB6cX.jpg</video:thumbnail_loc>

            <video:title>Implicit transcendentals</video:title>

            <video:description><![CDATA[
Implicit equations often hide trigonometric functions. How do you differentiate mixed terms involving inverse sine and cosine to isolate dy by dx? Watch the full derivation. Solved: Determine the expression for \frac{dy}{dx} for the relationship y^2 \cos x + 3y = \sin^{-1} x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/Lie5yIB6cX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e_LGh3a4rm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1079/e_LGh3a4rm.jpg</video:thumbnail_loc>

            <video:title>Use of phantom atoms</video:title>

            <video:description><![CDATA[
Multiple bonds complicate priority assignment because standard atomic number comparison fails. How do you expand double and triple bonds into phantom atoms to apply Cahn-Ingold-Prelog rules correctly? This lesson demonstrates the duplication method for carbonyl and nitrile groups.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1079/e_LGh3a4rm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pRAa9B995G</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/pRAa9B995G.jpg</video:thumbnail_loc>

            <video:title>Enantiomers</video:title>

            <video:description><![CDATA[
Enantiomers are non-superimposable mirror images that confuse flat drawings. How do you represent 3D chirality accurately on paper? This lesson demonstrates perspective formulas and Fischer projections for correct structural depiction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/pRAa9B995G.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EtDJ3FYMeq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/EtDJ3FYMeq.jpg</video:thumbnail_loc>

            <video:title>Perspective formula</video:title>

            <video:description><![CDATA[
Perspective formulas show 3D arrangement of chiral centres. How do you position substituents to guarantee the correct R-configuration for alanine? This walkthrough demonstrates precise wedge-dash placement. Solved: Draw the structure of (R)-Alanine using the perspective formula\begin{array}{ccc} \mathrm{CH_3} & \mathrm{CH} & \mathrm{COO^-} \\ & |^+ & \\ & \mathrm{NH_3} & \end{array} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/EtDJ3FYMeq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/g0AgrHUrmPBM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/g0AgrHUrmPBM.jpg</video:thumbnail_loc>

            <video:title>Accumulated area function</video:title>

            <video:description><![CDATA[
Area under a curve defines a total. How does this total change as the upper limit moves? We construct the accumulated area function from this geometric base.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/g0AgrHUrmPBM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7uWi2hxbetZg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/7uWi2hxbetZg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: The forces acting on the bob of the pendulum are its weight W (W = 2N) and the tension T in the cord. When the pendulum reaches the limits of its swing at \theta = 30^{\circ}, it can be shown that the resultant of W and T is perpendicular to the cord. Determine the magnitude of T in this position. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/7uWi2hxbetZg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739465859165.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/l-g97qal0dKj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/l-g97qal0dKj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Cable AB is 65 ft long and the tension in that cable is 3900 lb.Determine (a) the x, y, and z components of the force exerted by the cable on the anchor B. (b) the angles \Theta_x, \Theta_y, and \Theta_z defining the direction of that force. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/l-g97qal0dKj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739794914507.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/TSiQy9DCpK1d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/TSiQy9DCpK1d.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: A ship is towed through a narrow channel by applying forces to three ropes attached to its bow. Determine the magnitude and orientation \theta of the force \vec{F} so that the resultant force is in the direction of line a and the magnitude of \vec{F} is as small as possible. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/TSiQy9DCpK1d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739466458710.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/AAwD1YAzdW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1084/AAwD1YAzdW.jpg</video:thumbnail_loc>

            <video:title>Energy profiles</video:title>

            <video:description><![CDATA[
Reactions with multiple steps form short-lived intermediates between transition states. How do you read activation energy for each step from one energy profile? This lesson maps the full pathway and defines every barrier clearly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1084/AAwD1YAzdW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uTmxAdZ0Uk1P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/53/uTmxAdZ0Uk1P.jpg</video:thumbnail_loc>

            <video:title>Infinity</video:title>

            <video:description><![CDATA[
Meaning and use of infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/53/uTmxAdZ0Uk1P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5vPWFtxXlf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/5vPWFtxXlf.jpg</video:thumbnail_loc>

            <video:title>Reaction mechanism</video:title>

            <video:description><![CDATA[
Reactions occur through specific molecular pathways, not by chance. How do individual steps combine to form the overall balanced equation? This lesson defines reaction mechanisms and explains bond changes during the process.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/5vPWFtxXlf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RQH5juPpgt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/RQH5juPpgt.jpg</video:thumbnail_loc>

            <video:title>Organic reaction pathways</video:title>

            <video:description><![CDATA[
Organic reactions follow distinct electronic pathways. How do polar ionic and radical mechanisms differ in bond cleavage? This lesson distinguishes nucleophile-electrophile attraction from homolytic fission.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/RQH5juPpgt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8Rsr6Bl8xh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1084/8Rsr6Bl8xh.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Reactions require molecular collisions and bond reorganisation to proceed. How do you distinguish the transition state from reactants and products on an energy profile? This lesson defines activation energy, Gibbs free energy, and exergonic versus endergonic pathways clearly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1084/8Rsr6Bl8xh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OaDiHSTBolsL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/OaDiHSTBolsL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: In order to move a wrecked truck, two cables are attached at A and pulled by winches B and C as shown. Knowing that the tension in cable AB is 2 kips, determine the components of the force exerted at A by the cable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/OaDiHSTBolsL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739795640066.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sYwEqHx64Gvu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/sYwEqHx64Gvu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: A cable extends from point C to point E. It exerts a 50-lb force T on the plate at C that is directed along the line from C to E. Express T in terms of components. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/sYwEqHx64Gvu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739796005275.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WV9rOctGjdNR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/WV9rOctGjdNR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: (a) A foot valve for a pneumatic system is hinged at B. Knowing that \alpha = 28^{\circ} , determine the moment of the 16-N force about point B by resolving the force into horizontal and vertical components.(b) A foot valve for a pneumatic system is hinged at B. Knowing that \alpha = 28^{\circ} , determine the moment of the 16-N force about point B by resolving the force into components along ABC and in a direction perpendicular to ABC. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/WV9rOctGjdNR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738687799211.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/uk80rItiWOLm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/uk80rItiWOLm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: (a) The cable exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If \theta = 30^{\circ} , determine the placement x of the boom at B so that this force creates a maximum moment about point O. What is the moment?(b) The cable exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If x = 10 m, determine the angle \theta of the boom so that this force creates a maximum moment about point O. What is the moment? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/uk80rItiWOLm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688321281.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/1MbaeBG12F</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1085/1MbaeBG12F.jpg</video:thumbnail_loc>

            <video:title>Molecularity</video:title>

            <video:description><![CDATA[
Molecularity counts the species colliding in an elementary step. How do you tell unimolecular from bimolecular events without confusing them with reaction order? This lesson defines both terms and separates molecularity from kinetics cleanly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1085/1MbaeBG12F.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qZ5WTLM4OqOf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/10/qZ5WTLM4OqOf.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on ratio division of a line and collinearity. Solved: Relative to the origin O, the position vectors of two points P and Q are (-6\underline{k})\underline{i}-2\underline{j}+8(1+k)\underline{k} and (2k+13)\underline{i}-\underline{j}-32k\underline{k}.Given that OPQ is a straight line, find the value of the constant k 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/10/qZ5WTLM4OqOf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DEg2xmm95PNo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/DEg2xmm95PNo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: A 12-lb circular plate of 7-in, radius is supported as shown by three wires, each of 25-in, length. Determine the tension i each wire, knowing that \alpha=30^0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/DEg2xmm95PNo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739876332511.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/GnKN2MpLJKlX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/GnKN2MpLJKlX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: A uniform steel ring 60in, in diameter and weighing 600lb is lifted by three cables, each 50in long, attached at points A, B, and C as shown. Compute the tension in each cable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/GnKN2MpLJKlX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739876810241.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/EWoiAhEWTIOc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/EWoiAhEWTIOc.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: The object at D is supported by boom AO and cables AB, AC and AD, which are parallel to x, y, and z axes, respectively. If the cables and the boom have the failure strengths given below, determine the largest mass m_D that can be supported. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/EWoiAhEWTIOc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740068591180.JPEG</image:loc>
            </image:image>
            
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740068629926.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/yUgyOCx8E5L4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/yUgyOCx8E5L4.jpg</video:thumbnail_loc>

            <video:title>Root clearing</video:title>

            <video:description><![CDATA[
Radicals block standard integration rules. How do you remove the root and handle the resulting differential? This walkthrough clears the square root for direct calculation. Solved: Evaluate the indefinite integral \int \frac{1}{1 + \sqrt{x}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/yUgyOCx8E5L4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aTVLLmW_aXMY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Thumbnails/138/aTVLLmW_aXMY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating eigenvalues and eigenvectors. Solved: Obtain the eigenvalues and corresponding eigenvectors of the matrixA=\left[ \begin{array}{ccc} 4 & 6 & 6 \\ 1 & 3 & 2\\ -1 & -5 & -2 \end{array} \right] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/a7EBeEYMAY/Previews/138/aTVLLmW_aXMY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sn82DchXyno3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/Sn82DchXyno3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The boom is intended to support two vertical loads F_1 and F_2. If the cable CB can sustain a maximum load of 1500 N before it fails, determine the critical loads if F_1=2F_2. Also, what is the magnitude of the maximum reaction at pin A? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/Sn82DchXyno3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736823805445.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vSz95XkyNAoY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/336/vSz95XkyNAoY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of frictional forces on flat belts. Solved: A flat belt is used to transmit a couple from drum B to drum A. Knowing that the coefficient of the static friction is 0.40 and that the allowable belt tension is 450N , determine the largest couple that can be exerted on drum A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/336/vSz95XkyNAoY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746868389434.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ZjbOEp1PyEpU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/ZjbOEp1PyEpU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Determine the stiffness k of each spring so that the 30-N force cause the bar to tip \theta=15^{\circ} when the force is applied. Originally the bar is horizontal and the springs are unstretched. Neglect the weight of the bar. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/ZjbOEp1PyEpU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736862981608.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/K2Vuaxr_Dcz_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/K2Vuaxr_Dcz_.jpg</video:thumbnail_loc>

            <video:title>Inequality of means (1)</video:title>

            <video:description><![CDATA[
Apply the Arithmetic Mean-Geometric Mean inequality to solve specific minimisation and maximisation problems. You will follow a step-by-step calculation to prove bounds for algebraic expressions and identify when equality occurs. This walkthrough demonstrates the practical utility of mean comparisons. Solved: 13. For any positive real number x, prove that x + \frac{16}{x} \ge 8. Identify the value of x for which equality holds. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/K2Vuaxr_Dcz_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7LIyHyhvMJmz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/54/7LIyHyhvMJmz.jpg</video:thumbnail_loc>

            <video:title>Domain of functions</video:title>

            <video:description><![CDATA[
Domain of functions and its calculation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/54/7LIyHyhvMJmz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RtsGpId4W2Qv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/RtsGpId4W2Qv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: If a vertical force of 2.5KN is applied to the hook at A, determine the tension in each of the three cables for equilibrium. Set d=1m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/RtsGpId4W2Qv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739875879380.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-_L-0b36gprm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/-_L-0b36gprm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: The coefficients of friction between the load and the flatbed trailer shown are u_s=0.40 and u_k =0.35. Knowing that the speed of the rig is 55 mi/h, determine the shortest time in which the rig can be brought to a stop if the load is not to shift. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/-_L-0b36gprm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748265776034.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/o7guxlrAd-wj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/o7guxlrAd-wj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: In the event of an emergency, a nuclear reactor is shut down by dropping the control rod R, having a weight of 20 lb, into the reactor core C. If the rod is immersed in "heavy" water, which offers a drag resistance to downward motion of F_D = (0.25v) lb, where v is the velocity of the rod in ft/s, determine the distance s it must descend into the reactor core when it attains a speed of 15 ft/s. The rod is released from rest when s = 0. Neglect the effect of buoyancy. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/o7guxlrAd-wj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742298681407.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/d-tZrVqmL3O4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/d-tZrVqmL3O4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: A sailor is being rescued using a boatswain's chair that is suspended from a pulley that can roll freely on the support ACB and is pulled at a constant speed by cable CD. Knowing that \alpha = 30^\circ and \beta = 10^\circ and that the combined weight of the boatswain's chair and the sailor is 200 lb, determine the tension (a) in the support cable ACB,(b) in the traction cable CD. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/d-tZrVqmL3O4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739471418521.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nl8LZraloxQw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/nl8LZraloxQw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: Knowing the forces in members A and C, determine the force F_B and F_D acting on the members B and D that are required for equilibrium. The force system is concurrent at point O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/nl8LZraloxQw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739471722402.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/UkZGKG7hIg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1087/UkZGKG7hIg.jpg</video:thumbnail_loc>

            <video:title>Overview</video:title>

            <video:description><![CDATA[
Organic reactions fall into four general types based on bond changes. How do you tell addition from substitution, elimination, or rearrangement just by inspecting reactants and products? This lesson classifies all four types and defines their structural signatures precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1087/UkZGKG7hIg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pm-_by_hyCY7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/220/Pm-_by_hyCY7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on matrix representations of linear maps. Solved: Let IR^3\to IR^2 be defined by T(x_1,x_2,x_3)=(x_1-x_2+x_3,x_2-x_3). Let IR^3 have the standard basis and let IR^2 have the basis C=[{(1,1),(1,-1)}].(a) Find the matrix representation of T with respect to these bases.(b) Calculate T(1,-1,2) directly and by using the matrix of T. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/220/Pm-_by_hyCY7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t5fMuR02P_9a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/t5fMuR02P_9a.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using parameters measured relative to a reference frame in rotation. Solved: At the instant \theta =60^\circ , link CD has an angular velocity \omega_{CD} =4rad/s and an angular acceleration \alpha_{CD}=2rad/s^2 . Determine the angular velocity and angular acceleration of rod AB at this instant. The collar at C is pin connected to DC and slides over AB. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/t5fMuR02P_9a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745661461419.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/aFzF7xfUTd7j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/299/aFzF7xfUTd7j.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on addition of vectors in three dimensions. Solved: Knowing that the tension is 510lb in cable AB and 4 25lb in cable AC, determine the magnitude and direction of the resultant forces exerted at A by the two cables. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/299/aFzF7xfUTd7j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739872998612.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/rnDWLqkaU81K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/rnDWLqkaU81K.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: Team A and team B consists of four members of total mass 320 kg and 330 kg, respectively. If the average coefficients of static and kinetic friction of team A are \mu_s = 0.52 and \mu_k = 0.5, and for team B, \mu_s = 0.48 and \mu_k = 0.46, which team will win the tug of war? Also, what is the acceleration of the losing team if the winning team develops its maximum static friction? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/rnDWLqkaU81K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742307177352.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/MwzN9O5U7n5T</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/MwzN9O5U7n5T.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
Worked examples on dependent motion analysis with unaligned cables. Solved: A crate A is being pulled up an inclined ramp by winch retracting the cord at a constant rate v_0=2ft/s. Letting h=1.5ft, determine the speed of the crate when d=4ft 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/MwzN9O5U7n5T.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742049782503.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/U3HBdoIbTHTt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/U3HBdoIbTHTt.jpg</video:thumbnail_loc>

            <video:title>Mono-chlorination</video:title>

            <video:description><![CDATA[
Branched alkanes yield multiple chlorination isomers. How do you calculate the percentage yield of each product from relative reactivity rates? We determine the exact distribution for 2-methylbutane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/U3HBdoIbTHTt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cGQDObt4f_WR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/322/cGQDObt4f_WR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the analysis of frames. Solved: For the frame and loading shown, determined the force acting on member ABC (a) at B (b) at C 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/322/cGQDObt4f_WR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739274846374.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Hwl9lFQJfs8p</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/Hwl9lFQJfs8p.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 120-g slider has a speed v=1.4m/s as it passes point A of the smooth guide, which lies in a horizontal plane. Determine the magnitude R of the force which the guide exerts on the slider (a) just before it passes point A of the guide and (b) as it passes point B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/Hwl9lFQJfs8p.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745331166911.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/B8UnJo46oB_0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/322/B8UnJo46oB_0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the analysis of frames. Solved: For the frame and loading shown, determine the components of all forces acting on member ABE. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/322/B8UnJo46oB_0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739271765631.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-HeF7Jnk8P_H</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/333/-HeF7Jnk8P_H.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of problems involving dry friction - for particles. Solved: Considering only values of \theta less than 90^\circ , determine the smallest value of \theta required to start the block moving to the right when (a) W = 75 lb,(b) W = 100 lb. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/333/-HeF7Jnk8P_H.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741106642112.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Bk1VIn04TVIO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/Bk1VIn04TVIO.jpg</video:thumbnail_loc>

            <video:title>Rational inverse</video:title>

            <video:description><![CDATA[
Learn how to derive the inverse of a rational function by cross-multiplying and factorising to isolate the new subject. You will master the algebraic steps to handle variables in both the numerator and denominator. This walkthrough ensures you can flip complex fractional relationships accurately. Solved: Given the rational function f(x) = \frac{3x + 2}{x - 5}, derive the formula for its inverse f^{-1}(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/Bk1VIn04TVIO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bDvGu3HwF7sw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/bDvGu3HwF7sw.jpg</video:thumbnail_loc>

            <video:title>Triple-factor twist</video:title>

            <video:description><![CDATA[
Three functions multiplied together need a special approach. How do you apply the product rule to a triple factor? Watch the pattern unfold. Solved: Differentiate y = x^2 e^x \sin x with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/bDvGu3HwF7sw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E4RfWqARlRRg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/616/E4RfWqARlRRg.jpg</video:thumbnail_loc>

            <video:title>Trigonometric functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of trigonometric functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/616/E4RfWqARlRRg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TIbfMcpRqX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/TIbfMcpRqX.jpg</video:thumbnail_loc>

            <video:title>Area equivalence</video:title>

            <video:description><![CDATA[
Definite integrals calculate total area under a curve. How does summing strips equal the exact geometric region? We link the limit process to physical area.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/TIbfMcpRqX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JUa9_4Z8zQKa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/JUa9_4Z8zQKa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating first and higher-order partial derivatives using the general methods of differentiation. Solved: Let f(x, y) = tan^{-1}(\frac y x ). Obtain f_{xx}, f_{xy}, f_{yx} and f_{yy}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/JUa9_4Z8zQKa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ruz3ovtF-0X6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/335/Ruz3ovtF-0X6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of frictional forces on square-threaded screws. Solved: The square - threaded screw of the C- clamp has a mean diameter of 9mm and a pitch of 1.5mm . The coefficient of static friction between the threads is 0.2 . If the torque C=1.25N . m is used to tighten the clamp, determine (a) the clamping force ; and (b) the torque required to loosen the clamp. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/335/Ruz3ovtF-0X6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746866936108.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JFPP4FZkyDRd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/212/JFPP4FZkyDRd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on linear dependence and independence of vectors in a vector space. Solved: Show that u=(a,b) and v=(c,d) \in IR are linearly independent if and only if ad-bc=0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/212/JFPP4FZkyDRd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/r33oMoaGL4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/r33oMoaGL4.jpg</video:thumbnail_loc>

            <video:title>Physical properties</video:title>

            <video:description><![CDATA[
Physical state and boiling point of alkanes depend on chain length and branching. Why does a branched isomer boil lower than its straight-chain counterpart despite identical mass? This lesson links molecular weight, viscosity, and volatility to structure precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/r33oMoaGL4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GoOskNx8oT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/GoOskNx8oT.jpg</video:thumbnail_loc>

            <video:title>Petroleum</video:title>

            <video:description><![CDATA[
Petroleum is a complex mixture of over 150 alkanes separated by boiling point. How does fractional distillation isolate specific fuel fractions from crude oil without chemical reaction? This lesson maps carbon chain lengths to commercial products like gasoline and kerosene precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/GoOskNx8oT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4S665XQ6mW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1089/4S665XQ6mW.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Get started with an overview of the course goals and the essential role of functional groups in chemistry. This lesson outlines how identifying specific atomic clusters helps predict molecular behaviour.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1089/4S665XQ6mW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DsSuYMRDfz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/DsSuYMRDfz.jpg</video:thumbnail_loc>

            <video:title>Classifying C and H atoms</video:title>

            <video:description><![CDATA[
Carbon and hydrogen atoms in alkanes are classified by their bonding environment. How do you tell primary from secondary or tertiary carbons just by counting attached groups? This lesson defines the classification rules and links hydrogen types to their parent carbon precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/DsSuYMRDfz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aW14FrxJpVdt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/399/aW14FrxJpVdt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on sample examination problems on limits of functions. Solved: 1.Evaluate \lim_{x\to \infty}\frac{3^x-3^-x}{3^x+3^-x} 2.Evaluate \lim_{x\to \infty}(\frac{\sin x}{x} )3.Evaluate \lim_{t\to \infty}(\sqrt{t+1}-\sqrt{t})4.Evaluate \lim_{x\to \infty}x^2e^-x 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/399/aW14FrxJpVdt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c0Lnu2mk9efM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/399/c0Lnu2mk9efM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on limits of real-valued single-variable functions - 2023/2024 mid-semester examination questions. Solved: 1.Find \lim_{x\to \frac{\Pi}{2}} {[\frac{\Pi}{2}}-x]^-1 cotx2.Let sgn(x) denote a signum function, then \lim_{x\to 10}(\frac{2sgn(x-10)}{2+sgn(sgn(10-x))}) is/does3.Find the limit of the function (2^\frac{-1}{x}-\frac{5}{(2^\frac{1}{x})x})^x as x\to\infty. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/399/c0Lnu2mk9efM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jotRbc8ISnVm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/jotRbc8ISnVm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: When s = 0, the spring of the firing mechanism is unstretched. If the arm is pulled back such that s = 100 mm and released , determine the speed of the 0.3-kg ball and the normal reaction of the circular track on the ball when \theta =60^\circ. Assume all surfaces of contact to be smooth. Neglect the mass of the spring and the size of the ball. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/jotRbc8ISnVm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747074626749.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/944lWZ8bEEZM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/84/944lWZ8bEEZM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on Newton's method of solution of equations in one variable. Solved: Show that f(x) = cos (\frac {\pi(x + 1)} {8}) + 0.148x - 0. 9062 = 0 has a root in (-1, 0) and a root in (0, 1). Calculate the negative root, correct to 4 decimal places. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/84/944lWZ8bEEZM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pFaBMlXObiRp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/395/pFaBMlXObiRp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on determining the condition of constraints, equilibrium and static determinacy of two-dimensional structures. Solved: Eight identical 500\times750-mm rectangular plates, each of mass m=40kg, are held in a vertical plane as shown. All connections consist of frictionless pins, rollers, or short links. In each case, determine whether (a) the plate is completely, partially, or improperly constrained, (b) the reactions are statically determinate or indeterminate, (c) the equilibrium of the plate is maintained in the position shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/395/pFaBMlXObiRp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738589466122.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/KB5ntUuPb6-Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/414/KB5ntUuPb6-Z.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on equations of lines, planes, curves and surfaces in three dimensions. Solved: Find the equations of the tangent line and normal plane to a space curve intersecting the surfaces x^2 + y^2 + z^2 = 4 and x + y +z = 1 at point (1,2,3). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/414/KB5ntUuPb6-Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2yjLDGmMvNZv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/403/2yjLDGmMvNZv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on sample examination questions on the convergence of infinite series. Solved: 1.Find the open interval of convergence of the series \sum_{n=1}^{\infty}\frac{(x-3)}{n} 2.Which of the following is true about Integral test for convergence of function f(x)?3.If [s_n] is the sequence of partial sums for a series \sum_{n=1}^{\infty}X_n of real numbers, then4.Find the limit of \sum_{n=1}^{\infty}e^n n! 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/403/2yjLDGmMvNZv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wOS2WIyxnpwJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/386/wOS2WIyxnpwJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc. Solved: Let f(x,y) = 1 be the mass density in the region R shown belowObtain:(a) the total mass,(b) the center of gravity,(c) moments of inertia I_x and I_y 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/386/wOS2WIyxnpwJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747319441074.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/CjJnK9k53CpC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/CjJnK9k53CpC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of real sequences. Solved: Prove that if x \geq 0 for all n \epsilon \mathbb{N} and \lim_{n\to\infty} \frac{x_{n+1}}{x_n} \ = L < 1,then {x_n} converges to 00 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/CjJnK9k53CpC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Xefe6pGrwz1B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/841/Xefe6pGrwz1B.jpg</video:thumbnail_loc>

            <video:title>Summary and practice questions</video:title>

            <video:description><![CDATA[
This lesson provides a comprehensive review of the mole concept, molar mass calculations, and the derivation of empirical and molecular formulae. You will solve integrated practice problems that combine these quantitative tools to ensure readiness for the subsequent course on reaction stoichiometry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/841/Xefe6pGrwz1B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jloPRXyIm4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/jloPRXyIm4.jpg</video:thumbnail_loc>

            <video:title>Charge pulse</video:title>

            <video:description><![CDATA[
A connected capacitor draws extra charge when a dielectric enters. How much additional charge flows from the battery to maintain constant voltage? We compute the charge pulse using capacitance scaling. Solved: A parallel-plate capacitor has plates of area 120\text{ cm}^2 separated by a 4.00\text{-mm} air gap. The capacitor is connected to a 150\text{-V} DC power supply. While the battery remains connected, a dielectric material with a dielectric constant of 5.00 is inserted to completely fill the space between the plates. Determine the magnitude of the additional charge that flows from the battery onto the capacitor plates. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/jloPRXyIm4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FTapa9oFYqH7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/FTapa9oFYqH7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: To loosen the cap of a peanut butter requires a moment about the z axis of 50 in . lb. If \vec{F_B} has the x, y and z direction cosines \frac{6}{11}, \frac{-9}{11} and \frac{2}{11} respectively and the forces \vec{F_A} and \vec{F_B} are a couple, determine the magnitude \vec{F_B} needed to loosen the cap. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/FTapa9oFYqH7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738865596211.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/3ftmIMHEgBwB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/3ftmIMHEgBwB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating the components of a force. Solved: The 500-lb force is to be resolved into two components acting along the axis of the struts AB and AC. If the component of force along AC is required to be 300 lb, directed from A to C, determine the magnitude of the force acting along AB and the angle \theta of the 500-lb force. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/3ftmIMHEgBwB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739467220249.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/bRW5MLjnoxBd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/323/bRW5MLjnoxBd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on the analysis of machines. Solved: Determine the couple moment M needed to create a force of F=200N on the slider block at C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/323/bRW5MLjnoxBd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739364194982.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/64cmX_s-p-jD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/64cmX_s-p-jD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (18)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: The rectangular plate is supported by hinges along its side BC and by the cable AE. If the cable tension is 300N, determine the projection onto line BC of the force exerted on the plate by the cable. Note that E is the mid-point of he horizontal upper edge of the structural support. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/64cmX_s-p-jD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739871520903.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/O6iLHcoKDXcv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/O6iLHcoKDXcv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: The rigid assembly which consist of light rods and two 1.2-kg spheres rotates freely about a vertical axis. The assembly is initially at rest and then a constant couple M=2N.m is applied for 5s. Determine the final angular velocity of the assembly. Treat the small spheres as particles. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/O6iLHcoKDXcv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749047306460.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/aeMsYu2pIMqQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/aeMsYu2pIMqQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: If a horizontal force P = 35 lb is applied to block, determine the acceleration of block B. Neglect friction. Block A weighs 15 lb and block B weighs 8 lb. Hint: Show that a_A = a_B tan 15^\circ. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/aeMsYu2pIMqQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742302266303.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/eo3vwP4MGCwU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/eo3vwP4MGCwU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: When \theta = 15^\circ, the car has a speed of 50 m/s which is increasing at 6m/s^2. Determine the angular velocity of the camera tracking the car at this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/eo3vwP4MGCwU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742222042168.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/aJMW_zGs4tTj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/421/aJMW_zGs4tTj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of problems involving dry friction - for rigid bodies. Solved: The car has a weight of 4000 lb and a center of gravity at G. If it pulls off the side of the road, determine the greatest angle of tilt \theta it can have without slipping or tripping over. the coefficient of static friction between its wheels and the ground is \mu_s = 0.4. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/421/aJMW_zGs4tTj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741107438467.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/2oZT6knlL22Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/2oZT6knlL22Z.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating power and efficiency of a machine by the principle of work and energy. Solved: The 50-Ib woman jogs up the flight of stairs in 5 seconds. Determine her average power output. Convert all given information to SI units and repeat your calculation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/2oZT6knlL22Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746950553339.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/UO3n8oNuxiK1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/UO3n8oNuxiK1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating power and efficiency of a machine by the principle of work and energy. Solved: The jeep has a weight of 2500Ib and an engine which transmits a power of 100hp to all the wheels. Assuming the wheels do not slip on the ground, determine the angle \theta of the largest incline the jeep can climb at a constant speed v=30ft/s . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/UO3n8oNuxiK1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746951727900.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/zO6qd0u1a-Ng</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/zO6qd0u1a-Ng.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 5-Ib packages ride on the surface of the conveyor belt. If the belt starts from rest and its speed increases to 2ft/s in 2s , determine the maximum angle \theta so that none of the packages slip on the inclined surface AB of the belt. The coefficient of static friction between the belt and a package is \mu_s=0.3 . At what angle \phi do the packages first begin to slip off the surface of the belt after the belt is moving at its constant speed of 2ft/s ? Neglect the size of the packages. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/zO6qd0u1a-Ng.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745662925481.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/qoMDcTM3m1ua</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/337/qoMDcTM3m1ua.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of frictional forces on thrust bearings - pivot (end) and collar bearings, disks. Solved: A 50-Ib electric floor polisher is operated on a surface for which the coefficient of kinetic friction is 0.25 . Assuming that the normal force per unit area between the disk and the floor is uniformly distributed, determine the magnitude Q of the horizontal forces required to prevent motion of the machine. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/337/qoMDcTM3m1ua.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746869247509.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/D6UnKiEpg3Yk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/613/D6UnKiEpg3Yk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
Worked examples on continuity of functions. Solved: Prove that if f is continuous at Land \lim_{x\to c}g(x)=L, then \lim_{x\to c} f(g(x))=f(L) 
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          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/613/D6UnKiEpg3Yk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2Ld4F72o5dbe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/543/2Ld4F72o5dbe.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on graphical analysis of erratic rectilinear motion problems. Solved: A retarding force acts on a particle moving initially with a velocity of 100m/s and gives it a deceleration as recorded by the oscilloscope record shown. Approximate the velocity of the particle at t=4s and t=8s . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/543/2Ld4F72o5dbe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746265740723.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WAHo2bM1zatY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nyhn0hHeuR/Thumbnails/1201/WAHo2bM1zatY.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Learn the organization of this learning track and how the NUC CCMAS syllabus maps to our modules. This lesson details the sequence of topics you will master to cover the complete curriculum.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nyhn0hHeuR/Previews/1201/WAHo2bM1zatY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dXtaqKvC0zCM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/543/dXtaqKvC0zCM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on graphical analysis of erratic rectilinear motion problems. Solved: A vacuum - propelled capsule for a high - speed tube transportation system of the future is being designed for operation between two stations A and B, which are 10km apart. If the acceleration and deceleration are to have a limiting magnitude of 0.6g and if velocities are to be limited to 400km/h , determine the minimum time t for the capsule to make the 10 - km trip. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/543/dXtaqKvC0zCM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746266398218.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/jd_zyFfeBVFe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/132/jd_zyFfeBVFe.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on Taylor and Maclaurin series expansion of differentiable functions. Solved: Obtain the Maclaurin series for \frac{1}{1-x} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/132/jd_zyFfeBVFe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m7u9Wf16UFgx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/m7u9Wf16UFgx.jpg</video:thumbnail_loc>

            <video:title>Limits transformation</video:title>

            <video:description><![CDATA[
Definite integrals demand new boundaries after substitution. How do you map x-limits to u-values for direct evaluation? This walkthrough transforms the limits to skip back-substitution. Solved: Evaluate the definite integral \int_{1}^{2} \frac{e^{1/x}}{x^{2}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/m7u9Wf16UFgx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xvSPuKze6PKa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/xvSPuKze6PKa.jpg</video:thumbnail_loc>

            <video:title>Trigonometric quotient</video:title>

            <video:description><![CDATA[
Trigonometric fractions demand precise simplification. How do you differentiate a reciprocal involving cosine and tidy up the result? Watch the method in action. Solved: Find the derivative of the function f(x) = \frac{1}{1 + \cos x}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/xvSPuKze6PKa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NiAWDTtHMe6N</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/NiAWDTtHMe6N.jpg</video:thumbnail_loc>

            <video:title>Nth derivative of a sum</video:title>

            <video:description><![CDATA[
Differentiating a sum is simple. How do you find the nth derivative of a polynomial series and evaluate it at a point? Watch the calculation. Solved: If f(x) = \sum_{n=0}^{12} \frac{x^n}{n!}, determine the numerical value of the 10th derivative f^{(10)}(2). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/NiAWDTtHMe6N.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TU9HVx5_EQnR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/564/TU9HVx5_EQnR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on identifying equivalence relations. Solved: Consider the relation R on \mathbb{N} defined by R = \{a R b \to a - b = 3k; a, b \epsilon \mathbb{N}, k \epsilon \mathbb{Z}\}. Show that R is an equivalence relation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/564/TU9HVx5_EQnR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ENE5insP1FxB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/557/ENE5insP1FxB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of systems of particles gaining or losing mass. Solved: At the instant of vertical launch, the rocket expels exhaust at the rate of 220kg/s with an exhaust velocity of 820m/s. If the initial vertical acceleration is 6.80m/s^2, calculate the total mass of the rocket and the fuel at launch. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/557/ENE5insP1FxB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1752747492501.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0b1UbrcFdkau</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/617/0b1UbrcFdkau.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
Worked examples on the proof of limits of functions. Solved: Prove that \lim_{x\to-1} \frac{x+1}{x^2-1}=\frac{-1}{2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/617/0b1UbrcFdkau.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ni6CH7xVxhg_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/402/ni6CH7xVxhg_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on sequences - 2023/2024 mid-semester examination questions. Solved: 1.Consider the following sequences : a_n=\frac{2n^2+3n^3}{3n^2+2n^3} , b_n= {[1+\frac{1}{n}]}^n , c_n=\sqrt(\frac{\sqrt2 +4n^3}{2n^2[2n+1]}) , n\in \mathbb{N} . Which of the following statements is true ?2.Consider the sequence [{d_n}]=[\frac{3n+2}{4-5n}] which of the following statements is false? 3.Consider the sequence: \frac{1}{2},4,\frac{1}{4},7,\frac{1}{8},10,... The 50th and 51st terms are, respectively4.Which of the following statements is not true about boundedness of sequences of real numbers? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/402/ni6CH7xVxhg_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TDtdW_cOx2Hk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/279/TDtdW_cOx2Hk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the method of Lagrange multiplier for examining stationary points of a function of two variables subject to a constraint. Solved: Find the maximum distance from the origin (0,0) to the curve 3x^2+3y^2+4xy-2=0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/279/TDtdW_cOx2Hk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fJzbnV-h2Srt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/89/fJzbnV-h2Srt.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on solution of first-order ordinary differential equations. Solved: Solve the following differential equations:\frac{dy}{dx} =\frac{2xy^2+x}{x^2y-y} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/89/fJzbnV-h2Srt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dHAtZzmoVA7f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/323/dHAtZzmoVA7f.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the analysis of machines. Solved: Arm ABC is connected by pins to a collar at B and to crank CD at C. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium when \theta=0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/323/dHAtZzmoVA7f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739364691767.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/kKfnFNYtd_Jr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/617/kKfnFNYtd_Jr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
Worked examples on the proof of limits of functions. Solved: Prove that \lim_{x\to0}x\sin(\frac{1}{x})=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/617/kKfnFNYtd_Jr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kLF7WfM7RkZH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/kLF7WfM7RkZH.jpg</video:thumbnail_loc>

            <video:title>Resolving vectors (1)</video:title>

            <video:description><![CDATA[
This is a problem-solving session focused on vector resolution. We will work through several examples, applying trigonometry to calculate the perpendicular components of vectors with different orientations. Solved: A displacement vector D has a magnitude of 10.0m and is directed at an angle of 30^\circ above the positive x-axis. Find its x- and y- components. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/kLF7WfM7RkZH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zQEOso_vw4VA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/zQEOso_vw4VA.jpg</video:thumbnail_loc>

            <video:title>Kinematics with calculus (2)</video:title>

            <video:description><![CDATA[
This example applies integration to 1D motion. We will integrate a known acceleration function to determine velocity, and then integrate velocity to determine position. Master this method. Solved: A particle's acceleration is given by a(t)=(6t-4)m/s^2. At time t=0, the particle is at x_o=5m and has an initial velocity v_o=-8m/s.(a) Find the particle's velocity v(t) as a function of time .(b) Find the particle's position x(t) as a function of time. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/zQEOso_vw4VA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PJkc3MhcF748</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/PJkc3MhcF748.jpg</video:thumbnail_loc>

            <video:title>Differentiating a position vector (1)</video:title>

            <video:description><![CDATA[
This is a practical, problem-solving lesson. Starting with a given position vector as a function of time, r(t), we will apply differentiation to derive the corresponding instantaneous velocity and acceleration vectors. Solved: The position of a particle is given by \vec{r}(t)=(3.0t^2-5.0)i+(2.0t^3+4.0t)j, where \vec{r} is in metres and t is in seconds, find 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/PJkc3MhcF748.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hNOOSvL5KH_m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/hNOOSvL5KH_m.jpg</video:thumbnail_loc>

            <video:title>Constant acceleration (2)</video:title>

            <video:description><![CDATA[
This second example reinforces the vector method for constant acceleration. We again apply the kinematic equations to independent x and y components. Master the application. Solved: A particle has an initial velocity \vec{v}_o=(4.0i)m/s and a constant acceleration \vec{a}=(2.0i+3.0j)m/s^2. It starts at the origin. At the instant the particle's x-coordinate is 12m, what is its y coordinate? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/hNOOSvL5KH_m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OEX0rcHiPZcc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/OEX0rcHiPZcc.jpg</video:thumbnail_loc>

            <video:title>Charle's law</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates precise application of Charles's Law to determine the change in gas volume or temperature at constant pressure. We detail the direct proportionality and the mandatory use of the absolute (Kelvin) temperature scale. Master this key volume-temperature relationship. Solved: A given chemical reaction produced 4.38\text{dm}^3 of \text{SO}_2 at 19^\circ\text{C} and 101\text{ kPa}. What would be the volume of \text{SO}_2 at 25^\circ\text{C} and 101\text{ kPa}? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/OEX0rcHiPZcc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8_OzlqD2_iPz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/8_OzlqD2_iPz.jpg</video:thumbnail_loc>

            <video:title>Synthetic preparations</video:title>

            <video:description><![CDATA[
Alkanes are synthesised through multiple distinct laboratory routes. How do you choose between hydrogenation, Wurtz coupling, Kolbe electrolysis, or Grignard hydrolysis for a specific target structure? This lesson maps each method to its reagents and limitations precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/8_OzlqD2_iPz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0QevUGnZF8Cj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/0QevUGnZF8Cj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: The mass of the bucket B is 180 kg. From t = 0 to t = 2 s, the x and y coordinates of the center of mass of the bucket are x = -0.2t^3 + 0.05t^2 +10 m,y = 0.1t^2 + 0.4t +6 m.Determine the x and y components of the force exerted on the bucket by its support at t = 1 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/0QevUGnZF8Cj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744042963057.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dUE9JntCmHYC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/dUE9JntCmHYC.jpg</video:thumbnail_loc>

            <video:title>Combined gas law</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates solving multi-variable gas system problems using the Combined Gas Law. We detail how to correctly isolate the unknown pressure, volume, or temperature variables. Master this essential technique for handling simultaneous changes in gas behaviour. Solved: A balloon contains 5.41\text{dm}^3 of helium at 24^\circ\text{C} and 101.5\text{ kPa}. Suppose the gas in the balloon is heated to 35^\circ\text{C} which causes the pressure to become 102.8\text{ kPa}. What is its new volume? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/dUE9JntCmHYC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ez50aMAIRv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/Ez50aMAIRv.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Start your calculus study by understanding the course goals and structure. This lesson sets the stage for mastering functions, limits, and continuity through direct and practical instruction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/Ez50aMAIRv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oIMELQUCgn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/oIMELQUCgn.jpg</video:thumbnail_loc>

            <video:title>Interval notation</video:title>

            <video:description><![CDATA[
Interval notation provides a concise way to describe sets of numbers on the real line. Master the use of brackets and parentheses to represent open, closed, and infinite sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/oIMELQUCgn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wvMTPyhn3k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/wvMTPyhn3k.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Master the coordinate system to plot graphs accurately. Use the x and y axes to identify patterns essential for engineering and science.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/wvMTPyhn3k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5otxiDZBNY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1104/5otxiDZBNY.jpg</video:thumbnail_loc>

            <video:title>Domain and range</video:title>

            <video:description><![CDATA[
The domain is the set of all valid inputs while the range is the resulting output set. This lesson explains how to find these values by looking for mathematical restrictions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1104/5otxiDZBNY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4MyVMu8dTu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/4MyVMu8dTu.jpg</video:thumbnail_loc>

            <video:title>Polynomials</video:title>

            <video:description><![CDATA[
Identify linear, quadratic, and cubic shapes by checking the highest power in the function. Use intercepts and turning points to sketch these curves accurately for technical work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/4MyVMu8dTu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dG82bBgeqY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/dG82bBgeqY.jpg</video:thumbnail_loc>

            <video:title>Trigonometric functions</video:title>

            <video:description><![CDATA[
Recognise the periodic repeating patterns of sine and cosine waves to sketch their shapes. Use amplitude and intercepts to plot these curves accurately on the axes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/dG82bBgeqY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iUaYIX58OWcD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/iUaYIX58OWcD.jpg</video:thumbnail_loc>

            <video:title>Buffer solutions (2)</video:title>

            <video:description><![CDATA[
This lesson covers advanced buffer calculations for both acidic and basic systems, including mixtures of nitrous acid with sodium nitrite and ammonia with ammonium chloride. You will use Ka and Kb values to determine the final pH through the Henderson-Hasselbalch equation. Master these multi-step worked examples to handle real-world buffer data. Solved: Question 2: Calculate the pH of a buffer solution that is 0.050 M \text{NH}*4\text{Cl}*{(aq)} and 0.040 M \text{NH}_{3(aq)}. Given that the K_b \text{ of NH}_3 = 1.8 \times 10^{-5} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/iUaYIX58OWcD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LiKoCTw6SER_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/LiKoCTw6SER_.jpg</video:thumbnail_loc>

            <video:title>Solution of weak acids (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the pH of a weak acid solution using the acid dissociation constant (Ka) and initial concentration. You will learn to set up an ICE table and apply the small x approximation to simplify the quadratic equation. Master these steps to solve for H+ ions. Solved: Calculate the pH and percentage dissociation in a solution containing 0.02M ethanoic acid, given that the acid dissociation constant is 1.8 \times 10^{-5}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/LiKoCTw6SER_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0rNNLkftIilw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1002/0rNNLkftIilw.jpg</video:thumbnail_loc>

            <video:title>Classifying numbers</video:title>

            <video:description><![CDATA[
Execute the systematic classification of values into natural, integer, rational, and irrational subsets through a rigorous problem walkthrough. You will master the mechanical identification of number types to ensure precise data stratification within the real number hierarchy. Solved: 1. Consider the following list of numbers:({-5, 0, \frac{2}{3}, \sqrt{7}, 4, \pi, \sqrt{-16}})Identify all the sets to which each number belongs from the following list:\mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{Q}', \mathbb{R}, \mathbb{C} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1002/0rNNLkftIilw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_W4Fby6Ldxov</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/_W4Fby6Ldxov.jpg</video:thumbnail_loc>

            <video:title>Bronsted-Lowry's definition</video:title>

            <video:description><![CDATA[
This lesson defines acids as proton donors and bases as proton acceptors. You will learn to identify conjugate acid-base pairs in reversible reactions and understand how this theory expands beyond aqueous solutions. Focus on the transfer of H+ ions to master this broader chemical definition.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/_W4Fby6Ldxov.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sx7rR8rsRpDb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/Sx7rR8rsRpDb.jpg</video:thumbnail_loc>

            <video:title>Buffer solutions (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the pH of an acidic buffer solution using the Henderson-Hasselbalch equation. You will learn to substitute molar concentrations of a weak acid and its salt to find the final pH. Master this calculation to predict the stability of buffered systems. Solved: Questions on buffer solutions (1) Calculate the pH of a buffer solution that is 0.15 M \text{HNO}_{2(aq)} and 0.20 M \text{NaNO}_{2(aq)} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/Sx7rR8rsRpDb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BAialAbYzg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1082/BAialAbYzg.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Organic reactions follow precise pathways rather than random chance. This course maps those mechanisms and the kinetics governing reaction speed across five core topics. We begin with this outline to show exactly what you will master.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1082/BAialAbYzg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kkzYSNpHQ4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/kkzYSNpHQ4.jpg</video:thumbnail_loc>

            <video:title>Composite functions</video:title>

            <video:description><![CDATA[
Learn how to combine two functions by using the output of one as the input for the other. You will master the notation and steps to solve these nested equations accurately. This lesson also explains how to determine the resulting domain for any composite relationship.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/kkzYSNpHQ4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Mey8hkdsPL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/Mey8hkdsPL.jpg</video:thumbnail_loc>

            <video:title>Quadratic vertex</video:title>

            <video:description><![CDATA[
Use the completing the square method or the vertex formula to find the turning point of a parabola. This walkthrough identifies the exact peak or trough of a quadratic curve. Solved: Find the coordinates of the turning point (vertex) for the parabola f(x) = x^2 - 16x + 60. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/Mey8hkdsPL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/obmArhaGrY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1106/obmArhaGrY.jpg</video:thumbnail_loc>

            <video:title>Inverse functions</video:title>

            <video:description><![CDATA[
Learn to reverse a function to find its original input from a given output. You will identify one-to-one functions using the horizontal line test and derive inverse formulas by swapping variables. This lesson also explains how the graph of an inverse reflects across the line y=x.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1106/obmArhaGrY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uN6xunqXYE9M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/uN6xunqXYE9M.jpg</video:thumbnail_loc>

            <video:title>Isolated conductor</video:title>

            <video:description><![CDATA[
Every conductor holds charge. How does a lone sphere store energy without a second plate? We define its inherent capacity using geometry and the reference at infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/uN6xunqXYE9M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7uvDif3N2ucb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/540/7uvDif3N2ucb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on composition of linear maps. Solved: Let T: \mathbb{R}^2 \to P_1 and S: P_1 \to P_2 be defined by T(a, b) = a + (a + b)x and S(p(x)) = x (p(x)). Find (S . T) (3, -2) and (S. T) (a, b). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/540/7uvDif3N2ucb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pfZ6VozwDpKI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/pfZ6VozwDpKI.jpg</video:thumbnail_loc>

            <video:title>Practice problems</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of diverse equilibrium scenarios through a series of rigorous practice problems. You will master the simultaneous application of Le Chateliers principle to concentration, pressure, and temperature stresses to ensure absolute predictive accuracy. Solved: 1. Consider the equilibrium involved in the oxidation of sulfur dioxide to sulfur trioxide: 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g), \Delta H^\circ < 0 What general temperature and pressure conditions would favor a maximum equilibrium yield of sulfur trioxide? Explain your reasoning. 2. What would you expect to be the effect of an increase of pressure on each of the following reactions? Would the pressure change cause the reaction to go to the right or left? a. N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) b. 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) c. CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g) d. H_2(g) + I_2(g) \rightleftharpoons 2HI(g) e. CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g) 3. A gaseous mixture containing 1.50 mmol of SO_2 and 0.75 mmol of O_2 is placed in a 1.00-L container and allowed to reach equilibrium at 700 K. For the reaction 2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g) the equilibrium constants are: K = 3.5 \times 10^2 at 700 K K = 1.2 \times 10^1 at 900 K 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/pfZ6VozwDpKI.mp4</video:content_loc>

          <video:duration>64</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MoSdjQzAXgXm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/989/MoSdjQzAXgXm.jpg</video:thumbnail_loc>

            <video:title>Stoichiometric relations (1)</video:title>

            <video:description><![CDATA[
Follow a step-by-step walkthrough to calculate equilibrium concentrations for the decomposition of phosphorus pentachloride into phosphorus trichloride and chlorine gas. You will master the transition from initial molar quantities and flask volume to final concentration values at 170 degrees Celsius. Solved: Examples: Phosphorus pentachloride gas, PCl_5(g), decomposes to phosphorus trichloride gas, PCl_3(g), and chlorine gas, Cl_2(g), at 170 ??C according to the equilibrium: PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) A chemist places 4.50 mol of phosphorus pentachloride gas into a 3.00 L sealed flask and heats it to 170 ??C. When equilibrium is reached, 0.600 mol of phosphorus trichloride gas is present. Calculate the equilibrium concentrations of PCl_5(g) and Cl_2(g). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/989/MoSdjQzAXgXm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v7_bhpWJaJ_a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/v7_bhpWJaJ_a.jpg</video:thumbnail_loc>

            <video:title>Charged conductors</video:title>

            <video:description><![CDATA[
Charged conductors maintain constant potential throughout their volume. Why is the internal electric field zero while the potential remains non-zero? We clarify this common trap and define the equilibrium state.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/v7_bhpWJaJ_a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lrX06L3nnpUH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/lrX06L3nnpUH.jpg</video:thumbnail_loc>

            <video:title>Buffer solutions (3)</video:title>

            <video:description><![CDATA[
This lesson covers advanced buffer problems, including calculating pH changes when a strong base like NaOH is added to an acetic acid system. You will compare these results to pH shifts in pure water to observe buffer capacity. Master these calculations to quantify how buffers resist change. Solved: A buffered solution contains 0.10M acetic acid (\text{CH}_3\text{COOH}) and 0.10M sodium acetate (\text{CH}_3\text{COONa}) (i) Calculate the pH of the solution (ii) Calculate change in pH when 0.010 mole of solid NaOH is added to 1.0 L of the buffered solution. Compare this pH change with the change that occurs when 0.010 mole of solid NaOH is added to 1.0 L of water 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/lrX06L3nnpUH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PVoKScKBy9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1082/PVoKScKBy9.jpg</video:thumbnail_loc>

            <video:title>Bond fission types</video:title>

            <video:description><![CDATA[
Bond fission determines whether a reaction produces radicals or ions. Does equal electron sharing create different intermediates than unequal splitting? This lesson distinguishes homolytic from heterolytic fission and defines the resulting carbocations and carbanions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1082/PVoKScKBy9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D6nbkLaaABLf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/D6nbkLaaABLf.jpg</video:thumbnail_loc>

            <video:title>Precipitation (1)</video:title>

            <video:description><![CDATA[
This worked example demonstrates the calculation of precipitate mass from known volumes and concentrations of aqueous reactants. You will apply stoichiometric ratios to identify the limiting reagent and determine the final product yield. Accuracy in this procedure is vital for analytical gravimetry. Solved: Example 1:What volume of 0.10M \text{Na}_3\text{PO}_4 is required to precipitate all the lead(II) ions from 150.0mL of 0.250M \text{Pb}(\text{NO}_3)_2? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/D6nbkLaaABLf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/h_TbAVBkReU8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/982/h_TbAVBkReU8.jpg</video:thumbnail_loc>

            <video:title>Change in oxidation state</video:title>

            <video:description><![CDATA[
This lesson precisely correlates changes in oxidation state with the process of oxidation and reduction. You will learn that an increase in oxidation state defines oxidation, while a decrease defines reduction. Correctly tracking these changes across a reaction is the necessary starting point for balancing all complex redox equations. Solved: \text{Balancing Redox Reactions by Change in Oxidation State Method}\text{MnO}_{2(s)} + \text{Al}_{(s)} \rightarrow \text{Mn}_{(s)} + \text{Al}_2\text{O}_{3(s)} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/982/h_TbAVBkReU8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wBPuRMO0Q_7s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/982/wBPuRMO0Q_7s.jpg</video:thumbnail_loc>

            <video:title>Acidic medium (1)</video:title>

            <video:description><![CDATA[
This lesson focuses specifically on balancing redox reactions under acidic conditions using the half-reaction method. You will learn the precise steps for balancing oxygen atoms using water and hydrogen atoms using H+. Mastering this protocol is vital for accurately quantifying reactions performed in acid solutions. Solved: \text{for example:}\text{Consider the reaction below in acid medium}\text{Cu}_{(s)} + \text{NO}_{3(aq)}^{-} \rightarrow \text{Cu}^{2+}_{(aq)} + \text{NO}_{(g)} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/982/wBPuRMO0Q_7s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/g8Xe3tEDAmyU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/g8Xe3tEDAmyU.jpg</video:thumbnail_loc>

            <video:title>Neutralisation (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to determine the mass of water produced and the concentration of excess ions when mixing nitric acid and potassium hydroxide solutions. You will identify the limiting reagent and perform stoichiometric calculations to quantify post-reaction solution properties. Solved: Example 2:In an experiment, 30.0mL of 0.240\text{M HNO}_3 and 56.0\text{cm}^3 of 0.330M KOH were mixed. Calculate the amount of water formed in the resulting reaction. Which is the concentration of hydrogen ions or hydroxide ions in excess after the completion of the reaction?? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/g8Xe3tEDAmyU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dZLTmO5iM4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/dZLTmO5iM4.jpg</video:thumbnail_loc>

            <video:title>One-sided limits</video:title>

            <video:description><![CDATA[
Evaluate how a function behaves as it approaches a point from the left or right side separately. You will master the notation for these one-sided trends and identify when they do not meet at the same value. This skill is vital for investigating jumps or gaps in complex graphs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/dZLTmO5iM4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tBNz7iuZon</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/tBNz7iuZon.jpg</video:thumbnail_loc>

            <video:title>Direct substitution</video:title>

            <video:description><![CDATA[
If a function is well-behaved at a point, find the limit by simply plugging the value into the expression. This is always the first method to try when evaluating any limit.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/tBNz7iuZon.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yO4w7d5xkq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/yO4w7d5xkq.jpg</video:thumbnail_loc>

            <video:title>Existence of limits</video:title>

            <video:description><![CDATA[
Determine if a two-sided limit exists by checking if the left-hand and right-hand limits meet at the same finite value. You will identify cases where limits fail to exist due to jump discontinuities, vertical asymptotes, or oscillating behaviour. This check is the final test for limit existence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/yO4w7d5xkq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/65Wkp5VRz3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/65Wkp5VRz3.jpg</video:thumbnail_loc>

            <video:title>Intuitive limit concept</video:title>

            <video:description><![CDATA[
What if a function breaks exactly at the coordinate you need to solve? We examine the nearby numbers to guess the hidden result before it arrives. The solution reveals itself once you track the approach from two directions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/65Wkp5VRz3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x_d9Wyb3mjAW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/970/x_d9Wyb3mjAW.jpg</video:thumbnail_loc>

            <video:title>Systems of units</video:title>

            <video:description><![CDATA[
This lesson establishes why a single, coherent system of units is non-negotiable for science. It introduces the International System of Units (SI) as the required global standard, highlighting its advantages over other historical or regional systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/970/x_d9Wyb3mjAW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3rKRCrHkzdR6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/3rKRCrHkzdR6.jpg</video:thumbnail_loc>

            <video:title>Simplifying logarithms (2)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for simplifying advanced logarithmic expressions involving fractional exponents and nested bases. You will learn to resolve terms where the logarithm appears as an index and apply the change of base formula to find exact values for non-standard expressions. Solved: 2. Find the exact value of e^{\log_{e^2} 16}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/3rKRCrHkzdR6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x2PgQ7ZRScjP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/x2PgQ7ZRScjP.jpg</video:thumbnail_loc>

            <video:title>Redox reaction (2)</video:title>

            <video:description><![CDATA[
This lesson provides a worked solution for determining the percentage composition of a mixture containing tin(II) oxide and tin(IV) oxide. You will apply redox titration data using potassium dichromate to calculate the mass of oxidisable SnO and derive the remaining percentage of SnO2. Solved: Example 2A sample is known to be a mixture of SnO and \text{SnO}_2. A portion of the mixture weighing 2.00g is dissolved in dilute acid and titrated with 0.150M \text{K}_2\text{Cr}_2\text{O}_7 solution, 18.5mL being required. What percentage of the mixture is \text{SnO}_2? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/x2PgQ7ZRScjP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tEgxauu7sbrF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1009/tEgxauu7sbrF.jpg</video:thumbnail_loc>

            <video:title>Deductions from the laws</video:title>

            <video:description><![CDATA[
This lesson examines identities derived from the primary laws, including the logarithm of unity, inverses, and reciprocal arguments. You will also learn to simplify complex terms where both the base and argument are raised to powers by applying the ratio of their exponents.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1009/tEgxauu7sbrF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vIPxZ0QvcQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/vIPxZ0QvcQ.jpg</video:thumbnail_loc>

            <video:title>Parallel-plate geometry</video:title>

            <video:description><![CDATA[
Calculate the capacitance of a real-world component given its physical dimensions. This walkthrough demonstrates how area and plate separation influence the total charge storage capacity. Solved: A parallel-plate capacitor is designed with a plate area A = 5.50 \text{ cm}^2 and a separation distance d = 2.50 \text{ mm}. (a) Determine the capacitance of this device. (b) If the capacitor is connected to a 15.0 \text{-V} DC source, calculate the magnitude of the charge stored on the positive plate. (c) Find the surface charge density on the plates and (d) the strength of the uniform electric field established between them. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/vIPxZ0QvcQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jCVDfH7TxHHF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/838/jCVDfH7TxHHF.jpg</video:thumbnail_loc>

            <video:title>Mole and molar mass</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates the accurate calculation of molar mass for various compounds and shows its application as the essential factor for all mass-to-mole conversions. Solved: Illustration:Consider the following gas samples: 4.0 g of hydrogen gas, 4.0 g of helium gas, 1.0 mol of fluorine gas, 44.0 g of carbon dioxide gas, and 146 g of sulfur hexafluoride gas. Arrange the gas samples in order of increasing number of total atoms present. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/838/jCVDfH7TxHHF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5aGWjNJxVD5t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/5aGWjNJxVD5t.jpg</video:thumbnail_loc>

            <video:title>Chemical formulae (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates using partial percentage composition and the overall molecular mass to determine the unknown coefficient of an element in a complex molecular formula. Solved: An amino acid with the formula C_aH_bN_xO_2 contains 41.3% C and 8.1% H. Determine x from this information, given that [M_w = 174, C=12, H=1, N=14, O=16] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/5aGWjNJxVD5t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SUyNbay86m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1082/SUyNbay86m.jpg</video:thumbnail_loc>

            <video:title>Stability trends</video:title>

            <video:description><![CDATA[
Carbocations and carbanions follow opposite stability orders based on alkyl substitution. Why does adding carbon groups stabilise a positive charge but destabilise a negative one? This lesson explains the reversed trends for methyl, primary, secondary, and tertiary intermediates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1082/SUyNbay86m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cpvjfS2VkHP_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/cpvjfS2VkHP_.jpg</video:thumbnail_loc>

            <video:title>Reciprocal derivative</video:title>

            <video:description><![CDATA[
Spot a fraction where the top is the derivative of the bottom. Why waste time on full substitution when the answer hides in plain sight? This lesson shows you how to write the log result instantly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/cpvjfS2VkHP_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nsmHD_SRy_1o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/984/nsmHD_SRy_1o.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates advanced dilution calculations, including determining the resulting molarity when mixing multiple solutions. You will resolve complex problems where both volume and solute amounts change across different components. Accurate execution of these multi-step solutions is critical for industrial reagent mixing. Solved: What is the strength of a solution prepared by mixing a 0.250 \text{ dm}^3 of 0.35M NaOH with 0.150 \text{ dm}^3 of 0.45M NaOH? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/984/nsmHD_SRy_1o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e_2IB7Tl7vL0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/843/e_2IB7Tl7vL0.jpg</video:thumbnail_loc>

            <video:title>Inspection</video:title>

            <video:description><![CDATA[
This lesson provides the precise, step-by-step methodology for balancing chemical equations by inspection. You will learn how to adjust stoichiometric coefficients to enforce the conservation of mass principle across synthesis, decomposition, and displacement reactions. Mastering this foundational skill is mandatory for all subsequent stoichiometric calculations. Solved: Example: Balance the equation for the combustion of ethanol 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/843/e_2IB7Tl7vL0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vdEegxKhYC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/vdEegxKhYC.jpg</video:thumbnail_loc>

            <video:title>Factorisation (1)</video:title>

            <video:description><![CDATA[
Direct substitution gives 0/0—now what? See how factorisation resolves the undefined form to reveal the limit's actual value. Solved: Evaluate \lim_{x \to -6} \frac{x^2 - 36}{x + 6}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/vdEegxKhYC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6CpctWV3cUOw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/984/6CpctWV3cUOw.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
This lesson provides structured walkthroughs for applying the dilution equation to stock solution preparation. You will calculate required volumes and final concentrations through multiple practical scenarios. Mastery of these calculations is essential for accurate reagent formulation. Solved: Illustration:How would you prepare a 500 \text{cm}^3 of 1.0M HCl from a commercial reagent that is 35% HCl with a specific gravity of 1.18? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/984/6CpctWV3cUOw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qum4SpJqjrN9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/983/qum4SpJqjrN9.jpg</video:thumbnail_loc>

            <video:title>More worked examples</video:title>

            <video:description><![CDATA[
This lesson provides integrated worked examples to reinforce the interconversion between molarity and mass concentration. You will solve multi-step problems requiring precise substance amount calculations from given volumes and masses. Mastery of these examples ensures computational accuracy for subsequent titration protocols. Solved: * Calculate the molar concentration of 9.25g of sulfuric acid in 750 \text{cm}^3 of solution 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/983/qum4SpJqjrN9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yIOMEpmwmB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/yIOMEpmwmB.jpg</video:thumbnail_loc>

            <video:title>Special trigonometric limits</video:title>

            <video:description><![CDATA[
What happens when trigonometric functions shrink toward 0/0 and block your working? A fixed value waits inside the undefined gap. Watch how we isolate it without guesswork.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/yIOMEpmwmB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NFQlvoyYPQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/NFQlvoyYPQ.jpg</video:thumbnail_loc>

            <video:title>Rationalisation</video:title>

            <video:description><![CDATA[
Roots block your working and leave an indeterminate form. What if a single algebraic flip wipes out the blockage? Watch how we clear the fraction and expose the exact limit.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/NFQlvoyYPQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tSmp4YWhRT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/tSmp4YWhRT.jpg</video:thumbnail_loc>

            <video:title>Factorisation</video:title>

            <video:description><![CDATA[
Direct substitution fails and leaves zero in the numerator and the denominator. What if splitting the expression cancels the fault and reveals the true value? Watch how we clear the blockage to find the answer.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/tSmp4YWhRT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iaulVMN5y5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/iaulVMN5y5.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity</video:title>

            <video:description><![CDATA[
Investigate how functions behave as the input grows without bound. You will learn to compare the degrees of polynomials to determine if a limit is zero, a constant, or infinite.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/iaulVMN5y5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U9_Cn8D2GSp7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/U9_Cn8D2GSp7.jpg</video:thumbnail_loc>

            <video:title>Precipitation (2)</video:title>

            <video:description><![CDATA[
This advanced worked example focuses on determining the concentration of ions remaining in solution after a precipitation reaction. You will calculate the moles of excess reactant and the final solution volume to find the residual molarity. Solved: Example 2:What mass of silver chloride will be precipitated from the reaction of 100.0mL of 0.20M silver nitrate with 100.0mL of 0.15M calcium chloride? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/U9_Cn8D2GSp7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a3BFwyahHokn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/853/a3BFwyahHokn.jpg</video:thumbnail_loc>

            <video:title>Effect of catalysts</video:title>

            <video:description><![CDATA[
Analyse why catalysts increase reaction rates without altering the equilibrium position or the equilibrium constant. You will master the mechanical distinction between kinetic acceleration and thermodynamic stability to ensure precise predictions of system behaviour.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/853/a3BFwyahHokn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mTDLr_uqoqbY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/mTDLr_uqoqbY.jpg</video:thumbnail_loc>

            <video:title>Calculating solubility product (1)</video:title>

            <video:description><![CDATA[
This lesson provides a step-by-step walkthrough for calculating the solubility product constant from a given molar solubility. You will learn to write the dissolution equation for silver chloride and correctly apply the stoichiometry of its ions to determine the Ksp value. Solved: For illustration:The molar solubility of AgCl in water at 25??C is 1.3 \times 10^{-5} \text{ mol L}^{-1}.i. Write the dissolution equilibriumii. Calculate the value of K_{sp} at this temperature 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/mTDLr_uqoqbY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/t1KNBjQpoJQ2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/t1KNBjQpoJQ2.jpg</video:thumbnail_loc>

            <video:title>Calculating solubility product (2)</video:title>

            <video:description><![CDATA[
This lesson covers advanced Ksp calculations for salts with multiple ions like calcium fluoride. You will learn how to handle stoichiometric coefficients when converting molar solubility into a solubility product constant and solve for unknown ion concentrations at 25??C. Solved: Example 2:The molar solubility of \text{CaF}_2 @ 25??C is 2.0 \times 10^{-4} \text{ mol L}^{-1}.Calculate K{sp}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/t1KNBjQpoJQ2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f24ssxpfAJjj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/f24ssxpfAJjj.jpg</video:thumbnail_loc>

            <video:title>Calculating solubility product (3)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the solubility product constant for complex salts like aluminium sulphide. You will learn to correctly apply the powers and stoichiometric ratios in the Ksp expression when dealing with multiple cations and anions in a saturated solution. Solved: Example 3:The molar solubility of \text{Al}_2\text{S}_3 in water at a given temperature is 1.5 \times 10^{-6} \text{ mol L}^{-1}. Determine the value of K{sp} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/f24ssxpfAJjj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pmYKtU_QzvWM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/pmYKtU_QzvWM.jpg</video:thumbnail_loc>

            <video:title>Back-titration</video:title>

            <video:description><![CDATA[
This lesson provides a worked solution for determining the concentration of a sulphuric acid sample by titrating excess hydroxide ions with hydrochloric acid. You will master the two-stage calculation protocol required to resolve unknown concentrations in complex back-titration scenarios. Solved: Example 4:A 0.500L sample of \text{H}_2\text{SO}_4 solution was analyzed by taking a 100.0mL aliquot and adding 50.0mL of 0.213M NaOH. After the reaction occurred, an excess hydroxide ions remained in the solution. The excess base required 13.21mL of 0.103M HCl for neutralization. Calculate the molarity of the original sample of \text{H}_2\text{SO}_4 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/pmYKtU_QzvWM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m9Pt94FhhB36</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9RUraQiImy/Thumbnails/985/m9Pt94FhhB36.jpg</video:thumbnail_loc>

            <video:title>Neutralisation (1)</video:title>

            <video:description><![CDATA[
This lesson provides a worked solution for determining the volume of 0.200M hydrochloric acid required to neutralise 25.0mL of 0.50M sodium hydroxide. You will apply the 1-to-1 stoichiometric ratio to calculate exact equivalence. Solved: For example:What volume of a 0.200M HCl is needed to neutralize 25.0mL of a 0.50M NaOH solution? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9RUraQiImy/Previews/985/m9Pt94FhhB36.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DWibcToxVx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/DWibcToxVx.jpg</video:thumbnail_loc>

            <video:title>Continuity at points</video:title>

            <video:description><![CDATA[
Continuity ensures a graph stays unbroken at a fixed input. Which three conditions must match to prove a smooth connection at that exact point? Watch the lesson to apply the full test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/DWibcToxVx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vkxomlB40yPa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/vkxomlB40yPa.jpg</video:thumbnail_loc>

            <video:title>Solving equations with unknown index (6)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving non-linear simultaneous equations where variables appear as exponents. You will learn to linearise these systems using logarithms to solve for multiple unknowns across different bases efficiently. Solved: 6. Solve the simultaneous equations 2^{x+y} = 63^{x-y} = 4. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/vkxomlB40yPa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8vFMjhX88g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/8vFMjhX88g.jpg</video:thumbnail_loc>

            <video:title>Continuity on intervals</video:title>

            <video:description><![CDATA[
A smooth graph must stay unbroken across an entire stretch, not just at single points. How do you verify the endpoints when one-sided limits replace standard limits? Watch the lesson to apply the interval test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/8vFMjhX88g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CNtmbtoDHzcC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1011/CNtmbtoDHzcC.jpg</video:thumbnail_loc>

            <video:title>Solving equations with unknown index (5)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for solving simultaneous equations with unknown indices and resolving exponential forms that reduce to quadratics through substitution. You will learn to manage multiple variables and apply advanced algebraic shifts to isolate unknowns in complex systems. Solved: 5. Solve for x if7^{4x+2} = 9^{3x-1} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1011/CNtmbtoDHzcC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gGqxT6q1kwEd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/979/gGqxT6q1kwEd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
This lesson applies de Broglie???s relation to particles of different masses. It reinforces how momentum determines wavelength and links microscopic motion to quantum behaviour. Solved: Questions for illustration1. Neutron diffraction is used in determining the structures of molecules.a. Calculate the de Broglie wavelength of a neutron moving at 1.00% of the speed of light.b. Calculate the velocity of a neutron with a wavelength of 75 pm (1 \text{ pm} = 10^{-12} \text{ m}).2. An atom of a particular element is traveling at 1% of the speed of light. The de Broglie wavelength is found to be 3.31 \times 10^{-3} \text{ pm}. Which element is this?These questions were copied from Chemical Principles by Steven R. Zumdahl and Donald J. DeCoste Chapter 12, Questions 35 and 37 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/979/gGqxT6q1kwEd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sVFM2jZOqtKT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/sVFM2jZOqtKT.jpg</video:thumbnail_loc>

            <video:title>Constant scaling</video:title>

            <video:description><![CDATA[
Spot a fraction where the top is a scaled version of the derivative. How do you balance the constant to get the log result? This walkthrough shows you how to adjust by sight. Solved: Find \int \frac{x}{x^{2} + 10} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/sVFM2jZOqtKT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/09Xy9qXVT2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/09Xy9qXVT2.jpg</video:thumbnail_loc>

            <video:title>Types of discontinuity</video:title>

            <video:description><![CDATA[
Discontinuity tears a smooth graph into isolated sections. How do you spot removable and non-removable discontinuities without plotting? Watch the video to classify each case correctly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/09Xy9qXVT2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SFwdf8b_nFCv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/SFwdf8b_nFCv.jpg</video:thumbnail_loc>

            <video:title>Direct log jump</video:title>

            <video:description><![CDATA[
Spot a fraction where the top is the derivative of the bottom. Why write out substitution when the log answer is instant? This walkthrough shows you how to solve it by sight. Solved: Determine\int \frac{2x + 5}{x^{2} + 5x + 1} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/SFwdf8b_nFCv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FzkjtDBxDCZo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/997/FzkjtDBxDCZo.jpg</video:thumbnail_loc>

            <video:title>Illustrations</video:title>

            <video:description><![CDATA[
Execute a rigorous walkthrough of constructing Cartesian products using numerical and symbolic sets. You will master the systematic generation of ordered pairs and the verification of product cardinalities, establishing the precise mapping techniques required for defining complex mathematical relations. Solved: 1. Given A ={x \in \mathbb{Z} : 1 \le x \le 4},B = {y \in \mathbb{Z} : 2 < y \le 5},obtain B \times A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/997/FzkjtDBxDCZo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fMeYh0CpeNv3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/972/fMeYh0CpeNv3.jpg</video:thumbnail_loc>

            <video:title>Dimensional homogeneity (1)</video:title>

            <video:description><![CDATA[
A worked example applying the principle of dimensional homogeneity. We will test the dimensional validity of common physical formulae, identifying both correct and incorrect equations. This is the core application of dimensional analysis. Solved: 2. Suppose that two quantities A and B have different dimensions. Which of the following arithmetic operations would NOT be physically meaningful?A + BA / BABB-A 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/972/fMeYh0CpeNv3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZpDCuasvgWdS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/ZpDCuasvgWdS.jpg</video:thumbnail_loc>

            <video:title>Algebra of sets (2)</video:title>

            <video:description><![CDATA[
Verify advanced set identities by mapping three-set algebraic expressions to their geometric counterparts. You will isolate nested regions to prove complex equalities visually, establishing the rigorous spatial logic required to validate sophisticated analytical arguments. Solved: 4. Simplify (A \cup B) \cap (A \cup B') using Venn diagrams. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/ZpDCuasvgWdS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ad6_DLBRGcfA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/970/ad6_DLBRGcfA.jpg</video:thumbnail_loc>

            <video:title>Fundamental and derived quantities</video:title>

            <video:description><![CDATA[
This lesson defines the critical distinction between fundamental and derived quantities. We establish that all measurable properties are either defined independently or are constructed from a small set of base quantities. This hierarchy is the foundation of the SI system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/970/ad6_DLBRGcfA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_Tk7dmCZ97OO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/972/_Tk7dmCZ97OO.jpg</video:thumbnail_loc>

            <video:title>Finding dimensions</video:title>

            <video:description><![CDATA[
This is a practical, problem-solving session. We will systematically derive the dimensional formulae for a set of key physical quantities, such as force, energy, and pressure. Mastery of this methodical process is required before proceeding to the next topic. Solved: 1. Obtain the dimension of each of the following quantities:a. Densityb. Workc. Powerd. Acceleration 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/972/_Tk7dmCZ97OO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7X2CcUZid8DI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/7X2CcUZid8DI.jpg</video:thumbnail_loc>

            <video:title>Finding angle between vectors</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates calculating the angle between two vectors. We apply the definition of the scalar product. Master this standard procedure. Solved: 6. Calculate the angle between the two vectors \vec{a} = 3.0\underline{i} + 3.0\underline{j} + 3.0\underline{k} and \vec{b} = 2.0\underline{i} + 1.0\underline{j} + 3.0\underline{k}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/7X2CcUZid8DI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RbXm_oGzVVPH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1397/RbXm_oGzVVPH.jpg</video:thumbnail_loc>

            <video:title>Isomerism</video:title>

            <video:description><![CDATA[
Alkenes exhibit both structural and geometrical isomerism due to their rigid double bond. How do you distinguish positional isomers from cis-trans forms when the carbon skeleton stays identical? This lesson defines both types and links restricted rotation to spatial arrangement precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1397/RbXm_oGzVVPH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j6D9wRoFem</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1110/j6D9wRoFem.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
Review the entire course from function definitions to continuity proofs. This summary reinforces the key procedural steps and concepts needed for advanced undergraduate mathematics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1110/j6D9wRoFem.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R_2uN2jqVh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/R_2uN2jqVh.jpg</video:thumbnail_loc>

            <video:title>Intermediate Value Theorem</video:title>

            <video:description><![CDATA[
Use the Intermediate Value Theorem to prove that a function crosses a certain value within an interval. This walkthrough shows how sign changes indicate the presence of a root. Solved: Prove that the equation x^3 - 2x - 5 = 0 has at least one real root in the interval [2, 3]. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/R_2uN2jqVh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YHe7vZjcS0di</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/YHe7vZjcS0di.jpg</video:thumbnail_loc>

            <video:title>Standard projectiles (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates the systematic solution to another standard ground-to-ground projectile problem. We resolve the initial velocity into components and use the derived trajectory equations to calculate the maximum height and horizontal range. Solved: 2. A projectile is fired with a speed of 50.0 \text{ m/s} at an angle of 60.0^\circ above the horizontal. Determine the magnitude and direction of its velocity vector 2.0\text{s} after launch. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/YHe7vZjcS0di.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WfBxOOxUJKQa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/WfBxOOxUJKQa.jpg</video:thumbnail_loc>

            <video:title>General projectiles (1)</video:title>

            <video:description><![CDATA[
This lesson covers the general case of a projectile launched at an angle from an elevated position. As the motion is asymmetric, standard range formulas do not apply. We rigorously apply the component kinematic equations to determine the time of flight and impact parameters. Solved: 5. A stone is thrown from the top of a building with an initial velocity of 20.0 \text{ m/s} at an angle of 30.0^\circ above the horizontal. The building is 45.0\text{m} high. How long does it take for the stone to reach the ground? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/WfBxOOxUJKQa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qOdYZdxoCPlG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/977/qOdYZdxoCPlG.jpg</video:thumbnail_loc>

            <video:title>Relative velocity (2)</video:title>

            <video:description><![CDATA[
This worked example calculates the velocity of a boat moving across a flowing river relative to the bank. You will apply vector addition to perpendicular velocity components to determine the resultant magnitude and direction. Mastery of this two-dimensional analysis is critical for navigation. Solved: 2. A boat heads due North across a river with a speed of 10.0\text{ m/s} relative to the water. The river flows due East at 5.0\text{ m/s} relative to the bank. What is the velocity of the boat relative to the bank? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/977/qOdYZdxoCPlG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ial8FFuyHltp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/ial8FFuyHltp.jpg</video:thumbnail_loc>

            <video:title>Horizontal projectiles (1)</video:title>

            <video:description><![CDATA[
We analyse the specific case of a projectile launched horizontally from a height. With an initial vertical velocity of zero, the vertical analysis simplifies to free fall. We calculate the time of flight based solely on the drop height and determine the final horizontal displacement. Solved: 3. A rescue plane is flying horizontally at a speed of 40.0 \text{ m/s} at a height of 100\text{m} above the ground. It drops a relief package. How far horizontally from the release point does the package strike the ground? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/ial8FFuyHltp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fdjCfVvETZhc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/fdjCfVvETZhc.jpg</video:thumbnail_loc>

            <video:title>Motion parameters (3)</video:title>

            <video:description><![CDATA[
This comprehensive worked example involves calculating the centripetal acceleration and speed for a satellite in orbit. We will use the orbital period and the sum of the Earth's radius and altitude to find the velocity and subsequent acceleration of the satellite. Solving this real-world application problem confirms your ability to apply circular motion principles. Solved: 3. An Earth satellite moves in a circular orbit 640 km above Earth's surface with a period of 98.0 min. What are(a) the speed, and(b) the magnitude of the centripetal acceleration.[Take R_{e} = 6371 \text{ km}] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/fdjCfVvETZhc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N_SFBsKwmiGD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/N_SFBsKwmiGD.jpg</video:thumbnail_loc>

            <video:title>Simplifying surds (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to simplify complex surds by combining multiple roots and reducing large values. You will learn to apply multiplication and division properties to condense expressions into their most efficient and accurate forms. Solved: 2. Find a and b if 2 + 5\sqrt{3} = 6 + a + (3 + b)\sqrt{12}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/N_SFBsKwmiGD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NCHWhS3DEbeU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/NCHWhS3DEbeU.jpg</video:thumbnail_loc>

            <video:title>Rationalising denominators (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates rationalising denominators with compound surds by multiplying both parts of the fraction by the conjugate. You will learn to eliminate radicals from complex denominators to reach a simplified, rational result. Solved: 4. Simplify \frac{6}{4 + \sqrt{10}}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/NCHWhS3DEbeU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TvIqGx_HJWfa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/TvIqGx_HJWfa.jpg</video:thumbnail_loc>

            <video:title>Free-body diagrams (1)</video:title>

            <video:description><![CDATA[
Master the construction of free-body diagrams by isolating a body from its environment and representing all external force vectors acting upon it. This lesson focuses on the mechanical resolution of weight and normal force for a crate positioned on an inclined plane. Solved: 1. A 15.0\text{-kg} crate is held stationary on a frictionless ramp by a rope attached parallel to the incline. The ramp is at angle 25.0^\circ above the horizontal. Construct the free-body diagram for the crate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/TvIqGx_HJWfa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VdYmy2ikXh4A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/917/VdYmy2ikXh4A.jpg</video:thumbnail_loc>

            <video:title>Free-body diagrams (2)</video:title>

            <video:description><![CDATA[
Execute the systematic construction of free-body diagrams for a pulley-coupled system through a rigorous problem walkthrough. You will master the simultaneous isolation of multiple bodies and the mapping of internal tension vectors to ensure accurate force resolution. Solved: 2. Block A sits on a frictionless horizontal table. It is connected by a massless string over a frictionless pulley to block B, which hangs freely over the edge. The system is released and begins to accelerate. Construct the free-body diagram for both blocks. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/917/VdYmy2ikXh4A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sfYoq_OGFHn8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/918/sfYoq_OGFHn8.jpg</video:thumbnail_loc>

            <video:title>Terminal velocity</video:title>

            <video:description><![CDATA[
Execute the systematic calculation of terminal velocity by balancing gravitational force against fluid drag. You will master the mechanical resolution of zero net acceleration states to determine the constant velocity limit for objects falling through resistive media. Solved: 2. A skydiver with a mass of m = 80\text{ kg} is falling through the air. The density of air is \rho = 1.2\text{ kg/m}^3. Calculate his terminal velocity when(a) he falls belly-down with effective cross-sectional area A = 0.70\text{ m}^2, and the drag coefficient is C = 0.50.(b) he deploys a parachute, with effective cross-sectional area A = 45\text{ m}^2, and the drag coefficient changes to C = 1.50 (since parachutes are designed to capture air). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/918/sfYoq_OGFHn8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vK_yyFKjdmo_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/vK_yyFKjdmo_.jpg</video:thumbnail_loc>

            <video:title>Sub-atomic particles</video:title>

            <video:description><![CDATA[
This is a worked example lesson applying the properties of sub-atomic particles to solve for atomic composition. We will calculate the number of protons, neutrons, and electrons for any given atom or ion. Solved: Questions to illustrate sub-atomic particles(1) How many protons, neutrons, and electrons are in each of the following atoms or ions?a. ^{24}_{12}\text{Mg}d. ^{59}_{27}\text{Co}^{3+}g. ^{79}_{34}\text{Se}^{2-}b. ^{24}_{12}\text{Mg}^{2+}e. ^{59}_{27}\text{Co}h. ^{63}_{28}\text{Ni}c. ^{59}_{27}\text{Co}^{2+}f. ^{79}_{34}\text{Se}i. ^{59}_{28}\text{Ni}^{2+}(2) What is the symbol for an ion with 63 protons, 60 electrons, and 88 neutrons? If an ion contains 50 protons, 68 neutrons, and 48 electrons, what is its symbol?These questions were copied from Chemical Principles by Steven S. Zumdahl and Donald J. DeCoste 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/vK_yyFKjdmo_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kAvD1Wv8zKkH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/kAvD1Wv8zKkH.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions</video:title>

            <video:description><![CDATA[
Piecewise functions use different rules for specific intervals on the x-axis. Sketch each segment only within its domain and Mark whether endpoints are included or excluded.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/kAvD1Wv8zKkH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/04KNdw_sxmNL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/04KNdw_sxmNL.jpg</video:thumbnail_loc>

            <video:title>Simplifying surds (1)</video:title>

            <video:description><![CDATA[
Learn to simplify surds by extracting the largest perfect square factor from under the radical. This walkthrough demonstrates how to reduce complex roots into their simplest basic forms for easier calculation. Solved: 1. Simplify \sqrt{12} \times \sqrt{18}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/04KNdw_sxmNL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l1OK5KxzbuRc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/l1OK5KxzbuRc.jpg</video:thumbnail_loc>

            <video:title>Roots of compound surds (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step process of finding the square root of a compound surd by equating it to a binomial expression. You will learn to form and solve simultaneous equations to resolve nested radicals into their simplest, separate forms. Solved: 7. Find the square root of 7 + \sqrt{40}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/l1OK5KxzbuRc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wa9W5L2KU6sa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/Wa9W5L2KU6sa.jpg</video:thumbnail_loc>

            <video:title>Roots of compound surds (2)</video:title>

            <video:description><![CDATA[
This walkthrough provides further practice on finding square roots of compound surds using algebraic substitution. You will learn to handle more complex nested radicals by setting up and solving equations to extract the separate rational and irrational components accurately. Solved: 8. Find the square root of 11 - 4\sqrt{6}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/Wa9W5L2KU6sa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cFdilpH15oZw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1026/cFdilpH15oZw.jpg</video:thumbnail_loc>

            <video:title>Proving fractional series (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step induction proof for a series with product denominators. You will learn to manipulate the algebraic sum using the inductive hypothesis and common denominators to reach the final goal. Solved: 1. Show that \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \dots + \frac{1}{n(n+1)} = \frac{n}{n+1} for all natural numbers n. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1026/cFdilpH15oZw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1VX6XQaeUKn8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1025/1VX6XQaeUKn8.jpg</video:thumbnail_loc>

            <video:title>Proving series (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the formal proof for the sum of the first n natural numbers. You will learn to verify the base case for n equals one and use the inductive hypothesis to prove the general formula through algebraic addition. Solved: 1. Prove by mathematical induction that 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2} for all natural numbers n \ge 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1025/1VX6XQaeUKn8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7vZli7Jh4lH4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1020/7vZli7Jh4lH4.jpg</video:thumbnail_loc>

            <video:title>Rationalising denominators (4)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates rationalising denominators that contain cube roots by applying the sum or difference of cubes identities. You will learn how to determine the correct quadratic-style conjugate needed to eliminate cubic radicals and convert the denominator into a rational integer.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1020/7vZli7Jh4lH4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QU9oz_yZRcDR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/QU9oz_yZRcDR.jpg</video:thumbnail_loc>

            <video:title>Proving bijections</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for proving a function is bijective by showing it is both injective and surjective. You will learn the formal algebraic steps to verify one-to-one and onto properties to confirm a perfect correspondence. Solved: 5. Prove that the function f: \mathbb{R} \to \mathbb{R} defined by f(x) = 2x + 7 is a bijection. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/QU9oz_yZRcDR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zt6v_nGCTont</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1105/zt6v_nGCTont.jpg</video:thumbnail_loc>

            <video:title>Piecewise jumps</video:title>

            <video:description><![CDATA[
Solve a piecewise function problem with a sudden jump. Plot segments and find where the graph breaks. Use this walkthrough to master sketching gaps in functions. Solved: Sketch the graph of the piecewise function p(x) = \begin{cases} x, & x < 0 \\ x+8, & x \ge 0 \end{cases} and determine the magnitude of the "jump" at the origin. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1105/zt6v_nGCTont.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mGtrHukb_Z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/mGtrHukb_Z.jpg</video:thumbnail_loc>

            <video:title>Rational function</video:title>

            <video:description><![CDATA[
Rational functions need the quotient rule. How do you differentiate a fraction with polynomials on top and bottom? See the solution step by step. Solved: If y = \frac{x^2 + 4}{x^2 + 1}, obtain an expression for \frac{dy}{dx}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/mGtrHukb_Z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DMFIN_O_Pq_4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/DMFIN_O_Pq_4.jpg</video:thumbnail_loc>

            <video:title>Composite functions</video:title>

            <video:description><![CDATA[
This walkthrough shows you how to solve composite function problems by substituting one formula into another. You will learn the correct order of operations to find final expressions and values for nested mappings. Solved: 3. If f(x) = x^2 - 2x - 3 and g(x) = x + 1, find the composite function (f \circ g)(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/DMFIN_O_Pq_4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C8KEnRHYy3Ej</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1027/C8KEnRHYy3Ej.jpg</video:thumbnail_loc>

            <video:title>Proving divisibility (1)</video:title>

            <video:description><![CDATA[
This walkthrough proves that n cubed plus 2n is divisible by 3 for all positive integers. You will learn to substitute the inductive hypothesis and factorise the resulting expression to show it remains a multiple of 3 for n equals k plus one. Solved: 1. Prove that n^3 + 2n is divisible by 3, for all positive integers n. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1027/C8KEnRHYy3Ej.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KQ9Kp_M2Ozc5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/KQ9Kp_M2Ozc5.jpg</video:thumbnail_loc>

            <video:title>Inverse functions</video:title>

            <video:description><![CDATA[
This lesson demonstrates the step-by-step process of finding the inverse of a function by rearranging algebraic formulas. You will learn to swap variables and solve for the new subject to reverse any one-to-one mapping. Solved: 4. Find the inverse function f^{-1}(x) given that f(x) = \frac{3x-1}{x+2}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/KQ9Kp_M2Ozc5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2uW7RRenjdsx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/2uW7RRenjdsx.jpg</video:thumbnail_loc>

            <video:title>Algebraic operations</video:title>

            <video:description><![CDATA[
This lesson provides a practical walkthrough for adding, subtracting, multiplying, and dividing functions using algebraic rules. You will learn to simplify resultant expressions and accurately determine their new domains through step-by-step calculations. Solved: 2. Given f(x) = x^2 - 2x - 3 and g(x) = x + 1, find the expressions for(i) (f+g)(x),(ii) (f \cdot g)(x),(iii) \left(\frac{f}{g}\right)(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/2uW7RRenjdsx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mZDhujWhwRna</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/mZDhujWhwRna.jpg</video:thumbnail_loc>

            <video:title>Algebraic operations</video:title>

            <video:description><![CDATA[
This lesson covers how to add, subtract, multiply, and divide functions to create new expressions. You will learn to determine the resulting domain and range after performing these algebraic operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/mZDhujWhwRna.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CJpizC_dIcoG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/CJpizC_dIcoG.jpg</video:thumbnail_loc>

            <video:title>Bijective functions</video:title>

            <video:description><![CDATA[
This lesson explains bijective functions, which are both injective and surjective, creating a perfect one-to-one correspondence between sets. You will learn why only these functions allow for a unique inverse mapping.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/CJpizC_dIcoG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CNiIwAdMxLKc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1028/CNiIwAdMxLKc.jpg</video:thumbnail_loc>

            <video:title>Proving inequalities (2)</video:title>

            <video:description><![CDATA[
This walkthrough proves a complex inequality involving powers and multiples of n. You will learn to use transitivity and algebraic estimation to link the inductive hypothesis to the final goal for n equals k plus one. Solved: 2. Prove that n^2 > n + 1 for all positive integers n \ge 2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1028/CNiIwAdMxLKc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uCL7_JwYrUTV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1027/uCL7_JwYrUTV.jpg</video:thumbnail_loc>

            <video:title>Proving divisibility (3)</video:title>

            <video:description><![CDATA[
Learn to prove that the square of any even positive integer is divisible by four. We define n as 2m and use algebraic substitution to verify the result efficiently. Solved: 3. Prove that, for every even positive integer n, n^2 is divisible by 4. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1027/uCL7_JwYrUTV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K7LwomN_2tyO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1109/K7LwomN_2tyO.jpg</video:thumbnail_loc>

            <video:title>Intermediate value theorem</video:title>

            <video:description><![CDATA[
Continuous functions cannot skip values between two endpoints. How do you prove a root lies strictly inside a closed interval without solving the full equation? Watch the lesson to spot the sign change and apply the theorem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1109/K7LwomN_2tyO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kb3E0XpFOG0u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1030/kb3E0XpFOG0u.jpg</video:thumbnail_loc>

            <video:title>Subsets of a finite set</video:title>

            <video:description><![CDATA[
This walkthrough proves that a set with n elements has 2 to the Power N Subsets. You will learn to use the inductive hypothesis to show how adding one new element doubles the total number of possible subsets. Solved: 2. Prove that a set containing n elements has exactly 2^n subsets for all n \ge 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1030/kb3E0XpFOG0u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EqeJYy48TpXm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1025/EqeJYy48TpXm.jpg</video:thumbnail_loc>

            <video:title>Proving series (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step proof for a standard arithmetic series formula. You will learn to verify the base case and use the inductive hypothesis to prove that adding the next term in the sequence maintains the general summation identity. Solved: 2. Prove that 1 + 4 + 7 + \dots + (3n - 2) = \frac{n(3n - 1)}{2}, for all n \ge 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1025/EqeJYy48TpXm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ItFfVx8yJa0D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1027/ItFfVx8yJa0D.jpg</video:thumbnail_loc>

            <video:title>Proving divisibility (2)</video:title>

            <video:description><![CDATA[
This walkthrough solves a complex divisibility proof involving exponents. You will learn to manipulate powers and extract common factors to show an expression remains a multiple of a given integer for n equals k plus one. Solved: 2. Prove that 6^n - 1 is divisible by 5 for any positive integer n. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1027/ItFfVx8yJa0D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/STTaagFimaH_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1030/STTaagFimaH_.jpg</video:thumbnail_loc>

            <video:title>Power of matrices</video:title>

            <video:description><![CDATA[
This walkthrough shows how to prove formulas for the nth power of a matrix using induction. You will learn to multiply the matrix by the inductive hypothesis and use trigonometric or algebraic identities to verify the result for n equals k plus one. Solved: 1. Given a matrix A = \begin{pmatrix} 1 & 1 \ 0 & 1 \end{pmatrix}, prove that A^n = \begin{pmatrix} 1 & n \ 0 & 1 \end{pmatrix} for all n \ge 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1030/STTaagFimaH_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3yuZsktZ454O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1026/3yuZsktZ454O.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson explains the systematic method for proving fractional series formulas. You will learn to apply the inductive hypothesis by finding common denominators and using factorisation to simplify complex algebraic fractions into the required goal.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1026/3yuZsktZ454O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NqiS0oU0CxI1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1026/NqiS0oU0CxI1.jpg</video:thumbnail_loc>

            <video:title>Proving fractional series (2)</video:title>

            <video:description><![CDATA[
This walkthrough shows how to prove a complex fractional summation formula using induction. You will learn to use common denominators and factorisation to link the inductive hypothesis to the final goal for n equals k plus one. Solved: 2. Prove that \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \frac{1}{7 \cdot 9} + \dots + \frac{1}{(2n+1)(2n+3)} = \frac{n}{3(2n+3)}, for all n \ge 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1026/NqiS0oU0CxI1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/k6toW7pxDkXP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1027/k6toW7pxDkXP.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson explains the systematic method for proving divisibility using induction. You will learn to express divisibility as a linear equation and use the inductive hypothesis to isolate factors, proving that an expression is a multiple of a given integer.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1027/k6toW7pxDkXP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/20vEBdamwAum</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1028/20vEBdamwAum.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson teaches the specific steps for proving mathematical inequalities using induction. You will learn to establish the base case and use transitivity and algebraic estimation to link the inductive hypothesis to the final inequality goal.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1028/20vEBdamwAum.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zh4m1c9ODXQh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/zh4m1c9ODXQh.jpg</video:thumbnail_loc>

            <video:title>Parity and orthogonality</video:title>

            <video:description><![CDATA[
Spot symmetry in a definite integral over a balanced interval. Why calculate area when odd functions cancel to zero and even ones just double? This lesson shows you how to solve by inspection.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/zh4m1c9ODXQh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jcV63pbxOqH4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/jcV63pbxOqH4.jpg</video:thumbnail_loc>

            <video:title>Addition rule</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to apply the addition rule to solve problems involving independent choices. You will learn to identify separate events and add their outcomes to find the total number of ways a single selection can be made. Solved: 2. A student wants to buy a single drink from a shop. The shop has 5 different brands of malt and 7 different brands of soft drinks. In how many ways can the student make a choice? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/jcV63pbxOqH4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kNtZ_xN2_OUB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1028/kNtZ_xN2_OUB.jpg</video:thumbnail_loc>

            <video:title>Proving inequalities (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the induction proof for an inequality involving a power of n. You will learn to manipulate exponential terms and use logical estimation to prove that the relationship holds for n equals k plus one. Solved: 1. Prove that 2^n > n for all positive integers n \ge 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1028/kNtZ_xN2_OUB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N_zjvjh102I_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1029/N_zjvjh102I_.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson explains the steps for proving explicit formulas for sequences defined by recurrence relations. You will learn to use the inductive hypothesis to link the current term to the next and verify that the general formula holds for every position in the sequence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1029/N_zjvjh102I_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xh4r0E4G5Eyg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/xh4r0E4G5Eyg.jpg</video:thumbnail_loc>

            <video:title>Addition rule</video:title>

            <video:description><![CDATA[
The addition rule applies to independent choices where you must pick one option or another. You find the total outcomes by adding the number of ways each separate event can occur.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/xh4r0E4G5Eyg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w2nwxAyZ2KQP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/w2nwxAyZ2KQP.jpg</video:thumbnail_loc>

            <video:title>Subtraction rule</video:title>

            <video:description><![CDATA[
The subtraction rule calculates the number of favourable outcomes by subtracting unwanted cases from the total possibilities. This method is the most efficient way to solve problems involving "at least" or "at most" conditions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/w2nwxAyZ2KQP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ONh4ulfSTMt_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/ONh4ulfSTMt_.jpg</video:thumbnail_loc>

            <video:title>Division rule</video:title>

            <video:description><![CDATA[
The division rule removes duplicate counts when several distinct sequences represent the same outcome. You divide the total permutations by the number of redundant arrangements to ensure each unique selection is counted exactly once.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/ONh4ulfSTMt_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OtQk5zjWNT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/OtQk5zjWNT.jpg</video:thumbnail_loc>

            <video:title>Linearity</video:title>

            <video:description><![CDATA[
Complex sums do not need complex methods. How can you split a long expression into simple parts for easy differentiation? See how linearity breaks down the problem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/OtQk5zjWNT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OMM6nGEBHQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/OMM6nGEBHQ.jpg</video:thumbnail_loc>

            <video:title>Rates of change</video:title>

            <video:description><![CDATA[
Speed varies at every instant. How do you distinguish average speed from the exact rate at a single point? Watch to grasp this key difference.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/OMM6nGEBHQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Db_x07BAI0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1112/Db_x07BAI0.jpg</video:thumbnail_loc>

            <video:title>Constant, identity and power</video:title>

            <video:description><![CDATA[
Differentiation need not always start from scratch. How do you instantly handle constants, x, and simple powers without first principles? Watch to learn the three rules that speed up your work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1112/Db_x07BAI0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ouqm08iqyv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1111/ouqm08iqyv.jpg</video:thumbnail_loc>

            <video:title>Derivative proofs (2)</video:title>

            <video:description><![CDATA[
Trigonometric derivatives rely on limits. How do sum-to-product identities prove the derivative of sin x? Watch to see the proof unfold.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1111/ouqm08iqyv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ATltEzfr_CFX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1032/ATltEzfr_CFX.jpg</video:thumbnail_loc>

            <video:title>Arrangements (2)</video:title>

            <video:description><![CDATA[
This lesson provides further worked examples on selecting and ordering objects from a larger set. You will practice using the nPr formula to solve more complex word problems and numerical arrangements where order is the primary requirement. Solved: 2. A bank wants to create 4-digit ATM pins using the digits from 1 to 6. If no digit can be repeated in a single pin, how many different ATM pins can be created? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1032/ATltEzfr_CFX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f_INqlFG_NGh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/f_INqlFG_NGh.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: A car of mass m travels along the cloverleaf interchange. The position of the car is given by x = \frac b 2 (sin \frac {\pi t} {4t_o} + sin \frac {3\pi t} {4t_o})y = \frac b 2 (cos\frac {\pi t} {4t_o} - cos\frac {3\pi t} {4t_o})where b = 240 m, and t_o = 12 s is the time of travel between O and A. Determine the smallest coefficient of friction between the tires and the road that would prevent the car from skidding at A (note that t = t_o when the car is at A) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/f_INqlFG_NGh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744389392759.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/jy71KIpzrdan</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/jy71KIpzrdan.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: If the cord is subjected to a constant force of F=300N and the 15-kg smooth collar starts from rest at A, determine the velocity of the collar when it reaches point B. Neglect the size of the pulley. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/jy71KIpzrdan.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746785854704.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/L_otaGJbMPyq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1042/L_otaGJbMPyq.jpg</video:thumbnail_loc>

            <video:title>Calculating derangements (1)</video:title>

            <video:description><![CDATA[
Apply the derangement formula to solve practical problems involving three to five objects. This lesson demonstrates how to calculate the number of ways items can be completely mismatched using step-by-step arithmetic. You will master the process of finding subfactorials for small sets. Solved: 1. An intern at a hospital has 5 blood test reports from 5 different patients. In his haste, he places one report into each of 5 addressed envelopes without checking the names. In how many ways can he do this such that none of the patients receives their correct report? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1042/L_otaGJbMPyq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W8pz6jGvokqO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1035/W8pz6jGvokqO.jpg</video:thumbnail_loc>

            <video:title>Restricted arrangements (3)</video:title>

            <video:description><![CDATA[
This lesson solves problems where specific items are fixed in set positions or restricted from certain spots. You will learn to lock items into place first then calculate the remaining arrangements for other objects. Practice these worked examples to master logic for rigid positioning rules. Solved: 3. A shelf has 7 distinct books: 4 Physics books and 3 chemistry books. In how many ways can these books be arranged in a row such that at least two chemistry books are kept together? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1035/W8pz6jGvokqO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vEz7txe_FA_E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1031/vEz7txe_FA_E.jpg</video:thumbnail_loc>

            <video:title>Division rule</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to remove redundant arrangements by dividing the total count by the number of duplicate patterns. You will learn to use this method to find the number of unique selections when the order of certain items does not matter. Solved: 4. A decorator has 4 flags to hang in a row. 3 of the flags are exactly the same (identical green flags) and 1 is a yellow flag. In how many unique ways can these flags be arranged? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1031/vEz7txe_FA_E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5EOIGNqBW08x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/5EOIGNqBW08x.jpg</video:thumbnail_loc>

            <video:title>Isolated conducting sphere</video:title>

            <video:description><![CDATA[
Every conductor has capacitance. How do you calculate storage capacity for an isolated sphere using only its radius? We apply the geometric formula to two vastly different scales. Solved: Determine the capacitance of an isolated conducting sphere with a radius of R = 12.0 \text{ cm}. Further, calculate the capacitance of a much larger isolated conducting sphere with a radius of R = 5.40 \times 10^6 \text{ m}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/5EOIGNqBW08x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8D7mliMQwNK7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1041/8D7mliMQwNK7.jpg</video:thumbnail_loc>

            <video:title>Determining geometries (1)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples on calculating the number of straight lines and triangles possible from a set of points. You will learn to use the nC2 and nC3 formulas while subtracting collinear points to ensure accuracy. It is a practical guide to mastering basic geometric counting. Solved: 1. There are 10 points in a plane. How many triangles can be formed if:(a) No three points are collinear?(b) 4 of the points lie on the same straight line? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1041/8D7mliMQwNK7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LTKlmKEKPzr0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/LTKlmKEKPzr0.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: (a) A 40-Ib suitcase slides from rest 20ft down the smooth ramp. Determine the point where it strikes the ground at C. How long does it take to go from A to C?(b) Solve (a) if the suitcase has an initial velocity down the ramp of V_A = 10ft/s and the coefficient of kinetic friction along AB is\mu_k=0.2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/LTKlmKEKPzr0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744533426398.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/CfCxMzPUF7jv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1041/CfCxMzPUF7jv.jpg</video:thumbnail_loc>

            <video:title>Determining geometries (3)</video:title>

            <video:description><![CDATA[
This lesson explains how to calculate the number of quadrilaterals possible from n points where no three are collinear. You will learn to use the combination formula to select sets of four points and solve problems where some points lie on parallel lines. Master these techniques to handle complex shape-counting tasks in geometry. Solved: 3. How many quadrilaterals (4 sides) can be formed from 8 points in a plane where no three points are collinear? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1041/CfCxMzPUF7jv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sC9eyk5_0cL7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/397/sC9eyk5_0cL7.jpg</video:thumbnail_loc>

            <video:title>Statical determinacy</video:title>

            <video:description><![CDATA[
When is a three-dimensional structure said to statically-determinate?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/397/sC9eyk5_0cL7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PfrcpgHQLUtX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1007/PfrcpgHQLUtX.jpg</video:thumbnail_loc>

            <video:title>Irreducible quadratic factors</video:title>

            <video:description><![CDATA[
Resolve rational expressions where the denominator includes quadratic factors that cannot be factorised into linear terms. This walkthrough demonstrates the correct setup using a linear numerator for the quadratic term and the steps to solve for all constants by equating coefficients. Solved: 4. Resolve the following into partial fractions: \frac{4x^2-x+1}{(x-1)(x^2+1)} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1007/PfrcpgHQLUtX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nHiVpgwcLnpS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/nHiVpgwcLnpS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: The 1-kg collar B slides on the vertical bar and has a pin that slides in the curved slot. The vertical bar moves with the constant velocity v = 2 m/s, The y axis points upward. What are the x and y components of the total force exerted on the collar by the vertical bar and the slotted bar when x = 0.25 m? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/nHiVpgwcLnpS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744394544429.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/8WKX2yrij7Xr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/8WKX2yrij7Xr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: A 500-g collar can slide without friction along the semicircular rod BCD. The spring is of constant 320N/m and its deformed length is 200 mm. Knowing that the collar is released from rest at B, determine (a) the speed of the collar as it passes through C,(b) the force exerted by the rod on the collar at C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/8WKX2yrij7Xr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747074893174.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/PzqknY46eXDc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/PzqknY46eXDc.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: A projectile of mass m is fired into a liquid at an angle \theta_0 with an initial velocity v_0 as shown. If the liquid develops a frictional or drag resistance on the projectile which is proportional to its velocity i.e F=Kv, where K is a constant, determine the x and y components of its position at any instant. Also, what is the maximum distance x_{max} that it travels? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/PzqknY46eXDc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/genx3t2A_evq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1039/genx3t2A_evq.jpg</video:thumbnail_loc>

            <video:title>Expansion to n terms (1)</video:title>

            <video:description><![CDATA[
Apply the general formula to expand binomials with negative indices to a set number of terms. You will learn to calculate coefficients using the descending product method and identify when the series is valid for specific x-values. This walkthrough ensures accuracy in creating infinite series. Solved: 1. Expand (1 - x)^{-2} up to the 4th term and state the condition for validity. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1039/genx3t2A_evq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j9wpqx2RH_F7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1039/j9wpqx2RH_F7.jpg</video:thumbnail_loc>

            <video:title>Expansion to n terms (2)</video:title>

            <video:description><![CDATA[
Apply the general formula to expand binomials with fractional powers like square and cube roots. You will learn to calculate coefficients for these indices and identify the range of x-values where the infinite series converges. This walkthrough ensures you can handle rational powers with precision. Solved: 2. Expand \sqrt{1+2x} as a series in ascending powers of x, up to the term carrying x^3. State the range of values of x for which the expansion is valid. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1039/j9wpqx2RH_F7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O_VeWhifR9sf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/O_VeWhifR9sf.jpg</video:thumbnail_loc>

            <video:title>Finding an unknown value</video:title>

            <video:description><![CDATA[
Learn to solve for unknown constants by comparing expansion coefficients to given values. This walkthrough shows how to set up and solve algebraic equations derived from the general term formula. Mastering this technique allows you to work backwards from a known expansion result to find missing variables. Solved: 5. In the expansion of (1 + ax)^6, the coefficient of x^3 is 160. Find the value of a. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/O_VeWhifR9sf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/drOgbsnAnKta</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/drOgbsnAnKta.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the method of undetermined coefficients. Solved: Determine an appropriate guess for the particular solution for the following equations:1 y^{""} - 2y' = 8xe^{2x}2 y^{"""} - 3y^{""} - y'+ 3y = {x^2}e^x3 \frac{d^2y} {dx^2} + 4y = x^2cos2x + 3sin2x 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/drOgbsnAnKta.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tLSvrdqJWvxV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/319/tLSvrdqJWvxV.jpg</video:thumbnail_loc>

            <video:title>Load transmission</video:title>

            <video:description><![CDATA[
How load is transmitted to the joints in trusses - use of purlins in roof trusses, stringers, floor beam and deck in bridge trusses.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/319/tLSvrdqJWvxV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SCxPirKE8GqR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/SCxPirKE8GqR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A crane column support a 16-kip load as shown. Replace the load with an equivalent system consisting of an axial force along AB and a couple. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/SCxPirKE8GqR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739178511503.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0fH1miEkTQtw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/418/0fH1miEkTQtw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating line or double integrals using Green's theorem. Solved: Verify Green's theorem for the integral \oint_C \,[(x^2+y^2) dx, (x+2y)dy] taken round the boundary curve C defined below 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/418/0fH1miEkTQtw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747320068876.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WTCcstlK8xJi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/WTCcstlK8xJi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: If blocks A and B of mass 10 kg and 6 kg, respectively, are placed on the inclined plane and released, determine the force developed in the link. The coefficients of kinetic friction between the blocks and the inclined plane are \mu_A = 0.1 and \mu_B = 0.3. Neglect the mass of the link. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/WTCcstlK8xJi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742307922272.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/isP6QJJdZ85D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1038/isP6QJJdZ85D.jpg</video:thumbnail_loc>

            <video:title>Proof</video:title>

            <video:description><![CDATA[
Verify the Binomial Theorem using mathematical induction by testing the base case and proving the transition from k to k+1. This rigorous proof confirms the formula works for every positive integer power. You will learn to use algebraic manipulation to link successive expansions logically.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1038/isP6QJJdZ85D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GXuyP_wjADLE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1038/GXuyP_wjADLE.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Understand the formal binomial formula and how combinations replace manual counting for large powers. You will learn the general structure of an expansion and how indices determine each term. This lesson introduces the tools needed to calculate specific coefficients without drawing triangles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1038/GXuyP_wjADLE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eV12GA3gHPvw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/eV12GA3gHPvw.jpg</video:thumbnail_loc>

            <video:title>Identifying specific terms (2)</video:title>

            <video:description><![CDATA[
Learn to find terms for complex expressions with negative signs and fractions. You will use the general formula to isolate specific term numbers and calculate their final numerical values. This walkthrough shows how to handle algebraic signs and power laws during substitution for absolute accuracy. Solved: 2. Find the 5th term in the expansion of (3x - \frac{y}{2})^7. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/eV12GA3gHPvw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1L7uW2HvgJOa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/1L7uW2HvgJOa.jpg</video:thumbnail_loc>

            <video:title>Finding a specific coefficient</video:title>

            <video:description><![CDATA[
Learn to find the numerical coefficient of a specific power of x without expanding the entire bracket. This walkthrough shows how to equate the index of the general term to the required power to solve for r. You will then substitute this value to calculate the final coefficient accurately. Solved: 3. Find the coefficient of x^6 in the expansion of (x+2)^9. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/1L7uW2HvgJOa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c_g3hQciS_aS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1039/c_g3hQciS_aS.jpg</video:thumbnail_loc>

            <video:title>First term not 1</video:title>

            <video:description><![CDATA[
Learn to expand binomials where the first term is not 1 by factoring out the leading constant. This walkthrough shows how to adjust the expression to fit the standard format before applying the general formula. Mastering this step ensures your infinite series remains valid and accurate. Solved: 3. Expand (8+x)^{1/3} up to the term carrying x^2 and state the condition for validity. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1039/c_g3hQciS_aS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZtA5E_R_rr9E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1038/ZtA5E_R_rr9E.jpg</video:thumbnail_loc>

            <video:title>Expanding binomials (1)</video:title>

            <video:description><![CDATA[
Apply the binomial formula to expand algebraic expressions with positive integer powers. You will learn to substitute values into the general formula to find each term and its corresponding coefficient systematically. This walkthrough ensures you can handle expansions accurately without manual errors. Solved: 1. Expand (a+2)^5 using the binomial expansion formula. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1038/ZtA5E_R_rr9E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EMi59vtZSE6P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1039/EMi59vtZSE6P.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Understand how binomial expansions change when the power is negative or a fraction. You will learn why these expressions create infinite series instead of ending at a fixed term. This lesson introduces the general formula and the conditions required for these expansions to be valid.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1039/EMi59vtZSE6P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qadVSHWgUwRJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/qadVSHWgUwRJ.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Understand how to pick out any single term from a long expansion using the general term formula. You will learn to identify the position of a term and its corresponding powers without expanding the whole bracket. This skill saves time when solving for specific coefficients or constants.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/qadVSHWgUwRJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kzXlqobzz5wa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/kzXlqobzz5wa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: The sliders A and B are connected by a light rigid bar and move with negligible friction in the slots, both of which lie on a horizontal plane. For the position shown, the hydraulic cylinder imparts a velocity and acceleration to slider A of 0.4 m/s and 2 m/s^2, respectively, both to the right. Determine the acceleration of slider B and the force in the bar at this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/kzXlqobzz5wa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742305767306.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5kCwX1lx0ZGw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/5kCwX1lx0ZGw.jpg</video:thumbnail_loc>

            <video:title>Finding the constant term</video:title>

            <video:description><![CDATA[
Learn to identify the term independent of x by setting its total power to zero within the general formula. This walkthrough demonstrates how to solve for r and calculate the resulting constant value. Use this method to find the fixed number in any expansion without writing out the full series. Solved: 4. Find the constant term in the expansion of (x^2 + \frac{2}{x})^6. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/5kCwX1lx0ZGw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wrAo9BSbNYDj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/wrAo9BSbNYDj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A derigible is tethered by a cable attached to its cabin at B. If the tension in the cable is1040N, replace the force exerted by the cable at B with an equivalent system formed by two parallel forces applied at A and C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/wrAo9BSbNYDj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739179091081.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/YMM6cbnLC58H</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/YMM6cbnLC58H.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion. Solved: Coal is discharged from a tailgate A of a dump truck with an initial velocity v_A = 2 m/s \measuredangle { 50^\circ}. Determine the radius of curvature of the trajectory described by the coal(a) at point A,(b) at the point of trajectory 1 m below point A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/YMM6cbnLC58H.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742217626753.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/y3ASp3I3bvT-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/y3ASp3I3bvT-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: A spring AB of constant k is attached to a support at A and to a collar of mass m. The unstretched length of the spring is l. Knowing that the collar is released from rest at x = x_o and neglecting friction between the collar and the horizontal rod, determine the magnitude of the velocity of the collar as it passes through point C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/y3ASp3I3bvT-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742299284909.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ARSc1cvpW9WD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/561/ARSc1cvpW9WD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on identifying reflexive relations. Solved: Which of the following relations is reflexive?(a) The relation R on a set of university students where xRy if and only if x and y are in the same department.(b) The relation "is the brother of" on the children of a family.(c) The relation R in [1,2,3], where R=[(1,1),(1,2),(3,2),(3,3)].(d) The relation "is the mother of" on a set of residents in a country.(e) The relation R in IR where xRy if and only if x=y. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/561/ARSc1cvpW9WD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4WXBgX0AqK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/4WXBgX0AqK.jpg</video:thumbnail_loc>

            <video:title>Quotient rule</video:title>

            <video:description><![CDATA[
Dividing functions creates a new challenge. How do you differentiate a fraction without using first principles every time? See the shortcut in action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/4WXBgX0AqK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j2JXOdCOQQLA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/j2JXOdCOQQLA.jpg</video:thumbnail_loc>

            <video:title>Chlorination</video:title>

            <video:description><![CDATA[
Alkane chlorination produces mixtures of isomers. How do you predict which hydrogen gets replaced and identify every possible product? We map the substitution patterns for methane through butane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/j2JXOdCOQQLA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zz_a25HhCnbo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/zz_a25HhCnbo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: (a) What is the magnitude of the acceleration of the 20-lb collar A along the smooth bar at the instant shown?(b) Determine the magnitude of the acceleration of the 20-lb collar A along the bar at the instant shown if the coefficient of kinetic friction between the collar and the bar \mu_k = 0.2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/zz_a25HhCnbo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742304236109.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/vqm1kEJACJ36</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/vqm1kEJACJ36.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: The 2 kg block slides along the inclined plane under the action of the constant force P = 32 N. If the block is released from rest at x = 0, determine the maximum velocity of the block and the value of x when it occurs. Neglect friction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/vqm1kEJACJ36.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742303984473.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ZGBPHtbUtFPI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/ZGBPHtbUtFPI.jpg</video:thumbnail_loc>

            <video:title>Endothermic and exothermic reactions</video:title>

            <video:description><![CDATA[
Exothermic reactions release heat to the surroundings and have a negative enthalpy change, while endothermic reactions absorb heat and have a positive enthalpy change. This lesson explains how to identify these two reaction types based on energy flow and temperature changes in the environment.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/ZGBPHtbUtFPI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XyJDNrDktOjZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/XyJDNrDktOjZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: A precast concrete wall section is temporarily held by two cables as shown. Knowing that the tension in able BD is 900 N, determine the moment about point O of the force exerted by the cable at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/XyJDNrDktOjZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738679099358.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Y_iA3vtsDhM5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/Y_iA3vtsDhM5.jpg</video:thumbnail_loc>

            <video:title>Enthalpy change</video:title>

            <video:description><![CDATA[
Enthalpy is a state function because its value depends only on the current state of the system, not the path taken to get there. This lesson explains why this property is essential for calculating energy changes using initial and final states. You will see how this simplifies complex chemical calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/Y_iA3vtsDhM5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RWctjm11HAT8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/RWctjm11HAT8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: The force F=(400i-100j-700k) lb acts at the end of the beam. Determine the moment of the force about point O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/RWctjm11HAT8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738678274472.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/d8I6Sv9urE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/d8I6Sv9urE.jpg</video:thumbnail_loc>

            <video:title>Derived rules</video:title>

            <video:description><![CDATA[
The general chain rule handles all composites, yet repeated expansion slows calculation. How do you derive direct shortcuts for powers, roots, exponentials and logarithms from the master formula? Watch this.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/d8I6Sv9urE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KDSOsJa7hd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/KDSOsJa7hd.jpg</video:thumbnail_loc>

            <video:title>Reciprocal rule advantage</video:title>

            <video:description><![CDATA[
A constant numerator allows a shortcut. Why use the full quotient rule when linearity rule works faster? See the efficient method here. Solved: Differentiate f(x) = \frac{10}{x^2 + 5x}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/KDSOsJa7hd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pbaG4KqgQT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/pbaG4KqgQT.jpg</video:thumbnail_loc>

            <video:title>General rule</video:title>

            <video:description><![CDATA[
Nested functions hide their true rate of change. How do you differentiate a function inside another without expanding it? Watch to learn the universal shortcut.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/pbaG4KqgQT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Anfn3kKAZvN8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/Anfn3kKAZvN8.jpg</video:thumbnail_loc>

            <video:title>Hess's law</video:title>

            <video:description><![CDATA[
Hess’s Law states that the total enthalpy change of a reaction is the same regardless of the number of steps taken. This principle allows you to calculate the heat of a reaction by adding the enthalpy changes of individual intermediate steps. It is a direct consequence of enthalpy being a state function.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/Anfn3kKAZvN8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RSjwF6nEJ2Dt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1044/RSjwF6nEJ2Dt.jpg</video:thumbnail_loc>

            <video:title>Calculating enthalpy of phase changes (1)</video:title>

            <video:description><![CDATA[
This lesson shows how to calculate the molar enthalpy of vaporisation for benzene using energy and mass data. You will learn to convert mass to moles to determine the heat required for a complete phase change. Mastering this calculation is essential for predicting energy needs during boiling. Solved: A sample of benzene was heated to its boiling point. Subsequent heating required 61.6 kJ of energy to vaporize 156.4 g of benzene. Which is the enthalpy of vaporization of benzene? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1044/RSjwF6nEJ2Dt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QvduttSHVoES</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1045/QvduttSHVoES.jpg</video:thumbnail_loc>

            <video:title>Enthalpy change from bond energies (2)</video:title>

            <video:description><![CDATA[
Estimate the enthalpy change for the reaction between methane and fluorine gases using average bond energies. You will calculate the total energy used to break C-H and F-F bonds and subtract the energy released from forming C-F and H-F bonds. Solved: Estimate the enthalpy change at 298 K for the following reaction using the given bond energies:\text{CH}_4(g) + 4\text{ F}_2(g) \rightarrow \text{CF}_4(g) + 4\text{ HF}(g)BondAverage Bond Energy (kJ/mol)\text{C}-\text{H}413\text{F}-\text{F}158\text{C}-\text{F}485\text{H}-\text{F}565 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1045/QvduttSHVoES.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wM6j3ycBh4qB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/wM6j3ycBh4qB.jpg</video:thumbnail_loc>

            <video:title>Condition</video:title>

            <video:description><![CDATA[
A particle is in equilibrium when the vector sum of all forces acting upon it is zero. This condition ensures the object has no acceleration, staying at rest or moving with constant velocity. It is the absolute requirement for stability in any mechanical system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/wM6j3ycBh4qB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oLYOQiiddQvS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1045/oLYOQiiddQvS.jpg</video:thumbnail_loc>

            <video:title>Standard enthalpy change</video:title>

            <video:description><![CDATA[
Standard enthalpy change is the heat energy shift of a reaction when all reactants and products are in their most stable forms at 1 bar of pressure. This lesson defines these standard conditions and explains why they are necessary for comparing reaction energies consistently across chemistry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1045/oLYOQiiddQvS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_1zrByEJ3Av_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1045/_1zrByEJ3Av_.jpg</video:thumbnail_loc>

            <video:title>Spontaneity</video:title>

            <video:description><![CDATA[
A spontaneous reaction occurs naturally without constant outside help. This lesson explains the factors that determine if a process will happen on its own. You will learn to distinguish between naturally occurring changes and those that require a continuous energy supply.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1045/_1zrByEJ3Av_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RG_lhZlYI_p9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1044/RG_lhZlYI_p9.jpg</video:thumbnail_loc>

            <video:title>Endothermic and exothermic changes</video:title>

            <video:description><![CDATA[
Phase changes like melting and boiling absorb heat and are endothermic, while freezing and condensation release heat and are exothermic. You will learn to identify these changes by the direction of energy flow. This knowledge is essential for predicting if a process requires or emits energy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1044/RG_lhZlYI_p9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OqA2pfdE8gMG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/OqA2pfdE8gMG.jpg</video:thumbnail_loc>

            <video:title>Enthalpy of formation</video:title>

            <video:description><![CDATA[
Standard enthalpy of formation is the heat change when one mole of a substance forms from its elements in their standard states. You will learn how these values serve as a reference point for calculating total reaction enthalpy. Elements in their most stable form have a formation value of zero.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/OqA2pfdE8gMG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/My9WMaAt4y5D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1045/My9WMaAt4y5D.jpg</video:thumbnail_loc>

            <video:title>Bond dissociation energy</video:title>

            <video:description><![CDATA[
Bond enthalpy is the energy needed to break one mole of a chemical bond in the gas phase. You will learn to calculate reaction heat by subtracting the energy of bonds made from the energy of bonds broken. Breaking bonds takes in heat, while making new bonds gives it out.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1045/My9WMaAt4y5D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zWkcPlBOwlVb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/zWkcPlBOwlVb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: A 6-ft-long fishing rod AB is securely anchored in the sand of a beach. After a fish takes the bait, the resulting force in the line is 6 lb. Determine the moment about A of the force exerted at the line at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/zWkcPlBOwlVb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738680765246.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/IY_4WUMiF9td</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/IY_4WUMiF9td.jpg</video:thumbnail_loc>

            <video:title>Finding the middle term</video:title>

            <video:description><![CDATA[
Learn to identify the middle term position based on whether the power n is even or odd. This walkthrough shows how to calculate the specific term using the general formula for one or two central terms. Mastering this allows you to find the expansion's symmetrical centre quickly. Solved: 6. Find the middle term in the expansion of (x+3y)^{10}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/IY_4WUMiF9td.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ne5v996oLZtm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/Ne5v996oLZtm.jpg</video:thumbnail_loc>

            <video:title>Change in internal energy</video:title>

            <video:description><![CDATA[
This lesson shows how to calculate the change in internal energy for a neutralisation reaction using calorimetry data. You will learn to determine the calorimeter's heat capacity first, then use it to find the heat released during the reaction. No work is done because volume is constant. Solved: A constant-volume calorimeter was calibrated using a reaction that released 2.50 kJ of heat, causing the temperature of the calorimeter to rise by 4.20 °C. In a subsequent experiment, 75.0 mL of 0.150 M \text{HNO}_3(aq) was mixed with 75.0 mL of 0.150 M \text{KOH}(aq) in the same calorimeter. The temperature increased by 1.75 °C. Calculate the change in internal energy, \Delta U, for the neutralization reaction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/Ne5v996oLZtm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DVX_zHkf7J13</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/DVX_zHkf7J13.jpg</video:thumbnail_loc>

            <video:title>Enthalpy of formation</video:title>

            <video:description><![CDATA[
This video demonstrates how to calculate the total enthalpy change of a reaction using standard heats of formation. You will learn to apply the formula by subtracting the total energy of reactants from that of the products. Follow the step-by-step calculation to master this essential skill. Solved: 1. Methane is the primary component of natural gas. Calculate the standard enthalpy change for the complete combustion of methane:\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g)Use the following standard enthalpies of formation (\Delta H^\circ_f in kJ/mol):\text{CH}_4(g): -74.6\text{CO}_2(g): -393.5\text{H}_2\text{O}(g): -241.82. Hydrogen peroxide decomposes to water and oxygen. Calculate the standard enthalpy change for the reaction:2\text{H}_2\text{O}_2(l) \rightarrow 2\text{H}_2\text{O}(l) + \text{O}_2(g)Use the following standard enthalpies of formation (\Delta H^\circ_f in kJ/mol):\text{H}_2\text{O}_2(l): -187.8\text{H}_2\text{O}(l): -285.8 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/DVX_zHkf7J13.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ywlGFfN1P4M9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/ywlGFfN1P4M9.jpg</video:thumbnail_loc>

            <video:title>Hess's law</video:title>

            <video:description><![CDATA[
This video demonstrates how to calculate the standard enthalpy of formation for methanol using Hess's Law. You will learn how to rearrange and sum multiple thermochemical equations to find the heat of a target reaction. Master the technique of cancelling intermediate species to get the final result. Solved: Methanol, \text{CH}_3\text{OH}, is a common liquid fuel and industrial solvent. Its standard enthalpy of formation from its elements is difficult to measure directly. Calculate the standard enthalpy for the reaction:\text{C}(gr) + 2\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{CH}_3\text{OH}(l)from the following experimental data:i. \text{CH}_3\text{OH}(l) + \frac{3}{2}\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)\Delta H^\circ = -726 \text{ kJ}ii. \text{C}(gr) + \text{O}_2(g) \rightarrow \text{CO}_2(g)\Delta H^\circ = -394 \text{ kJ}iii. \text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l)\Delta H^\circ = -286 \text{ kJ} 
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          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/ywlGFfN1P4M9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IDtN59QWZ_1B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/IDtN59QWZ_1B.jpg</video:thumbnail_loc>

            <video:title>Halogenation</video:title>

            <video:description><![CDATA[
Halogenation yields mixed products based on hydrogen reactivity. How do you convert relative rates into actual product masses? We calculate the exact weight of each chloropropane formed.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/IDtN59QWZ_1B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rU6RHDliaA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/rU6RHDliaA.jpg</video:thumbnail_loc>

            <video:title>Absolute value function</video:title>

            <video:description><![CDATA[
Absolute value has a sharp corner. How do you write its gradient as a single formula? See how the signum function captures this change.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/rU6RHDliaA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uBlWPFcFCRAD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/uBlWPFcFCRAD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: Determine the magnitude of the moment of the force F = { 50i - 20j - 80k } N about member C A of the tripod. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/uBlWPFcFCRAD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738694536249.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Nb1_sZcprAuT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/Nb1_sZcprAuT.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: In the pipe assembly shown, points B and C lie in the x y plane and force F is parallel to the z axis. If a twisting moment (torque) of 50 N . m will cause a pipe to begin twisting in the flange fitting at O or at either end of the elbow fitting at A. Determine the first fitting that twists and the value of F that causes it. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/Nb1_sZcprAuT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738693876236.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/17VRDtwWJ_ZE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/17VRDtwWJ_ZE.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating the moment of a force about an arbitrary axis. Solved: The board is used to hold the end of the cross lug wrench in the position shown when the man applies a force of F = 100 N. Determine the magnitude of the moment produced by this force about the x axis. Force F lies in a vertical plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/17VRDtwWJ_ZE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738692900609.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xpeFrZt4qgsP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/xpeFrZt4qgsP.jpg</video:thumbnail_loc>

            <video:title>Conjugates and conjugate transposes</video:title>

            <video:description><![CDATA[
Meaning of conjugates and conjugate transposes for matrices with complex entries.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/xpeFrZt4qgsP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kh7AgwqoUEcI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1045/kh7AgwqoUEcI.jpg</video:thumbnail_loc>

            <video:title>Enthalpy change from bond energies (1)</video:title>

            <video:description><![CDATA[
Estimate the enthalpy change for the reaction of chlorine and fluorine gases using average bond energies. You will learn to calculate the total energy needed to break reactant bonds and subtract the energy released by forming product bonds. This step-by-step example uses a simple energy balance. Solved: 1. Estimate the enthalpy change at 298 K for the reaction below, given the average bond energies listed.\text{Cl}_2(g) + 3\text{ F}_2(g) \rightarrow 2\text{ ClF}_3(g)BondAverage Bond Energy (kJ/mol)\text{Cl}-\text{Cl}242\text{F}-\text{F}158\text{Cl}-\text{F}253 Would you like me to show the calculation for the bond enthalpy estimate of this reaction? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1045/kh7AgwqoUEcI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_8qIBlDpPOqJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/_8qIBlDpPOqJ.jpg</video:thumbnail_loc>

            <video:title>Predicting reaction entropies</video:title>

            <video:description><![CDATA[
To predict if a reaction is truly spontaneous, you must compare the entropy change of the system with that of its surroundings. This lesson explains how heat released to or absorbed from the environment alters external disorder. You will also learn to predict the sign of the entropy change of a reaction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/_8qIBlDpPOqJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WbI6SnovFqw-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/WbI6SnovFqw-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: A regular tetrahedron has six edges of length a. A point P is directed as shown along edge BC. Determine the moment P about point OA. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/WbI6SnovFqw-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738695689891.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/cLx9DOONbQYZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/cLx9DOONbQYZ.jpg</video:thumbnail_loc>

            <video:title>Predicting reaction entropies (3)</video:title>

            <video:description><![CDATA[
Solve advanced entropy problems involving ionic dissolution, molecular complexity, and numerical calculations using standard molar data. This lesson walks you through comparing reaction pairs and applying the summation law to find total entropy changes. Master these final worked examples. Solved: Using the standard molar entropy (S^\circ) data provided below at 298 K, calculate \Delta S^\circ for the following reaction:2\text{H}_2\text{S}(g) + 3\text{O}_2(g) \rightarrow 2\text{SO}_2(g) + 2\text{H}_2\text{O}(g)Data:S^\circ[\text{H}_2\text{S}(g)] = 205.8 \text{ J K}^{-1}\text{mol}^{-1}S^\circ[\text{O}_2(g)] = 205.2 \text{ J K}^{-1}\text{mol}^{-1}S^\circ[\text{SO}_2(g)] = 248.2 \text{ J K}^{-1}\text{mol}^{-1}S^\circ[\text{H}_2\text{O}(g)] = 188.8 \text{ J K}^{-1}\text{mol}^{-1} Would you like me to show the calculation for the standard entropy change of this reaction? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/cLx9DOONbQYZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nD4eO0lfO3w0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/nD4eO0lfO3w0.jpg</video:thumbnail_loc>

            <video:title>Predicting reaction entropies (1)</video:title>

            <video:description><![CDATA[
Learn to predict the sign of entropy change by analysing state changes, molecular complexity, and variations in the number of gas moles. This walkthrough covers practical examples involving precipitation, allotropic shifts, and protein unfolding. You will master justifying predictions using standard thermodynamic principles. Solved: Predict the sign of \Delta S^\circ for the following reactions. Justify your prediction by considering not just the number of moles but also molecular complexity, state changes, and solvation.a) \text{Ag}^+(aq) + \text{Cl}^-(aq) \rightarrow \text{AgCl}(s)b) \text{C}(graphite) \rightarrow \text{C}(diamond)c) \text{Protein}(folded) \rightarrow \text{Protein}(unfolded) in aqueous solution.d) \text{H}_2(g) + \text{I}_2(s) \rightarrow 2\text{HI}(g) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/nD4eO0lfO3w0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sIzCxn_gIk8n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/sIzCxn_gIk8n.jpg</video:thumbnail_loc>

            <video:title>Effects of temperature</video:title>

            <video:description><![CDATA[
Temperature determines if the entropy term outweighs enthalpy to make a reaction spontaneous. This lesson explains how heating or cooling shifts the sign of Gibbs free energy for different reaction types. You will learn to identify the temperature at which a process becomes naturally feasible.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/sIzCxn_gIk8n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/anxegWnTiRH_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/anxegWnTiRH_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: End A of the bar moves to the left with a constant velocity v_A . Determine the angular velocity \omega and angular acceleration \alpha of the bar as a function of its position x . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/anxegWnTiRH_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744972767880.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ZlIb9H3XzlUK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/ZlIb9H3XzlUK.jpg</video:thumbnail_loc>

            <video:title>Limitation of the first law</video:title>

            <video:description><![CDATA[
Energy conservation alone cannot tell if a reaction will happen. The first law tracks heat and work but ignores the natural direction of processes. This lesson shows why we need entropy to predict if a change is spontaneous.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/ZlIb9H3XzlUK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J-uupdlvwR72</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/564/J-uupdlvwR72.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on identifying equivalence relations. Solved: R is a relation in \mathbb{R} \times \mathbb{R} such that for (a,b), (x,y) \epsilon \mathbb{R} \times \mathbb{R}, (a, b) R (x, y) if and only if y-b = 3x-3a. Show that R is an equivalence relation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/564/J-uupdlvwR72.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uB0eByao1vNX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Thumbnails/408/uB0eByao1vNX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on applications of first-order ordinary differential equations - 2022/2023 final semester examination questions. Solved: Given the equation (kirchoff's law) L \frac{dI}{dt}+RI=E(t) find an expression for the current in a circuit if the resistance is 12 \Omega , the inductance is 4H , a battery gives a constant voltage of 60V , and the switch is turned on when t=0 . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ifA3iuIjAY/Previews/408/uB0eByao1vNX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EZtstMAqAgQ8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/151/EZtstMAqAgQ8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on uniformly-accelerated motion problems. Solved: A group of students launches a model rocket in the vertical direction. Based on tracking data, they determine that the altitude of the rocket was 89.6ft at the end of the powered portion of the flight and that the rocket landed 16s later knowing that the decent parachute failed to deploy so that the rocket fell freely to the ground after reaching it maximum altitude and assuming that g=32.2ft/s^2, determine (a) the speed v_1 of the rocket at the end of the powered flight (b) the maximum altitude reached by the rocket. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/151/EZtstMAqAgQ8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742041849714.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xDGgNb3jxehf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/xDGgNb3jxehf.jpg</video:thumbnail_loc>

            <video:title>Deriving the general term (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to derive an explicit linear rule for an arithmetic sequence by identifying the common difference. You will master mapping term values to their positions to establish a precise algebraic formula for any term in the set. Solved: 5. Find the general term U_r for the sequence 5, 8, 11, 14, ... 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/xDGgNb3jxehf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tvI2Yrx93F25</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/tvI2Yrx93F25.jpg</video:thumbnail_loc>

            <video:title>Deriving the general term (4)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to derive a general rule for sequences with oscillating patterns by splitting terms into separate arithmetic and geometric components. You will master combining these distinct rules into a single piecewise or algebraic formula for the rth term. Solved: 8. Find the rule for the sequence 2, 4, 6, 16, 10, 36, 14, 64, ... 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/tvI2Yrx93F25.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RZ1Ge6XI_yc9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/RZ1Ge6XI_yc9.jpg</video:thumbnail_loc>

            <video:title>Deriving the general term (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to derive explicit rules for alternating geometric sequences by identifying common ratios and sign flips. You will master mapping negative bases to positions to establish precise formulae for switching patterns. Solved: 6. Find the rule for the sequence 3, -9, 27, -81, ... 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/RZ1Ge6XI_yc9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pdcY3aXukQmT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/pdcY3aXukQmT.jpg</video:thumbnail_loc>

            <video:title>Deriving the general term (3)</video:title>

            <video:description><![CDATA[
This walkthrough shows how to find the general rule for fractional sequences by solving for the numerator and denominator separately. You will learn to combine linear and exponential patterns into a single formula for the rth term. Solved: 7. Find the rth term of the sequence \frac{1}{2}, \frac{3}{4}, \frac{5}{8}, \frac{7}{16}, \frac{9}{32}, \dots 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/pdcY3aXukQmT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8WoKPKFh9k_i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/8WoKPKFh9k_i.jpg</video:thumbnail_loc>

            <video:title>Some classification of infinite series</video:title>

            <video:description><![CDATA[
Series are classified as convergent, divergent, or oscillatory based on the behaviour of their partial sums as more terms are added. This lesson explains how to identify if a series approaches a fixed value, grows without limit, or fluctuates between values.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/8WoKPKFh9k_i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2UkVk1KiaOy4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/2UkVk1KiaOy4.jpg</video:thumbnail_loc>

            <video:title>Entropy of phase transitions</video:title>

            <video:description><![CDATA[
Apply the formula for entropy change to specific phase transition problems using enthalpy and temperature values. This lesson provides step-by-step calculations for determining disorder changes during melting and boiling. You will learn to convert units correctly and solve for unknown variables. Solved: Example I. Given that the standard enthalpy of vaporization of acetone is 29.1 \text{ kJ mol}^{-1}, calculate the entropy change of vaporization of acetone at its boiling point of 52.6 \text{ °C}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/2UkVk1KiaOy4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f0QaLJmNAspc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/f0QaLJmNAspc.jpg</video:thumbnail_loc>

            <video:title>Generating terms (3)</video:title>

            <video:description><![CDATA[
This walkthrough covers generating terms from linear, alternating quadratic, and fractional exponential formulae. You will master substituting position values into these diverse explicit rules to calculate specific term values with technical precision. Solved: 3. Find the first three terms of the sequence U_r = \frac{r+1}{2^r}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/f0QaLJmNAspc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uyn1r6yQg3KW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/uyn1r6yQg3KW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on resultant of forces in two dimensions. Solved: Two forces P and Q are applied as shown at the point A of a hook support. Knowing that P=75N and Q=125N, determine graphically the magnitude and direction of their resultant using (a) the parallelogram law (b) the triangle law. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/uyn1r6yQg3KW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739367819078.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/jZ8_bljhHot9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/jZ8_bljhHot9.jpg</video:thumbnail_loc>

            <video:title>Trigonometric log jump</video:title>

            <video:description><![CDATA[
Spot a trig ratio as a hidden fraction. Why struggle when the top is the derivative of the bottom? This walkthrough shows you how to jump straight to the log answer. Solved: Find \int \tan x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/jZ8_bljhHot9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bHIZRqUQanHS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/bHIZRqUQanHS.jpg</video:thumbnail_loc>

            <video:title>Terms from sums</video:title>

            <video:description><![CDATA[
Extract individual terms of a sequence from a given sum formula by finding the difference between consecutive partial sums. This lesson establishes the algebraic identity for calculating the nth term from the total sum of n and n-1 terms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/bHIZRqUQanHS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3DWRm_O3z8vr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/3DWRm_O3z8vr.jpg</video:thumbnail_loc>

            <video:title>Condensing series (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates condensing arithmetic series into sigma notation by identifying the general rule and summation limits. You will master mapping term positions to index values to write exact mathematical rules for total sums. Solved: Write the series 3+6+9+12+15 in sigma notation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/3DWRm_O3z8vr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/f_9wzGjnbGA6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/f_9wzGjnbGA6.jpg</video:thumbnail_loc>

            <video:title>Geometric means (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the insertion of a single geometric mean between two numbers. You will master solving for the mean by calculating the square root of the product of the two boundary values. Solved: 4. Find the value of k if k - 2, k + 1 and k + 7 are three consecutive terms of a geometric progression. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/f_9wzGjnbGA6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RXP5Dyq707p_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/RXP5Dyq707p_.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
This lesson explains the algebraic rules for manipulating series, including the distributive and additive properties of sigma notation. You will learn to simplify complex summations by extracting constants and splitting combined terms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/RXP5Dyq707p_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6Ur1dvppwX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/6Ur1dvppwX.jpg</video:thumbnail_loc>

            <video:title>Implicit differentiation</video:title>

            <video:description><![CDATA[
Not every equation isolates y easily. How do you find the gradient when x and y are mixed up in one expression? Watch to learn the trick for differentiating these hidden relationships directly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/6Ur1dvppwX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aoz4TYeK1xnB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/aoz4TYeK1xnB.jpg</video:thumbnail_loc>

            <video:title>Finite geometric series</video:title>

            <video:description><![CDATA[
A finite geometric series is the sum of terms in an exponential progression where each term differs by a constant ratio. This lesson provides the standard formulae for calculating partial sums based on whether the common ratio is greater or less than one.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/aoz4TYeK1xnB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FvVm9HHT0757</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/FvVm9HHT0757.jpg</video:thumbnail_loc>

            <video:title>Expanding series (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step evaluation of a finite series using sigma notation. You will master expanding the summation rule and calculating the total accumulation by substituting integer values from the lower to the upper limit. Solved: 1. Evaluate the series \sum_{r=1}^{4} (2r+3). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/FvVm9HHT0757.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eoJeQ5KE4soN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/eoJeQ5KE4soN.jpg</video:thumbnail_loc>

            <video:title>Applying properties (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to split summations across addition and pull out constants to solve complex expressions using known results. You will master combining linear properties to break down series into simpler parts for faster calculation. Solved: 6. Given that \sum_{r=1}^{n} r = \frac{n(n+1)}{2}, find an expression for \sum_{r=1}^{n} (r+5). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/eoJeQ5KE4soN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZR4h2Eo2N2Kg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/ZR4h2Eo2N2Kg.jpg</video:thumbnail_loc>

            <video:title>Applying properties (3)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to solve summations containing both addition and constant multiples. You will master combining linearity properties to break down complex expressions into simpler, solvable parts. Solved: 7. Evaluate \sum_{r=1}^{5} (3r-2) using linearity properties. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/ZR4h2Eo2N2Kg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BDHKZPnQf5Rb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/BDHKZPnQf5Rb.jpg</video:thumbnail_loc>

            <video:title>Disconnected separation</video:title>

            <video:description><![CDATA[
Isolated charge remains constant. How does increasing plate separation affect stored energy when the battery is disconnected? We calculate the final energy and the mechanical work required. Solved: A parallel-plate vacuum capacitor has 12.0 \text{ mJ} of energy stored in it. The separation between the plates is 3.00 \text{ mm}. If the capacitor is disconnected from its power supply and the separation between the plates is then increased to 9.00 \text{ mm}, determine (a) the final energy stored in the capacitor and (b) the external work required to pull the plates apart. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/BDHKZPnQf5Rb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fMOJ6XvkydmQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/fMOJ6XvkydmQ.jpg</video:thumbnail_loc>

            <video:title>Deriving terms from sums</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to extract the rth term of a sequence by calculating the difference between successive partial sums. You will master the algebraic subtraction of the sum of the first n-1 terms from the sum of the first n terms to isolate a general rule. Solved: 8. The sum of the first n terms of a sequence is S_n = n^2 + 3n. Find the expression for its rth term. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/fMOJ6XvkydmQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wdaZCEcsx1ve</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/wdaZCEcsx1ve.jpg</video:thumbnail_loc>

            <video:title>Arithmetic means (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the insertion of multiple arithmetic means between two given values. You will master solving for the common difference by treating the boundary values as terms in a finite sequence to find the missing intermediate numbers. Solved: 7. Insert four arithmetic means between -2 and 13. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/wdaZCEcsx1ve.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pnMbpluWHOWJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/206/pnMbpluWHOWJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on manipulating Sines and Cosines using complex numbers. Solved: 1.Solve the equation \cos5\theta+5\cos3\theta+10\cos\theta=\frac{1}{2} completely2. For |r| < 1, show that \left( \sum_{n=0}^{\infty} r^{2n} \cos n\theta \right)^2 + \left( \sum_{n=0}^{\infty} r^{2n} \sin n\theta \right)^2 = \frac{1}{1 - 2r^2 \cos \theta + r^4}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/206/pnMbpluWHOWJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ywMsMqMSDSlK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/ywMsMqMSDSlK.jpg</video:thumbnail_loc>

            <video:title>Calculating parameters (3)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate the total number of terms in a finite arithmetic sequence by rearranging the general term formula. You will master isolating the unknown position variable using the first term, common difference, and the last known value. Solved: 3. How many terms are in the sequence 10,14,18,…,102? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/ywMsMqMSDSlK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TiobPFx4wtZZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/TiobPFx4wtZZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on moments of couples and their resultants. Solved: Two 80-N force are applied as shown to the corners B and D of a rectangular plate. (a) Determine the moment of the couple formed by the two forces by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples. (b) Use the result obtained to determine the perpendicular distance between lines BE and DF. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/TiobPFx4wtZZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738750139450.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ni94OwjQ8vyU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/ni94OwjQ8vyU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: Two parallel 60-N forces are applied as shown to the corners A and C of a 200-mm square plate. Determine the moment of the couple formed by two forces (a) by multiplying their magnitude by their perpendicular distance, (b) by resolving each force into horizontal and vertical component and adding the moments of the two resulting couples. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/ni94OwjQ8vyU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738751935129.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dETpUxInMZQq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/dETpUxInMZQq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on equilibrium of a particle in three dimensions. Solved: A container is supported by three cables that are attached to a ceiling as shown. Determine the weight W of the container, knowing that the tension in cable AB is 6KN. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/dETpUxInMZQq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739875555058.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/urYzvC_Ui15u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/urYzvC_Ui15u.jpg</video:thumbnail_loc>

            <video:title>Generating terms (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates evaluating linear and alternating quadratic rules to generate terms. You will master substituting position values into formulae containing indices and negative bases to resolve complex numerical patterns with precision. Solved: 2. Obtain the first three terms of the sequence u_r = (-1)^r \cdot r^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/urYzvC_Ui15u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hYBPgVu_ZYwR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/hYBPgVu_ZYwR.jpg</video:thumbnail_loc>

            <video:title>Generating terms (4)</video:title>

            <video:description><![CDATA[
This walkthrough covers generating terms from explicit linear, alternating, and fractional formulae, alongside recursive definitions. You will master substituting positions and previous terms into these rules to calculate specific values with technical precision. Solved: 4. A sequence is defined by u_1 = 4 and u_r = 3u_{r-1} - 2. Find the values of u_2 and u_3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/hYBPgVu_ZYwR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bypWU3gnKGi3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/bypWU3gnKGi3.jpg</video:thumbnail_loc>

            <video:title>Sum and term ratios</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving arithmetic progression problems involving ratios of terms and their sums. You will master using algebraic substitution to find the first term and common difference when given proportional relationships between different parts of a series. Solved: 10. The ratio of the sum of n terms of two different arithmetic progressions is (7n + 1) : (4n + 27). Find the ratio of their 11th terms. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/bypWU3gnKGi3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gg3KHp0fLnB_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/gg3KHp0fLnB_.jpg</video:thumbnail_loc>

            <video:title>Three consecutive terms</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the algebraic advantage of defining three consecutive arithmetic terms as a-d, a, and a+d. You will master solving for unknown variables by using their sum and product to eliminate the common difference. Solved: 9. The sum of three consecutive terms in an arithmetic progression is 18 and their product is 192. Find the three terms. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/gg3KHp0fLnB_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ul0Oekeru8WM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/Ul0Oekeru8WM.jpg</video:thumbnail_loc>

            <video:title>Generating terms (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate specific terms of a sequence by substituting position values into a given explicit formula. You will master the process of generating the first four terms by evaluating the linear expression at r equals one, two, three, and four. Solved: 1. Find the first four terms of a sequence whose general term is u_r = 5r - 3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/Ul0Oekeru8WM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0xPOxg92F8XG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/0xPOxg92F8XG.jpg</video:thumbnail_loc>

            <video:title>Arithmetic series</video:title>

            <video:description><![CDATA[
An arithmetic series is the sum of terms in a linear progression defined by a common difference. This lesson provides the standard formulae for calculating partial sums using the first term, common difference, and the last term.  
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          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/0xPOxg92F8XG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gmyrdMkbi0vI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/gmyrdMkbi0vI.jpg</video:thumbnail_loc>

            <video:title>Arithmetic mean</video:title>

            <video:description><![CDATA[
Define the arithmetic mean as the middle value between two terms in a linear progression. This lesson explains how to calculate a single mean or insert multiple means between numbers by finding the required common difference.  
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          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/gmyrdMkbi0vI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MbADLP0nzVsE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1013/MbADLP0nzVsE.jpg</video:thumbnail_loc>

            <video:title>Recurrence relations</video:title>

            <video:description><![CDATA[
Recurrence relations define each term in a sequence based on its preceding terms. This lesson explains how to generate subsequent values using a starting term and a recursive rule.  
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          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1013/MbADLP0nzVsE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gFYbGjO_acXR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/gFYbGjO_acXR.jpg</video:thumbnail_loc>

            <video:title>Reactions</video:title>

            <video:description><![CDATA[
Alkanes undergo combustion and free-radical substitution despite their inert nature. How does the chlorination of methane proceed through initiation, propagation, and termination steps without ionic intermediates? This lesson maps the radical mechanism and balances combustion equations precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/gFYbGjO_acXR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hmZ4GOxKQvLn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/hmZ4GOxKQvLn.jpg</video:thumbnail_loc>

            <video:title>Evaluating series (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate the sum of an arithmetic progression using the first term and the last term. You will master the algebraic steps for precise summation when the boundaries of the linear series are known. Solved: 4. Find the sum of the first 20 terms of an arithmetic progression where the first term is 5 and the 20th term is 75. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/hmZ4GOxKQvLn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2Ksy91w0bl14</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/2Ksy91w0bl14.jpg</video:thumbnail_loc>

            <video:title>Three consecutive terms</video:title>

            <video:description><![CDATA[
Learn to represent three consecutive terms in an arithmetic progression using a symmetric algebraic notation. This method simplifies calculations by making the common difference cancel out during summation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/2Ksy91w0bl14.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EaTlC_hiS_jC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/EaTlC_hiS_jC.jpg</video:thumbnail_loc>

            <video:title>Calculating parameters (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to solve for the specific position of a term within an arithmetic progression using the general term formula. You will master the algebraic steps to identify exactly when a sequence reaches a target value by rearranging for the unknown position variable. Solved: 2. A student saves ₦500 in the first week and increases the savings by ₦200 every week. By what week will the student save exactly ₦4,500? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/EaTlC_hiS_jC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/66QWVtiBfzxa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/66QWVtiBfzxa.jpg</video:thumbnail_loc>

            <video:title>Evaluating series (2)</video:title>

            <video:description><![CDATA[
This walkthrough shows how to calculate the sum of an arithmetic progression using the first term, common difference, and total number of terms. Master the algebraic steps to find the total sum for any linear series. Solved: 5. How many terms of the sequence 3,5,7,9,11,… must be added to obtain 120? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/66QWVtiBfzxa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EVygeXKAx_DE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/862/EVygeXKAx_DE.jpg</video:thumbnail_loc>

            <video:title>Experimental determination</video:title>

            <video:description><![CDATA[
This lesson explains how to measure reaction speed by tracking concentration changes over time using physical and chemical methods. You will learn to use concentration-time graphs to calculate average and instantaneous rates for different species.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/862/EVygeXKAx_DE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/asl_6UM3VsrF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/863/asl_6UM3VsrF.jpg</video:thumbnail_loc>

            <video:title>Concentration and rate law</video:title>

            <video:description><![CDATA[
This lesson explains the mathematical link between reactant concentration and reaction speed through the rate law equation. You will learn to identify the rate constant and reaction orders to predict how concentration changes influence the overall rate of a chemical change.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/863/asl_6UM3VsrF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NDOIxDg7URXq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/863/NDOIxDg7URXq.jpg</video:thumbnail_loc>

            <video:title>Determining reaction orders (1)</video:title>

            <video:description><![CDATA[
This lesson explains the methods used to determine reaction orders from experimental data. You will master the initial rates method and graphical analysis to find the specific exponents that link reactant concentrations to the overall rate.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/863/NDOIxDg7URXq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_3B9rW0ec1PU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/863/_3B9rW0ec1PU.jpg</video:thumbnail_loc>

            <video:title>Determining reaction orders (2)</video:title>

            <video:description><![CDATA[
This walkthrough concludes the previous illustration on determining reaction orders using the initial rates method. You will master the final algebraic steps to calculate the specific rate constant and establish the complete rate law for the reaction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/863/_3B9rW0ec1PU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iCDEE8_0TKsw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/iCDEE8_0TKsw.jpg</video:thumbnail_loc>

            <video:title>Geometric mean</video:title>

            <video:description><![CDATA[
Define the geometric mean as the middle value between terms in an exponential progression. This lesson explains how to calculate a single mean or insert multiple geometric means between numbers by determining the required common ratio.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/iCDEE8_0TKsw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eThNpSukHlYC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/eThNpSukHlYC.jpg</video:thumbnail_loc>

            <video:title>Condensing series (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates condensing fractional series into sigma notation by solving for numerator and denominator rules separately. You will master mapping term values to their index positions to derive a single algebraic formula for the total sum. Solved: 4. Express the series \frac{1}{2} + \frac{2}{3} + \frac{3}{4} + \dots + \frac{n}{n+1} using sigma notation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/eThNpSukHlYC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2o5m6qyixiV7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/2o5m6qyixiV7.jpg</video:thumbnail_loc>

            <video:title>Three consecutive terms</video:title>

            <video:description><![CDATA[
Represent three consecutive terms of a geometric progression as a/r, a, and ar to simplify algebraic products. This lesson explains how this notation allows the common ratio to cancel out, making it easier to solve for unknown variables in exponential sequences.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/2o5m6qyixiV7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oikdYbWayt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/oikdYbWayt.jpg</video:thumbnail_loc>

            <video:title>Successive differentiation</video:title>

            <video:description><![CDATA[
Change has a rate. How do you differentiate a function repeatedly to find the third or fourth derivative? See the pattern for successive differentiation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/oikdYbWayt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8V8kyV2qsOF0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/8V8kyV2qsOF0.jpg</video:thumbnail_loc>

            <video:title>Rebound heights</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates calculating the rebound height of a bouncing ball using geometric sequences. You will master applying the nth term formula to model energy loss and determine exact heights after multiple strikes on the ground. Solved: 13. A ball is dropped from a height of 20\text{m}. Each time it strikes the ground, it bounces back to 75%% of the height from which it fell. Find the height of the 6th bounce. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/8V8kyV2qsOF0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6_W5tfbWBfJ_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/6_W5tfbWBfJ_.jpg</video:thumbnail_loc>

            <video:title>Calculating parameters</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to find the first term and common ratio of a geometric progression given two specific terms. You will learn the algebraic steps to solve simultaneous equations and calculate these parameters accurately. Solved: 1. The second term of a geometric progression is 6 and the 5th term is 162. Find the first term and the common ratio. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/6_W5tfbWBfJ_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vyNy8Suo1vVJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/vyNy8Suo1vVJ.jpg</video:thumbnail_loc>

            <video:title>Calculating r from sums</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates calculating the common ratio using given sums of different numbers of terms in a geometric progression. You will master setting up simultaneous equations to eliminate the first term and solve for all possible values of r. Solved: 9. In a geometric progression, the sum of the first two terms is 9 and the sum of the first four terms is 45. Find the possible values of the common ratio. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/vyNy8Suo1vVJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7DsaEGZbu6gC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/7DsaEGZbu6gC.jpg</video:thumbnail_loc>

            <video:title>Evaluating series (3)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates calculating the sum of an arithmetic series where you must first solve for the total number of terms. You will master using the last term to find the sequence length before applying the final summation formula. Solved: 6. Find the sum of all two-digit positive integers that are divisible by 7. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/7DsaEGZbu6gC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FSC5pgBWINc5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/FSC5pgBWINc5.jpg</video:thumbnail_loc>

            <video:title>Geometric means (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the insertion of multiple geometric means between two given numbers. You will master calculating the required common ratio by treating the boundary values as the first and last terms of a sequence. Solved: 6. Find three geometric means between 5 and 80. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/FSC5pgBWINc5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XMz_mKwlS2Ns</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/XMz_mKwlS2Ns.jpg</video:thumbnail_loc>

            <video:title>Calculating minimum r</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates determining the minimum number of terms required for a geometric sequence to reach a target value. You will master using logarithms to solve exponential inequalities and find the smallest integer position that satisfies a specific threshold. Solved: 8. How many terms of the geometric progression 3, 6, 12, \dots are needed so that the rth term is at least 1,000,000? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/XMz_mKwlS2Ns.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/isbAnWFb_clq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/isbAnWFb_clq.jpg</video:thumbnail_loc>

            <video:title>Nested squares</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving geometry problems using geometric sequences. You will master determining the common ratio of areas for nested squares and calculating the area of specific squares within the sequence using the general term formula. Solved: 12. A square has a side length of 10\text{ cm}. A second square is formed by joining the midpoints of the sides of the first square. This process is repeated to form a third square.(a) Find the area of the first three squares.(b) Determine the common ratio of the sequence of areas.(c) Find the area of the 8th square. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/isbAnWFb_clq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pgUhxLd_TOza</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/76/pgUhxLd_TOza.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating continuity of real-valued two-variable functions. Solved: Investigate the continuity of \begin {cases} \frac {x^2 -y^2} {x^2 + y^2}, (x, y) \ne (0, 0) \\ 0, (x,y) = (0, 0) \end {cases} at (0, 0). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/76/pgUhxLd_TOza.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UmOUuVyT5rvc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/UmOUuVyT5rvc.jpg</video:thumbnail_loc>

            <video:title>Algebraic terms</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for variables when arithmetic progression terms are expressed algebraically. You will master setting up equations using the common difference property to find unknown values and define the specific progression. Solved: 11. The first three terms of an arithmetic progression are y, 3y + 2 and 7y - 4. Find the value of y and the 50th term of the progression. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/UmOUuVyT5rvc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jMlZzexl80gu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/jMlZzexl80gu.jpg</video:thumbnail_loc>

            <video:title>Evaluating series</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates calculating the sum of a geometric series where the common ratio is less than one. You will master applying the finite sum formula to find the total accumulation of terms in a decreasing sequence. Solved: 3. Calculate the sum of the first 6 terms of the geometric progression 8, 4, 2, \dots. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/jMlZzexl80gu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dPC2YxI5h0MT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/dPC2YxI5h0MT.jpg</video:thumbnail_loc>

            <video:title>Three consecutive terms (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for unknown variables when geometric terms are given as algebraic expressions. You will master using the common ratio property to set up equations and calculate the missing values to find the complete sequence. Solved: 7. Show that if \log x, \log y, \log z are three consecutive terms of an arithmetic progression, then x, y, z are in geometric progression. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/dPC2YxI5h0MT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gHjxUPTIb5ei</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/gHjxUPTIb5ei.jpg</video:thumbnail_loc>

            <video:title>Power sum identities (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate the sum of the cubes of the first n natural numbers using the standard power sum identity when the lower limit is not one. You will master applying the specific algebraic formula to find totals for cubed sequences efficiently. Solved: 4. Evaluate \sum_{r=4}^{12} r^3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/gHjxUPTIb5ei.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gWce9dAROaBr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/gWce9dAROaBr.jpg</video:thumbnail_loc>

            <video:title>Direct sums</video:title>

            <video:description><![CDATA[
Evaluate the sum of an arithmetic series by identifying the first term, common difference, and last term. We calculate the number of terms then apply the standard formula to find the total value. Solved: 12. Evaluate 3 + 6 + 9 + 12 + \dots + 270. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/gWce9dAROaBr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AomEvhtApXzi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/AomEvhtApXzi.jpg</video:thumbnail_loc>

            <video:title>Harmonic progressions</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for terms in a harmonic progression by using their reciprocals. You will master converting harmonic terms into an arithmetic progression to find the common difference and then calculating the required term. Solved: 1. Find the 10th term of the harmonic progression \frac{1}{2}, \frac{1}{5}, \frac{1}{8}, \dots 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/AomEvhtApXzi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NMgR4vIGNQ6c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/NMgR4vIGNQ6c.jpg</video:thumbnail_loc>

            <video:title>Arithmetic-geometric progressions</video:title>

            <video:description><![CDATA[
This walkthrough shows how to calculate the rth term of a sequence formed by multiplying arithmetic and geometric progressions. Master isolating the linear and exponential parts to build the general term formula. Solved: 2. Find the r\text{th} term of the sequence 3, 8, 20, 48, \dots 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/NMgR4vIGNQ6c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YKvvMzZxxCEu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/YKvvMzZxxCEu.jpg</video:thumbnail_loc>

            <video:title>Parameters from infinite sum</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for the first term or common ratio given the sum to infinity of a geometric series. You will master rearranging the infinite sum formula to calculate missing parameters accurately. Solved: 3. The sum to infinity of a geometric series is 20 and the common ratio is 0.6. Find the first term. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/YKvvMzZxxCEu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lPle3rvDGOmV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/665/lPle3rvDGOmV.jpg</video:thumbnail_loc>

            <video:title>Commands (3): touch and mkdir</video:title>

            <video:description><![CDATA[
Development starts with creating files and directories. This lesson introduces `touch` for instantly creating new files and `mkdir` for making new directories, the two fundamental commands for building any project's structure from the command line.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/665/lPle3rvDGOmV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ibz8mNj35Kpx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1397/ibz8mNj35Kpx.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Alkenes contain a carbon-carbon double bond formed by one sigma and one pi overlap. How does sp2 hybridisation create the trigonal planar geometry and restrict rotation around the double bond? This lesson defines the orbital structure, bond angles, and general formula precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1397/ibz8mNj35Kpx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BxhtLcPwtw2x</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/BxhtLcPwtw2x.jpg</video:thumbnail_loc>

            <video:title>Harmonic mean</video:title>

            <video:description><![CDATA[
Calculate average speed for round trips using the harmonic mean formula. This walkthrough demonstrates why simple averages fail and provides a step-by-step calculation for a car travelling between two points. Solved: 6. A car travels from point A to point B at 60\text{km/hr} and returns from B to A at 40\text{km/hr}. Find the average speed for the journey. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/BxhtLcPwtw2x.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/knaOoXAh1vHu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/knaOoXAh1vHu.jpg</video:thumbnail_loc>

            <video:title>Converting recurring decimals (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to convert a simple recurring decimal into a fraction using infinite geometric series. You will master expanding the decimal into a sequence of terms and applying the sum to infinity formula to find its exact fractional value. Solved: 4. Express 0.777... as a rational fraction in its simplest form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/knaOoXAh1vHu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Da7sG0Rtj18e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/Da7sG0Rtj18e.jpg</video:thumbnail_loc>

            <video:title>Depreciation</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate asset value loss using geometric sequences. You will master applying the rth term formula to model annual depreciation and find the final value of a laptop after several years of consistent reduction. Solved: 11. A laptop bought for \text{#500,000} loses 20%% of its value every year. What will be its value at the end of the 4th year? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/Da7sG0Rtj18e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sSvSLuHzy68U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/sSvSLuHzy68U.jpg</video:thumbnail_loc>

            <video:title>Power sum identities (1)</video:title>

            <video:description><![CDATA[
This walkthrough shows how to calculate the sum of the first n natural numbers and their squares using power sum identities. You will master applying the formula to find totals quickly without manual addition. Solved: 3. Evaluate \sum_{r=1}^{10} (r^2 + 2r). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/sSvSLuHzy68U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VdQFfX3udGjB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/VdQFfX3udGjB.jpg</video:thumbnail_loc>

            <video:title>Harmonic progressions</video:title>

            <video:description><![CDATA[
Harmonic progressions are sequences where the reciprocals of the terms form an arithmetic progression. This lesson explains how to identify these patterns and calculate the nth term by first resolving the underlying arithmetic sequence.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/VdQFfX3udGjB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MNEHbwDonA_7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/MNEHbwDonA_7.jpg</video:thumbnail_loc>

            <video:title>Converting recurring decimals (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates converting complex recurring decimals with non-repeating parts into exact fractions. You will master separating the constant part from the geometric progression and applying the sum to infinity formula to find the total value. Solved: 5. Express 0.1545454... as a rational fraction. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/MNEHbwDonA_7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yrDjNTc2yXgK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/yrDjNTc2yXgK.jpg</video:thumbnail_loc>

            <video:title>First law of thermodynamics</video:title>

            <video:description><![CDATA[
This lesson explains how energy cannot be created or destroyed, only changed from one form to another. You will learn to calculate internal energy changes using heat and work. Understanding this law is vital for tracking energy flow in chemical reactions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/yrDjNTc2yXgK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pn7BdIsY3Y2u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/287/Pn7BdIsY3Y2u.jpg</video:thumbnail_loc>

            <video:title>Circle of Apollonius</video:title>

            <video:description><![CDATA[
Convert a complex equation with a constant ratio of distances into its Cartesian form. This walkthrough demonstrates how to square both sides and complete the square to identify the centre and radius of the resulting circle. Solved: 1.What figure does |\frac{z}{z+3}|=1 describe?2. Describe and sketch the region defined by |z - 4| < 4 on the complex plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/287/Pn7BdIsY3Y2u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WkuE_XUOwfV8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/WkuE_XUOwfV8.jpg</video:thumbnail_loc>

            <video:title>Power sum identities</video:title>

            <video:description><![CDATA[
Learn the formulas for summing natural numbers, squares, and cubes. These identities allow you to calculate total values for integer power series quickly and accurately.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/WkuE_XUOwfV8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/40XbCMvm6QjM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/287/40XbCMvm6QjM.jpg</video:thumbnail_loc>

            <video:title>Equidistant points</video:title>

            <video:description><![CDATA[
Identify equations where the modulus represents equal distance from fixed points. A single fixed point defines a circle, while points equidistant from two fixed points form a perpendicular bisector. Recognising these algebraic patterns is essential for mapping boundaries in engineering and physics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/287/40XbCMvm6QjM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/k3NRw8W81EeH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/287/k3NRw8W81EeH.jpg</video:thumbnail_loc>

            <video:title>Equidistant points (2)</video:title>

            <video:description><![CDATA[
Derive the Cartesian equation and sketch the perpendicular bisector for points equidistant from two fixed coordinates. This walkthrough shows how to solve the modulus equation by substituting the rectangular form of a complex number to find the linear path on the Argand plane. Solved: 1.What figure does |z-(8+2i)|+|z-(5+6i)|=5 does not describe an ellipse on the complex plane?2. Describe the locus of \text{Re} \left( \frac{1}{z} \right) = \frac{1}{8} on the z-plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/287/k3NRw8W81EeH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/StqreoB0Zq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1113/StqreoB0Zq.jpg</video:thumbnail_loc>

            <video:title>Product rule</video:title>

            <video:description><![CDATA[
Multiplying functions breaks the power rule. How do you find the gradient of a product without expanding it first? Watch to learn the correct formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1113/StqreoB0Zq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wvTgyIPKhh6I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1032/wvTgyIPKhh6I.jpg</video:thumbnail_loc>

            <video:title>Arrangements (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to apply factorials and the nPr formula to solve basic arrangement problems. You will learn to calculate the total number of ways to order objects in a line when given specific set sizes and selection requirements. Solved: 1. In how many different ways can the letters of the word LAGOS be arranged? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1032/wvTgyIPKhh6I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MWFkGHSWfEoB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1033/MWFkGHSWfEoB.jpg</video:thumbnail_loc>

            <video:title>Cyclic arrangements (1)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples on arranging distinct objects around a circular table. You will apply the (n-1)! Formula to solve seating problems where clockwise and anticlockwise orders are considered distinct. Solved: 1. 6 students are to sit round a table for a meeting. In how many different ways can they be seated? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1033/MWFkGHSWfEoB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FP9HtglDaLrd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/856/FP9HtglDaLrd.jpg</video:thumbnail_loc>

            <video:title>Work and energy</video:title>

            <video:description><![CDATA[
This lesson explains energy as the capacity to do work or transfer heat. You will learn how work is done through volume changes against external pressure and how to distinguish between work done on or by a system. These concepts are the foundation for the first law of thermodynamics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/856/FP9HtglDaLrd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YbbD_coOoFzo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/856/YbbD_coOoFzo.jpg</video:thumbnail_loc>

            <video:title>System and surrounding</video:title>

            <video:description><![CDATA[
This lesson defines the system as the part of the universe being studied and the surroundings as everything else. You will learn to identify open, closed, and isolated systems based on how they exchange matter and energy. This distinction is vital for tracking heat and work in any chemical process.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/856/YbbD_coOoFzo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aLbOqYtmQmt8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1033/aLbOqYtmQmt8.jpg</video:thumbnail_loc>

            <video:title>Cyclic arrangements (2)</video:title>

            <video:description><![CDATA[
This lesson focuses on circular arrangements that can be turned over, such as beads on a necklace. You will learn to use the modified formula to remove duplicate counts caused by identical clockwise and anticlockwise orientations. Solved: 2. A jewelry maker has 7 different coloured beads to thread into a circular wire to make a necklace. In how many unique ways can the beads be arranged? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1033/aLbOqYtmQmt8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MGagi9vvZsET</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/MGagi9vvZsET.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
This lesson details the systematic workflow for solving particle equilibrium problems. It covers the standard sequence for constructing free-body diagrams and resolving forces to form equations for calculating unknown magnitudes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/MGagi9vvZsET.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MMN55mmuABbC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/MMN55mmuABbC.jpg</video:thumbnail_loc>

            <video:title>Zero-order reactions</video:title>

            <video:description><![CDATA[
Zero-order reactions maintain a constant speed regardless of reactant concentration. You will learn the integrated rate law equation and how to identify these reactions from linear concentration-time graphs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/MMN55mmuABbC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7Q6R8MK16gS3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/7Q6R8MK16gS3.jpg</video:thumbnail_loc>

            <video:title>Polyatomic ions</video:title>

            <video:description><![CDATA[
This lesson applies Lewis structure rules to polyatomic ions. We will draw the Tetrafluoroborate (BF4-), Hydronium (H3O+), and Disulfide (S22-) ions. The key step is adjusting the total valence electron count based on the overall charge.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/7Q6R8MK16gS3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6cDqv62k2Qk_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/997/6cDqv62k2Qk_.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Define the Cartesian product as the set of all possible ordered pairs where the first element belongs to set A and the second to set B. You will learn the formal notation and the rule that A cross B is only equal to B cross A when the sets are identical. This is the basis for all relations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/997/6cDqv62k2Qk_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UBRsrKwuceWU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FQr3njbcDJ/Thumbnails/1203/UBRsrKwuceWU.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson outlines the PHY 102 course structure and its alignment with the NUC CCMAS syllabus. You will learn how the modules are sequenced to cover all electricity and magnetism topics required for your university exams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FQr3njbcDJ/Previews/1203/UBRsrKwuceWU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EkMIi9O5zO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/EkMIi9O5zO.jpg</video:thumbnail_loc>

            <video:title>Reciprocal trigonometric functions</video:title>

            <video:description><![CDATA[
Secant, cosecant and cotangent appear in advanced physics. How do you differentiate these reciprocals without starting from scratch? Watch the quotient rule apply to primary trig functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/EkMIi9O5zO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H6bcsJy_5Xq6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1037/H6bcsJy_5Xq6.jpg</video:thumbnail_loc>

            <video:title>Use of Pascal's triangle</video:title>

            <video:description><![CDATA[
Watch how to apply Pascal's triangle coefficients to expand some binomials. You will learn to pair each number from the triangle with the decreasing and increasing powers of the two terms. This step-by-step calculation shows how to get the full expansion accurately. Solved: 1. Expand (x-2)^4 completely, using Pascal's triangle. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1037/H6bcsJy_5Xq6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jsvGQ6hPPFD5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1034/jsvGQ6hPPFD5.jpg</video:thumbnail_loc>

            <video:title>Arrangements with identical items (1)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples on arranging sets that contain identical items. You will apply the formula to remove duplicate patterns and calculate the unique total for word and digit problems. Solved: 1. In how many unique ways can the letters of the word ABUJA be arranged? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1034/jsvGQ6hPPFD5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wQHnZlfDng6t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/856/wQHnZlfDng6t.jpg</video:thumbnail_loc>

            <video:title>Heat capacities</video:title>

            <video:description><![CDATA[
This lesson explains heat capacity as the energy required to raise a substance's temperature. You will learn the difference between specific and molar heat capacity and how these values determine how much heat a system can absorb. It is the core concept for all calorimetry calculations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/856/wQHnZlfDng6t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yYmzuwyBSSPS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1037/yYmzuwyBSSPS.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides an overview of the Binomial Theorem course. You will understand the curriculum structure, including basic expansion patterns, the general formula for large powers, and applications for negative and fractional indices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1037/yYmzuwyBSSPS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/u2HHxewAL0Hs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1040/u2HHxewAL0Hs.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson outlines the course structure and the critical role of stoichiometry in predicting reaction outcomes. You will understand how chemical equations serve as quantitative recipes for industrial and laboratory processes. It sets the foundation for mastering mass conservation and reaction balancing.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1040/u2HHxewAL0Hs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jrhKMSxd1u1R</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/jrhKMSxd1u1R.jpg</video:thumbnail_loc>

            <video:title>Differences</video:title>

            <video:description><![CDATA[
Identify and shade the geometric regions representing set differences and symmetric differences in Venn diagrams. You will isolate elements unique to specific sets by excluding intersections, establishing the spatial logic required for data subtraction and comparative analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/jrhKMSxd1u1R.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8ix4bmiAuvEv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/8ix4bmiAuvEv.jpg</video:thumbnail_loc>

            <video:title>Multiple linear inequalities (1)</video:title>

            <video:description><![CDATA[
Solve multiple linear inequalities to find their common solution region. This walkthrough shows how to solve each part separately and then combine them on a single number line to identify the overlapping set. Mastering this is essential for handling systems with several constraints. Solved: 3. Given the inequalities 2(3-x) > 9 \dots (i)\frac{x+1}{2} + \frac{2x-1}{3} \ge 1 \dots (ii) Show the interval(s) where x lies if it satisfies (a) (i) or (ii) (b) (i) and (ii). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/8ix4bmiAuvEv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BlWelU1PUHOr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1024/BlWelU1PUHOr.jpg</video:thumbnail_loc>

            <video:title>Principle</video:title>

            <video:description><![CDATA[
This lesson explains the formal principle of mathematical induction as a logical proof method. You will learn the exact requirements for the base case and the inductive step to ensure a statement holds true for all natural numbers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1024/BlWelU1PUHOr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BuH_dnSz08Fh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1037/BuH_dnSz08Fh.jpg</video:thumbnail_loc>

            <video:title>Pascal's triangle</video:title>

            <video:description><![CDATA[
Build Pascal's triangle by adding adjacent numbers to find coefficients for binomial expansions. This visual tool helps you skip long multiplication and identify the numerical values needed for each term in a polynomial. Mastering this pattern ensures speed and accuracy in basic algebra.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1037/BuH_dnSz08Fh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F_1_I_hCQwMo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1042/F_1_I_hCQwMo.jpg</video:thumbnail_loc>

            <video:title>The derangement formula</video:title>

            <video:description><![CDATA[
This lesson derives the general formula for calculating derangements of n objects using the principle of inclusion and exclusion. You will learn to use subfactorials to find the total number of ways to arrange items so that none return to their original spots.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1042/F_1_I_hCQwMo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0yhhqDERm1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/0yhhqDERm1.jpg</video:thumbnail_loc>

            <video:title>Organic reagents</video:title>

            <video:description><![CDATA[
Organic reagents drive every reaction pathway. How do you distinguish electron-deficient electrophiles from electron-rich nucleophiles in a mechanism? This lesson defines both classes and their roles precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/0yhhqDERm1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hfFFxwdNkfMm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/hfFFxwdNkfMm.jpg</video:thumbnail_loc>

            <video:title>Rational inequality (1)</video:title>

            <video:description><![CDATA[
Apply a sign table to solve a rational inequality by identifying critical values from both the numerator and denominator. You will learn to determine valid intervals while excluding values that make the denominator zero, ensuring a precise solution set expressed in interval notation. Solved: 7. Solve the inequality \frac{2x-5}{x+3} \le 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/hfFFxwdNkfMm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CfLVJyZV2kPf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1041/CfLVJyZV2kPf.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson introduces how combinations are used to count geometric shapes formed by connecting points. You will learn the logic for determining the number of lines and triangles possible when points are non-collinear. It provides the framework for all geometric counting problems in this chapter.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1041/CfLVJyZV2kPf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bSfz7ReDKq_I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1032/bSfz7ReDKq_I.jpg</video:thumbnail_loc>

            <video:title>Arranging n of n objects</video:title>

            <video:description><![CDATA[
This lesson explains how to arrange every item in a given set using factorials. You will learn to calculate the total possible sequences when all available objects must be used in a specific order.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1032/bSfz7ReDKq_I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yE0C0M2R4e9I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1035/yE0C0M2R4e9I.jpg</video:thumbnail_loc>

            <video:title>Restricted arrangements (1)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples on arranging items with fixed starting or ending positions. You will learn to lock specific objects into place and calculate the permutations for the remaining available slots. Solved: 1. In how many ways can the letters of the word ORANGE be arranged if the word must be start with the letter O and end with the letter E? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1035/yE0C0M2R4e9I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ryU_OaJShWH9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1035/ryU_OaJShWH9.jpg</video:thumbnail_loc>

            <video:title>Always together</video:title>

            <video:description><![CDATA[
Learn how to treat items that must stay together as a single unit. You will master the tie-together method to calculate arrangements for groups that move as one. This logic simplifies complex counting where specific items never separate.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1035/ryU_OaJShWH9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZjLfMZSlE_EB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1035/ZjLfMZSlE_EB.jpg</video:thumbnail_loc>

            <video:title>Restricted arrangements (2)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples on arrangements with multiple constraints. You will learn to calculate total outcomes when several objects have restricted positions or specific placement rules simultaneously. Solved: 2. 5 boys and 3 girls are to be arranged in a row for a photograph. In how many ways can they be arranged if all 3 girls must sit together? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1035/ZjLfMZSlE_EB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WnMf5gM5bZu8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/WnMf5gM5bZu8.jpg</video:thumbnail_loc>

            <video:title>Algebraic properties (2)</video:title>

            <video:description><![CDATA[
Understand the transitive property for linking multiple comparisons and the addition property for combining inequalities. This lesson also covers how squaring or taking reciprocals of positive values affects the direction of the inequality sign. These rules are essential for maintaining logical flow in proofs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/WnMf5gM5bZu8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z8KpvvTAAnx_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1032/Z8KpvvTAAnx_.jpg</video:thumbnail_loc>

            <video:title>Arranging r of n objects</video:title>

            <video:description><![CDATA[
This lesson explains how to select and arrange a specific number of items from a larger group. You will master the nPr formula to calculate total outcomes when only a portion of the available objects is used in a specific order.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1032/Z8KpvvTAAnx_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AGdog_XBYtZy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/820/AGdog_XBYtZy.jpg</video:thumbnail_loc>

            <video:title>Thomson's cathode ray experiment</video:title>

            <video:description><![CDATA[
This lesson details J.J. Thomson's cathode ray experiment. The experiment provides the definitive evidence for the electron and allows for the calculation of its charge-to-mass ratio. This discovery proved the atom is divisible, refuting a key part of Dalton's theory.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/820/AGdog_XBYtZy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tH1i3fRDnQUs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1035/tH1i3fRDnQUs.jpg</video:thumbnail_loc>

            <video:title>Never together</video:title>

            <video:description><![CDATA[
Learn how to arrange items that must never stand next to each other. You will use the gap method to place these restricted items in the spaces between others. This technique ensures specific objects stay apart in any arrangement.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1035/tH1i3fRDnQUs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_bjx5s41ioe9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/845/_bjx5s41ioe9.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
This lesson rigorously defines oxidation-reduction (redox) reactions based on the core concepts of electron transfer and changes in oxidation state. You will learn the precise relationship between oxidation and reduction, establishing the necessary foundational understanding for assigning oxidation numbers. Mastery of these fundamental definitions is critical for all subsequent redox analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/845/_bjx5s41ioe9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T3nGb_Pnufdz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/T3nGb_Pnufdz.jpg</video:thumbnail_loc>

            <video:title>Free energy of reaction</video:title>

            <video:description><![CDATA[
Calculate the standard Gibbs free energy of reaction for the oxidation of ammonia using provided molar formation data. This walkthrough demonstrates how to apply the summation law by subtracting total reactant energy from product energy. Master this method to determine overall reaction spontaneity. Solved: Calculate the standard Gibbs free energy of the reaction4NH_{3(g)} + 5O_{2(g)} \rightarrow 4NO_{(g)} + 6H_{2}O_{(g)}Given that molar Gibbs free energy of formation as follows:NH_{3(g)} = -16.45 \text{ kJ}; NO_{(g)} = +86.55 \text{ kJ}H_{2}O_{(g)} = -228.57 \text{ kJ} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/T3nGb_Pnufdz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eaKiR8niIX0w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/eaKiR8niIX0w.jpg</video:thumbnail_loc>

            <video:title>Sign tables</video:title>

            <video:description><![CDATA[
Learn to use sign tables to solve quadratic and rational inequalities by testing intervals around critical points. You will track how positive and negative factors interact to determine the overall sign of an expression. This systematic approach ensures accuracy in complex region-based problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/eaKiR8niIX0w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BL8X8BtoV8fT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Thumbnails/884/BL8X8BtoV8fT.jpg</video:thumbnail_loc>

            <video:title>Calculating the sum to infinity</video:title>

            <video:description><![CDATA[
A worked example determining if a GP is convergent and, if so, calculating its sum to infinity. This demonstrates the application of the S??? formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iqVp8FuysG/Previews/884/BL8X8BtoV8fT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yc7LXxyCWzPj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1036/yc7LXxyCWzPj.jpg</video:thumbnail_loc>

            <video:title>Making selections (1)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples on picking a subset from a larger group using the nCr formula. You will learn to calculate total selections for basic committee and team problems where the order of items does not change the outcome. Solved: 1. A coach needs to select 3 players for a basketball team from a group of 10 available students. In how many ways can this be done? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1036/yc7LXxyCWzPj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/saW5LaZnR8SA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/saW5LaZnR8SA.jpg</video:thumbnail_loc>

            <video:title>Equations of motion (1)</video:title>

            <video:description><![CDATA[
This lesson isolates the horizontal component of projectile motion. We establish that this motion proceeds at a constant velocity because horizontal acceleration is zero. Master this independent motion principle to calculate the total horizontal displacement or range over time.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/saW5LaZnR8SA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7NhOIZ8vF6Id</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/694/7NhOIZ8vF6Id.jpg</video:thumbnail_loc>

            <video:title>Worked Example</video:title>

            <video:description><![CDATA[
This video provides a specific worked example for converting a hexadecimal number to another base. We will follow the two-step conversion process, solidifying your ability to convert between any two non-denary bases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/694/7NhOIZ8vF6Id.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WgQk6L38wpLM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/688/WgQk6L38wpLM.jpg</video:thumbnail_loc>

            <video:title>Binary and Octal System</video:title>

            <video:description><![CDATA[
This lesson introduces you to the binary (base 2) and octal (base 8) number systems. You'll learn their structure and how they differ from the decimal system. This is a critical step towards understanding computer programming and data representation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/688/WgQk6L38wpLM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GQNZl7VXKXjO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1036/GQNZl7VXKXjO.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
This lesson covers the fundamental identities of combinations used to simplify complex counting problems. You will master the symmetry rule, Pascal’s identity, and key deductions for cases where r equals zero, one, or n.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1036/GQNZl7VXKXjO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dZmOpSABdCjP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1044/dZmOpSABdCjP.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson explains why substances absorb or release heat during state changes at constant temperature. You will define enthalpies of fusion, vaporisation, and sublimation. These concepts are vital for calculating energy shifts in physical transitions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1044/dZmOpSABdCjP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/emdB2MVClV_k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/96/emdB2MVClV_k.jpg</video:thumbnail_loc>

            <video:title>Worked examples I</video:title>

            <video:description><![CDATA[
Worked examples on transformation of coordinates. Solved: Given that the x-y coordinates system is rotated by \theta=\frac{\pi}{4} to form a new coordinates system u-v,a)Sketch the new axes and obtain the rotation matrix Ab)If an ellipse is defined in the new coordinate system by \frac{u^2}{4}+\frac{v^2}{9}=1, what is its equation in the x-y coordinates system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/96/emdB2MVClV_k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kz7hSgj8RfhO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/kz7hSgj8RfhO.jpg</video:thumbnail_loc>

            <video:title>Standard projectiles (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates the systematic solution to a standard ground-to-ground projectile problem. We resolve the initial velocity into components and use the derived trajectory equations to calculate the maximum height and horizontal range. Solved: 1. A football is kicked with an initial speed of 20.0 \text{ m/s} at an angle of 30.0^\circ to the horizontal. Calculate(a) the maximum height reached,(b) the total time of flight, and(c) the horizontal range. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/kz7hSgj8RfhO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M9SzBXph6gaT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/827/M9SzBXph6gaT.jpg</video:thumbnail_loc>

            <video:title>Neutral molecules</video:title>

            <video:description><![CDATA[
This lesson details rules for drawing Lewis structures for neutral molecules like Sulfur Dichloride (SCl2), Dichlorodifluoromethane (CCl2F2), Phosgene (COCl2), and Carbon Dioxide (CO2). We apply the systematic method: count valence electrons, arrange bonds, and place lone pairs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/827/M9SzBXph6gaT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pkp4Yx3o4n1r</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/Pkp4Yx3o4n1r.jpg</video:thumbnail_loc>

            <video:title>Percent composition</video:title>

            <video:description><![CDATA[
This lesson defines percent composition and details its calculation for any compound. We establish why this mass-based ratio is the mandatory initial data for empirical formula determination. Solved: Calculate the mass percentages of the elements in ammonium nitrate;NH_4NO_3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/Pkp4Yx3o4n1r.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dPCOBiDvwUui</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1035/dPCOBiDvwUui.jpg</video:thumbnail_loc>

            <video:title>Fixed position</video:title>

            <video:description><![CDATA[
Understand how to calculate arrangements when certain items are locked in specific spots. You will learn to ignore fixed items and only permute the remaining objects to find the total number of possible results. This logic is vital for problems with restricted starting or ending positions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1035/dPCOBiDvwUui.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xQKVF_AKnwDC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/xQKVF_AKnwDC.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
A projectile is an object subject only to gravity, tracing a parabolic path. This lesson establishes the principle of independent motion: horizontal velocity remains constant, while the vertical component undergoes free-fall acceleration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/xQKVF_AKnwDC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1fNXhrs846CV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1041/1fNXhrs846CV.jpg</video:thumbnail_loc>

            <video:title>Determining geometries (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the number of diagonals in a polygon. You will apply the combination formula and subtract sides to determine diagonal counts accurately.  Use this example to master advanced geometric selections. Solved: 2. How many diagonals does a regular hexagon (6 sides) have? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1041/1fNXhrs846CV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xxT5UIle4zPA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1037/xxT5UIle4zPA.jpg</video:thumbnail_loc>

            <video:title>Binomal expression</video:title>

            <video:description><![CDATA[
Learn to identify binomial expressions as algebraic terms with two parts joined by a plus or minus sign. You will see how to label these parts and their powers before expanding them. This lesson sets the foundation for using the binomial formula to solve complex brackets quickly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1037/xxT5UIle4zPA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_GBZsk3ViGTM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/_GBZsk3ViGTM.jpg</video:thumbnail_loc>

            <video:title>Curved arrow notation</video:title>

            <video:description><![CDATA[
Curved arrows map electron flow in organic reactions. How do you correctly trace movement from lone pairs or bonds to predict products? This lesson defines arrow notation for tracking bond breaking and formation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/_GBZsk3ViGTM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e4WzUCN0yXOW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1397/e4WzUCN0yXOW.jpg</video:thumbnail_loc>

            <video:title>Physical properties</video:title>

            <video:description><![CDATA[
Physical state of alkenes depends on carbon chain length just like alkanes. Why do boiling points rise with molecular weight and how does branching alter volatility? This lesson maps carbon count to gas, liquid, or solid phases precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1397/e4WzUCN0yXOW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SMcZtkMDOkfR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/SMcZtkMDOkfR.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: The vectors F_A and F_B represent the forces exerted on the pulley by the belt. Their magnitudes are |F_A| = 80N and |F_B| = 60N. Graphically determine the magnitude of the total force the belt exerts on the pulley. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/SMcZtkMDOkfR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739464016975.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/b09XjmrNz0s_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/678/b09XjmrNz0s_.jpg</video:thumbnail_loc>

            <video:title>Creating HTML strings</video:title>

            <video:description><![CDATA[
This lesson focuses on template literals, the modern JavaScript syntax for creating multi-line strings. You will learn how to embed variables and expressions directly into a string to build dynamic HTML content efficiently.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/678/b09XjmrNz0s_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3TIr1bHacdAM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/3TIr1bHacdAM.jpg</video:thumbnail_loc>

            <video:title>Motion parameters</video:title>

            <video:description><![CDATA[
This lesson defines the fundamental quantities used to describe uniform circular motion: the period, frequency, tangential speed, and angular velocity. These parameters form the basis for the subsequent kinematic analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/3TIr1bHacdAM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LS_b7d0HaYW4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/LS_b7d0HaYW4.jpg</video:thumbnail_loc>

            <video:title>Symmetric difference</video:title>

            <video:description><![CDATA[
Define the symmetric difference as the collection of elements belonging to either of two sets but not to their intersection. You will apply the delta symbol to execute this operation, establishing the logical basis for isolating unique data points across overlapping systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/LS_b7d0HaYW4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4OJDSZw86vHE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/4OJDSZw86vHE.jpg</video:thumbnail_loc>

            <video:title>Algebra of sets (1)</video:title>

            <video:description><![CDATA[
Execute a step-by-step verification of distributive and De Morgan's laws using spatial mapping. You will resolve algebraic set identities through the systematic shading of geometric regions, establishing visual proof for complex symbolic equalities. Solved: 3. Using Venn diagrams, show that A \cap (B \cup C) = (A \cap B) \cup (A \cap C). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/4OJDSZw86vHE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U_IQpT_6ipkR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1036/U_IQpT_6ipkR.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson introduces combinations where the order of selection does not matter. You will learn to identify scenarios that require simple grouping rather than arrangement and understand how to use the nCr formula to find unique selections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1036/U_IQpT_6ipkR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BPKVYBVoeqxG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1033/BPKVYBVoeqxG.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson introduces circular arrangements where the starting point is not fixed. You will learn why cyclic permutations require one item to be fixed and how to calculate unique outcomes by removing rotational duplicates.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1033/BPKVYBVoeqxG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BgLMv7kWBk0i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/BgLMv7kWBk0i.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: Determine the angle \theta for connecting member A to the plate so that the resultant force of F_A and F_B are directed horizontally to the right. Also, what is the magnitude of the resultant force? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/BgLMv7kWBk0i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739464488860.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/uIU9OCkSNX2k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/7/uIU9OCkSNX2k.jpg</video:thumbnail_loc>

            <video:title>Scalar multiplication</video:title>

            <video:description><![CDATA[
Multiplication of a vector by a scalar.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/7/uIU9OCkSNX2k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iCfsuEwkprvQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/iCfsuEwkprvQ.jpg</video:thumbnail_loc>

            <video:title>Composite functions</video:title>

            <video:description><![CDATA[
This lesson explains how to combine two functions by using the output of the first as the input for the second. You will learn to calculate resultant values and determine the domain of these combined mappings.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/iCfsuEwkprvQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ni_m13uLDdN3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/Ni_m13uLDdN3.jpg</video:thumbnail_loc>

            <video:title>Two linear equations</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of dual linear systems using elimination and substitution methods through a rigorous problem walkthrough. You will master the mechanical alignment of variables and coefficients to determine precise coordinate solutions. Solved: 1. Solve the equations (i). x - 3y = -1 , (ii). 2x + 5y = 31 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/Ni_m13uLDdN3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aMvnpdvKHXgN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/aMvnpdvKHXgN.jpg</video:thumbnail_loc>

            <video:title>Calculating parameters (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for the first term and common difference using two known terms of an arithmetic progression. You will master setting up and solving simultaneous linear equations to identify the specific parameters governing a progression. Solved: 1. The fourth term of an arithmetic progression is 13 and the 9th term is 33. Determine the first term and the common difference. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/aMvnpdvKHXgN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/G2eXV_S9PRZC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/G2eXV_S9PRZC.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (2)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/G2eXV_S9PRZC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H3RcebbFof6Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/994/H3RcebbFof6Y.jpg</video:thumbnail_loc>

            <video:title>Element-wise proofs</video:title>

            <video:description><![CDATA[
Master the formal method of element-wise proof to verify set identities and subset relationships through rigorous logical inclusion. You will apply the double-inclusion strategy to construct watertight mathematical arguments by tracking arbitrary elements across complex set operations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/994/H3RcebbFof6Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lD6fw8zW08BG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1036/lD6fw8zW08BG.jpg</video:thumbnail_loc>

            <video:title>Making selections (2)</video:title>

            <video:description><![CDATA[
This lesson covers complex selections from multiple groups with specific membership constraints. You will learn to apply the product rule alongside combinations to solve advanced committee problems and selection tasks involving several sets of objects. Solved: 2. A committee of 5 is to be formed from 6 men and 4 women. In how many ways can this be done if the committee must contain exactly 3 men and 2 women? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1036/lD6fw8zW08BG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZM_IqIaYrjAj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/665/ZM_IqIaYrjAj.jpg</video:thumbnail_loc>

            <video:title>Opening your terminal</video:title>

            <video:description><![CDATA[
Theory is over; it is time for practical work. This lesson provides the exact steps to open the terminal application on your specific operating system, whether you are using Windows, macOS, or Linux.  
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          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/665/ZM_IqIaYrjAj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KCYCuv8uYgea</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/989/KCYCuv8uYgea.jpg</video:thumbnail_loc>

            <video:title>Stoichiometric relations (2)</video:title>

            <video:description><![CDATA[
Solve for equilibrium partial pressures in the reaction of carbon monoxide and chlorine to form phosgene using the constant Kp. This walkthrough demonstrates how to derive final species pressures when starting with 1.00 atm of each reactant in a 1.00 litre container. Solved: At a certain temperature, the equilibrium constant K_p = 25.0 for the reaction: CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g) If 1.00 atm of CO(g) and 1.00 atm of Cl_2(g) are introduced into a 1.00-L container, calculate the equilibrium partial pressures of all species. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/989/KCYCuv8uYgea.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K39Ah3_eIbMo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1042/K39Ah3_eIbMo.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson defines derangements as permutations where no element appears in its original place. You will learn the notation for subfactorials and identify scenarios where every item must be displaced. These basics form the foundation for using the derangement formula in complex problems.  
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          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1042/K39Ah3_eIbMo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EQ1_R2OGkJ2K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1036/EQ1_R2OGkJ2K.jpg</video:thumbnail_loc>

            <video:title>Making selections (3)</video:title>

            <video:description><![CDATA[
This lesson covers complex selections from multiple groups where specific minimum or maximum member requirements apply. You will learn to calculate total combinations by summing results from all valid case scenarios. Master these multi-step problems to handle advanced committee selection tasks. Solved: 3. A research team of 4 members is to be formed from 5 chemists and 6 biologists. In how many ways can the team be selected if it must contain at least 3 biologists? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1036/EQ1_R2OGkJ2K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jkF2SAIHtD7d</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/jkF2SAIHtD7d.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on rational powers and roots of complex numbers. Solved: 1.Find the square root of the following:(a) z=1+i(b) z=2(c) z=-2(d) z= -2i2. Find the 4th roots of \sqrt{3} + i. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/jkF2SAIHtD7d.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fn_Y3KzHaae9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Thumbnails/1042/fn_Y3KzHaae9.jpg</video:thumbnail_loc>

            <video:title>Calculating derangements (2)</video:title>

            <video:description><![CDATA[
This lesson covers advanced derangement problems where only some items are displaced while others remain fixed. You will learn to combine selection and subfactorial calculations to solve complex constraints. Practice these multi-step examples to handle exam-standard logic accurately. Solved: 2. 4 students — Olamide, Goodness, Aminah and Johnson — submit their assignments. In how many ways can the assignments be returned so that exactly two students receive their own? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qVmlldIBwx/Previews/1042/fn_Y3KzHaae9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rOFbifeyvvgV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1043/rOFbifeyvvgV.jpg</video:thumbnail_loc>

            <video:title>Identifying specific terms (1)</video:title>

            <video:description><![CDATA[
Learn to calculate the exact value of a specific term, such as the 5th or 7th term, without expanding the entire bracket. You will use the general term formula to find coefficients and powers for a given position. This walkthrough demonstrates how to map the term number to the correct r-value. Solved: 1. Find the 6th term in the expansion of (x+3)^8. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1043/rOFbifeyvvgV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3aMrP2gJJ5qZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1039/3aMrP2gJJ5qZ.jpg</video:thumbnail_loc>

            <video:title>Numerical approximation</video:title>

            <video:description><![CDATA[
Use the binomial expansion to calculate the approximate value of roots like square root of 1.02 to a specific number of decimal places. You will learn to choose the right x-value so the series converges quickly and provides high accuracy. This lesson proves how binomials solve real-world roots. Solved: 4. Using the first three terms of the expansion of (1+x)^{1/2}, find the value of \sqrt{1.02} to four decimal places. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1039/3aMrP2gJJ5qZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GWB2oXVw_Arq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/989/GWB2oXVw_Arq.jpg</video:thumbnail_loc>

            <video:title>Stoichiometric relations (3)</video:title>

            <video:description><![CDATA[
This lesson provides a walkthrough for calculating the equilibrium constant of a forward reaction and its reverse using measured concentrations of hydrogen, bromine, and hydrogen bromide. You will apply the reciprocal rule to verify the mathematical relationship between opposing reactions. Solved: For the gas-phase equilibrium H_2(g) + Br_2(g) \rightleftharpoons 2HBr(g) the following equilibrium concentrations were measured at 520 ??C: [H_2] = 1.25 \times 10^{-3} \text{ mol L}^{-1}[Br_2] = 3.40 \times 10^{-4} \text{ mol L}^{-1}[HBr] = 6.20 \times 10^{-3} \text{ mol L}^{-1} 1. Calculate the equilibrium constant K_c for the reaction as written. 2. Determine the value of the equilibrium constant for the reverse reaction 2HBr(g) \rightleftharpoons H_2(g) + Br_2(g) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/989/GWB2oXVw_Arq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SsZgGEu50vR7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/996/SsZgGEu50vR7.jpg</video:thumbnail_loc>

            <video:title>Operations on sets (2)</video:title>

            <video:description><![CDATA[
Analyze advanced set operations using three-set Venn diagrams to resolve complex spatial intersections and nested complements. You will map algebraic expressions to geometric regions, establishing the visual rigour required to verify multi-variable set identities and data overlaps. Solved: 2. At a tech summit in Ibadan, a group of 100 software developers were surveyed about the programming languages they use.28 use Python.30 use JavaScript.42 use Go.8 use Python and JavaScript.10 use JavaScript and Go.5 use Python and Go.20 use none of the languages.How many developers use all three languages? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/996/SsZgGEu50vR7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L9x39mnMK6Pc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/1021/L9x39mnMK6Pc.jpg</video:thumbnail_loc>

            <video:title>Evaluating functions</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the value of a function by substituting specific numbers or variables into the given formula. You will practice solving step-by-step examples to find exact outputs for various algebraic expressions. Solved: 1. Let f: \mathbb{R} \to \mathbb{R} be a function defined by f(x) = 3x^2 - 5x + 2. Evaluate f(2) and f(-1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/1021/L9x39mnMK6Pc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ibOnBXEImO2V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Thumbnails/1029/ibOnBXEImO2V.jpg</video:thumbnail_loc>

            <video:title>Proving general formulas (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the step-by-step induction proof for a basic recursive sequence. You will learn to use a recurrence relation and the inductive hypothesis to verify that a general formula correctly predicts every term in the sequence. Solved: 1. A sequence is defined by a_1 = 5, a_{n+1} = a_n + 4 for all n \ge 1. Prove that a_n = 4n + 1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/lfE0VkEYeR/Previews/1029/ibOnBXEImO2V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eVBQi0E_OqFG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1045/eVBQi0E_OqFG.jpg</video:thumbnail_loc>

            <video:title>Thermochemical equations</video:title>

            <video:description><![CDATA[
This lesson shows how to write a thermochemical equation for toluene combustion using calorimetry data. You will learn to calculate total heat released and convert it to molar enthalpy. Ensure your final equation includes the balanced chemical symbols and the correct sign for enthalpy change. Solved: When 0.256 \text{ g} of toluene, \text{C}_7\text{H}_8, burns completely in excess oxygen in a calibrated constant-pressure calorimeter with a heat capacity of 725 \text{ J} \cdot \text{°C}^{-1}, the temperature of the calorimeter increases by 11.2 \text{ °C}. Write the thermochemical equation for the combustion of toluene. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1045/eVBQi0E_OqFG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bL9XvprPtw0F</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/bL9XvprPtw0F.jpg</video:thumbnail_loc>

            <video:title>Evaluating infinite series</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate the sum of an infinite geometric series using the sum to infinity formula. You will master identifying the first term and common ratio to solve for the finite limit of a converging exponential sequence. Solved: 2. Evaluate 1 - \frac{2}{3} + \frac{4}{9} - \frac{8}{27} + \dots 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/bL9XvprPtw0F.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I5GHZBNrl2Ov</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/I5GHZBNrl2Ov.jpg</video:thumbnail_loc>

            <video:title>Distance between two points</video:title>

            <video:description><![CDATA[
Distance between two points in the Cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/I5GHZBNrl2Ov.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/awLu7SrDHszI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Thumbnails/1038/awLu7SrDHszI.jpg</video:thumbnail_loc>

            <video:title>Expanding binomials (2)</video:title>

            <video:description><![CDATA[
Apply the binomial formula to solve complex expressions featuring negative coefficients. This walkthrough demonstrates how to accurately substitute these values into the general formula while correctly tracking indices and signs. You will learn to simplify each term into its final form. Solved: 2. Expand (2x-3y)^4 completely, using the binomial formula. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NdggWbEh9N/Previews/1038/awLu7SrDHszI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ySn3t6j_bOuH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/856/ySn3t6j_bOuH.jpg</video:thumbnail_loc>

            <video:title>Calculating heat required</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate the heat needed to change a substance's temperature using its mass, specific heat capacity, and temperature change. You will work through practical examples applying the formula q equals mc delta T to solve for energy absorbed or released. Solved: (1) Ammonium perchlorate, \text{NH}_4\text{ClO}_4, is another common oxidizer used in rocket propellants. Calculate the heat required to raise the temperature of 15.0 g of \text{NH}_4\text{ClO}_4 from 20.0 °C to 650.0 °C. The specific heat capacity of \text{NH}_4\text{ClO}_4 is 1.20 J·g⁻¹·K⁻¹.(2) Calculate the heat required to raise the temperature of:(a) 75.0 g of water(b) 1.50 mol of \text{H}_2\text{O}(l)from 25.0 °C to 90.0 °C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/856/ySn3t6j_bOuH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WE4Xc9cOAl_0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/857/WE4Xc9cOAl_0.jpg</video:thumbnail_loc>

            <video:title>Practice questions</video:title>

            <video:description><![CDATA[
Solve common exam problems on calorimetry, Hess’s law, and standard heats of formation. These questions drill you on how to apply thermodynamic formulas to calculate enthalpy changes correctly. Use these worked examples to master all calculation methods covered in the enthalpy chapter. Solved: 1. Find \Delta H^\circ for \text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}(g).Given:(1) \quad \text{CO}(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H^\circ = -283.0 \text{ kJ}(2) \quad \text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H^\circ = -393.5 \text{ kJ}2. Calculate the standard enthalpy change for:\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)using the data below:a. \text{NH}_3(g) + \text{HCl}(g) \rightarrow \text{NH}_4\text{Cl}(s) \quad \Delta H^\circ = -176.1 \text{ kJ}b. \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \quad \Delta H^\circ = -92.4 \text{ kJ}c. \text{N}_2(g) + 4\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{NH}_4\text{Cl}(s) \quad \Delta H^\circ = -561.8 \text{ kJ} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/857/WE4Xc9cOAl_0.mp4</video:content_loc>

          <video:duration>67</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nR-_TD0jNp4M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/nR-_TD0jNp4M.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: If the resultant couple moment acting on the triangular block is to be zero, determine the magnitudes F and P. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/nR-_TD0jNp4M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738866381148.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/fUl_EhgD4p_X</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/fUl_EhgD4p_X.jpg</video:thumbnail_loc>

            <video:title>Rough horizontal surface</video:title>

            <video:description><![CDATA[
Calculate the maximum horizontal force required to overcome static friction on a rough surface. Use the coefficient of friction and equilibrium equations to resolve normal and frictional forces. This walkthrough provides the direct mathematical steps for solving friction problems. Solved: 5. A block of mass 10.0\text{ kg} is at rest on a rough horizontal surface. If the coefficient of static friction is 0.4, calculate the maximum horizontal force that can be applied to the block before it starts to move. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/fUl_EhgD4p_X.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8lS0xhDq9XWd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/92/8lS0xhDq9XWd.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
An overview of methods of determining the particular integral.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/92/8lS0xhDq9XWd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E26hY7QbaW2M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/1044/E26hY7QbaW2M.jpg</video:thumbnail_loc>

            <video:title>Calculating enthalpy of phase changes (2)</video:title>

            <video:description><![CDATA[
This lesson covers calculating enthalpy of vaporisation for ethanol and acetone using heat and mass data. You will also learn to determine iodine's vaporisation enthalpy by applying Hess’s Law to fusion and sublimation values. Master these multi-step problems to solve phase change energy tasks. Solved: 1. A sample of ethanol, \text{C}_2\text{H}_5\text{OH}, is heated to its normal boiling point of 78.4 °C. The heating is continued, and an additional 21.0 kJ of heat is supplied, causing 36.8 g of ethanol to vaporize completely. Calculate the enthalpy of vaporization of ethanol at its boiling point.2. A 42.5 g sample of acetone, (\text{CH}_3)_2\text{CO}, is heated to its normal boiling point. An additional 22.8 kJ of heat is then supplied, causing all of the acetone to vaporize.3. At 25 °C, the enthalpy of fusion of iodine is\Delta H_{fus} = 15.5 \text{ kJ mol}^{-1}and the enthalpy of sublimation of solid iodine at the same temperature is\Delta H_{sub} = 62.4 \text{ kJ mol}^{-1}.What is the enthalpy of vaporization of iodine at 25 °C? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/1044/E26hY7QbaW2M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dnnBNlesyp_8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/858/dnnBNlesyp_8.jpg</video:thumbnail_loc>

            <video:title>Predicting reaction entropies (2)</video:title>

            <video:description><![CDATA[
Compare reaction pairs to predict which has the more positive entropy change based on gas moles and phase changes. This lesson provides a step-by-step walkthrough for solving common problems involving decomposition, synthesis, and dissolution. You will learn to justify your predictions concisely. Solved: For each pair, predict which reaction has the more positive (or less negative) \Delta S^\circ. Explain concisely.a)(i) \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)(ii) 2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g)b)(i) \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g)(ii) 2\text{Fe}(s) + \frac{3}{2}\text{O}_2(g) \rightarrow \text{Fe}_2\text{O}_3(s)c)(i) Dissolving \text{KCl}(s) in water.(ii) Dissolving \text{CaCl}_2(s) in water (consider per mole of salt). 
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          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/858/dnnBNlesyp_8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_vtSdg_dOQRU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/_vtSdg_dOQRU.jpg</video:thumbnail_loc>

            <video:title>Free energy change</video:title>

            <video:description><![CDATA[
Apply the Gibbs-Helmholtz equation to calculate free energy change using given enthalpy, entropy, and temperature values. This walkthrough demonstrates how to convert units correctly to ensure energy balance and determine reaction feasibility. You will learn to solve for standard free energy. Solved: A_{(l)} \rightarrow A_{(g)}For the process above, calculate the change in molar Gibbs free energy at 1 atm and:(a) 350 \text{ °C}(b) 370 \text{ °C}Given that \Delta H_{vap} = 59.3 \text{ kJ mol}^{-1} \Delta S_{vap} = 109.1 \text{ J K}^{-1}\text{mol}^{-1}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/_vtSdg_dOQRU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZaE59CuM9pYn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/ZaE59CuM9pYn.jpg</video:thumbnail_loc>

            <video:title>Condition and procedure</video:title>

            <video:description><![CDATA[
Acceleration requires unbalanced forces. This lesson defines the standard procedure for drawing free-body diagrams, resolving vectors, and applying Newton’s second law. Use these steps to calculate the exact motion of any particle.  
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          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/ZaE59CuM9pYn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hv6q84DNPQwZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/hv6q84DNPQwZ.jpg</video:thumbnail_loc>

            <video:title>Procedure</video:title>

            <video:description><![CDATA[
Different kinds of rectilinear motion of particles problems and their solution methods.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/hv6q84DNPQwZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/u8SXbFMa3xOM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Rw58orddxs/Thumbnails/859/u8SXbFMa3xOM.jpg</video:thumbnail_loc>

            <video:title>Free energy of formation</video:title>

            <video:description><![CDATA[
Calculate the standard Gibbs free energy of formation for hydrogen fluoride using its standard enthalpy and molar entropy data. This walkthrough demonstrates how to combine these properties at 25 degrees Celsius to determine the energy change of the formation reaction. Solved: Calculate the standard Gibbs free energy of formation of \text{HF}(g) at 25\text{ °C} from its molar entropy and standard enthalpy of formation, given that:\Delta H^\circ_f (\text{HF}) = -271.1 \text{ kJ mol}^{-1}S^\circ_m (\text{HF}) = 88.7 \text{ J mol}^{-1} \text{K}^{-1}S^\circ_m (\text{H}_2) = 130.68 \text{ J mol}^{-1} \text{K}^{-1}S^\circ_m (\text{F}_2) = 202.78 \text{ J mol}^{-1} \text{K}^{-1} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Rw58orddxs/Previews/859/u8SXbFMa3xOM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ITCTYCbtPJzk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1014/ITCTYCbtPJzk.jpg</video:thumbnail_loc>

            <video:title>Applying properties (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates the application of linear properties to solve complex summations efficiently. You will master pulling constants outside sigma notation to simplify algebraic evaluations by using known partial sums. Solved: 5. Given that \sum_{r=1}^{10} r = 55, evaluate \sum_{r=1}^{10} 6r. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1014/ITCTYCbtPJzk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FZAdKXtoAQgh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/FZAdKXtoAQgh.jpg</video:thumbnail_loc>

            <video:title>Three consecutive terms (1)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for three consecutive terms using symmetric notation and the property of constant ratios. You will master using given products and sums to isolate the middle term and calculate the common ratio to identify the complete sequence. Solved: 5. The product of three consecutive terms of a geometric progression is 216 and their sum is 21. Find the terms. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/FZAdKXtoAQgh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x_9hNAYzAu8H</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1015/x_9hNAYzAu8H.jpg</video:thumbnail_loc>

            <video:title>Arithmetic means (2)</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates solving for unknown boundary values when the arithmetic mean is given. You will master the algebraic steps to calculate the first and last terms by using the relationship between the mean and the sum of extremes. Solved: 8. Find k if (k - 1), (2k + 1) and (6k + 3) are in arithmetic progression. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1015/x_9hNAYzAu8H.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zqz34ctW49mq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/zqz34ctW49mq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on representation, multiplication, division and powers (De-Moivre's theorem) of complex numbers in polar forms. Solved: 1.write the following in polar form(a) z=6+i\sqrt{3}(b) z=\frac{-1}{4}+i\frac{\sqrt{3}}{4}(c) z=-2(d) z=-4i2. Given z = 3 - 2i, what is z^6 in polar form? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/zqz34ctW49mq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y15wroO3N1g8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/203/Y15wroO3N1g8.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on representation, multiplication, division and powers (De-Moivre's theorem) of complex numbers in polar forms. Solved: 1.Complete the following in polar form(a) (\frac{1}{2}-i\frac{\sqrt{3}}{2})(-3+3i)(2\sqrt3+2i)(b) \frac{-4+4\sqrt{3}i}{3+3i}2. Find |z| and \text{Arg}(z) for the following:(a) z = (2\sqrt{3} + 2i)^8 (b) z = \frac{1}{(\sqrt{3} - i)^{10}} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/203/Y15wroO3N1g8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qJd_USd8sBCS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1017/qJd_USd8sBCS.jpg</video:thumbnail_loc>

            <video:title>Determining convergence</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to identify which infinite geometric series converge to a finite limit. You will master testing the common ratio against the required boundaries to determine if a series settles at a fixed sum or increases without bound. Solved: 1. Determine which of the following infinite series converge:(a) 16 + 12 + 9 + \dots(b) 2 - 4 + 8 - 16 + \dots(c) 1 + 1.1 + 1.21 + \dots 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1017/qJd_USd8sBCS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oY3gDa2pOGxV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/oY3gDa2pOGxV.jpg</video:thumbnail_loc>

            <video:title>Charged disk</video:title>

            <video:description><![CDATA[
A disk is a 2D surface. How do you integrate over area using concentric rings? We sum ring potentials to find the total voltage.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/oY3gDa2pOGxV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CsgvGUCtm3hH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1018/CsgvGUCtm3hH.jpg</video:thumbnail_loc>

            <video:title>Arithmetic-geometric series</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates calculating the sum of a series with both arithmetic and geometric properties. You will master using the common ratio to shift and subtract the series to isolate a standard geometric progression for final summation. Solved: 5. Find the sum of the first n terms of the series 1 + 2x + 3x^2 + 4x^3 + \dots 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1018/CsgvGUCtm3hH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XQwS66dD46w_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Thumbnails/1016/XQwS66dD46w_.jpg</video:thumbnail_loc>

            <video:title>Compound interests</video:title>

            <video:description><![CDATA[
This walkthrough demonstrates how to calculate investment growth using geometric sequences. You will master applying the rth term formula to determine investment values at specific years and finding total returns after compound interest is applied over time. Solved: 10. A student invests ₦ 100,000 at an annual interest rate of 10%, compounded annually.(a) Find the value of the investment at the start of the 6th year.(b) Find the total value of the investment after 10 years. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/XdyQdNr1Az/Previews/1016/XQwS66dD46w_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L0mmJ03XmyrN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/206/L0mmJ03XmyrN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on manipulating Sines and Cosines using complex numbers. Solved: 1.Find the expression for sin^3\theta in terms of sines and cosines of multiples of \theta2. Obtain an expression for \cos 3\theta in terms of powers of \sin \theta and \cos \theta. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/206/L0mmJ03XmyrN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IVX_dyq4mp8g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/204/IVX_dyq4mp8g.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on rational powers and roots of complex numbers. Solved: 1.Solve the equation z^3 + 64i=02. Solve z^2(1 - z^2) = 16. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/204/IVX_dyq4mp8g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0t8f9h0XhAwC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/205/0t8f9h0XhAwC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on representation, multiplication, division and powers of complex numbers in exponential form. Solved: 1.Find the 4th roots of z=-2i in euler form.2. Prove the formula e^{i\pi} = -1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/205/0t8f9h0XhAwC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/w358SpnJt2OT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1397/w358SpnJt2OT.jpg</video:thumbnail_loc>

            <video:title>Synthetic preparations</video:title>

            <video:description><![CDATA[
Alkenes are made industrially by cracking petroleum and in the lab via elimination reactions. How do you predict the major product when dehydration of an alcohol yields multiple alkene isomers? This lesson covers cracking, dehydration, dehydrohalogenation, and applies Zaitsev's rule precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1397/w358SpnJt2OT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qYfSIhHEJokt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/208/qYfSIhHEJokt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on logarithms of complex numbers. Solved: 1.Express the following in the form a+ib,a,b \in \mathbb{R}(a) log (-1+i)(b) log_2(-2)2. Evaluate the following: (a) 2^i (b) \cos^{-1}(-2) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/208/qYfSIhHEJokt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vAzuQYCOHk2g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Thumbnails/839/vAzuQYCOHk2g.jpg</video:thumbnail_loc>

            <video:title>Chemical formulae (5)</video:title>

            <video:description><![CDATA[
This lesson provides a worked example on calculating empirical and molecular formulae from experimental mass data. You will practice converting percentage composition to mole ratios and determining the actual molecular formula using molar mass. Use this walkthrough to master the step-by-step calculation. Solved: An organic compound is composed of 41.39 % C, 3.47 % H and the rest as oxygen. If 0.129 mol of the compound has a mass of 15.0g what are the empirical and molecular formulae of the compound? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/16j3kAAI2W/Previews/839/vAzuQYCOHk2g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/khfR8pEJyHKs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/206/khfR8pEJyHKs.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on manipulating Sines and Cosines using complex numbers. Solved: 1.If z = cos\theta + isin\theta, prove that \frac 2 {1+z} = 1 + itan(\frac \theta 2) and that \frac {1+z} {1-z} = icot(\frac \theta 2)2. Prove that \frac{1 + \sin \theta + i \cos \theta}{1 + \sin \theta - i \cos \theta} = \sin \theta + i \cos \theta. Hence or otherwise, show that \left[ 1 + \sin \left( \frac{\pi}{5} \right) + i \cos \left( \frac{\pi}{5} \right) \right]^5 + i \left[ 1 + \sin \left( \frac{\pi}{5} \right) - i \cos \left( \frac{\pi}{5} \right) \right]^5 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/206/khfR8pEJyHKs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oilUJuUUQcD2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/287/oilUJuUUQcD2.jpg</video:thumbnail_loc>

            <video:title>Equidistant points (1)</video:title>

            <video:description><![CDATA[
Identify the centre and radius from a modulus expression to define a circular locus. This walkthrough demonstrates how to interpret the algebraic pattern and sketch the resulting circle accurately on the Argand plane. Solved: 1.What figure does |\frac{z}{z+3}|=2, z \in \mathbb{c} describe on the complex plane?2. What geometric figure is described by \text{Arg } z = \lambda, z \in \mathbb{C}, where \lambda \in (-\pi/2, \pi/2). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/287/oilUJuUUQcD2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/szMgCm43cinQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1023/szMgCm43cinQ.jpg</video:thumbnail_loc>

            <video:title>More stoichiometric calculations (1)</video:title>

            <video:description><![CDATA[
This walkthrough covers multi-step problems to find the number of molecules and product masses. You will learn to use balanced equations to calculate water formation and predict the mass of copper produced from cuprite roasting. Solved: Example 3: For the reaction: \text{Ba(OH)}*{2(aq)} + 2\text{HClO}*{3(aq)} \rightarrow \text{Ba(ClO}_3)_2 + 2\text{H}_2\text{O} Calculate the respective number of moles and molecules of water formed when 0.100 mol \text{Ba(OH)}_2 is treated with 0.250 mol \text{HClO}_3. Example 4: A 0.600 mol sample of cuprite, \text{Cu}_2\text{S}, is roasted in excess oxygen to yield copper metal and sulphur dioxide. Calculate the mass of copper metal produced. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1023/szMgCm43cinQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jXweREIvZXaE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1023/jXweREIvZXaE.jpg</video:thumbnail_loc>

            <video:title>More stoichiometric calculations (2)</video:title>

            <video:description><![CDATA[
This walkthrough covers calculating product masses for reactions involving barium carbonate and copper-ammonia complexes. You will learn to use balanced chemical equations and stoichiometric ratios to determine the mass of ammonia required and the solid yield from gas-liquid reactions. Solved: Example: Calculate the mass of \text{BaCO}_3 produced when excess \text{CO}_2 is bubbled through a solution containing 0.125 mol \text{Ba(OH)}_2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1023/jXweREIvZXaE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EYS_rwIRKZf3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/707AP7eKHp/Thumbnails/1204/EYS_rwIRKZf3.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson outlines the AMS 102 course structure and its alignment with the NUC CCMAS syllabus. You will learn the specific sequence of modules needed to cover all mathematics topics required for your management science exams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/707AP7eKHp/Previews/1204/EYS_rwIRKZf3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vbyU6FrHIEEf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1023/vbyU6FrHIEEf.jpg</video:thumbnail_loc>

            <video:title>Limiting reagents (2)</video:title>

            <video:description><![CDATA[
This walkthrough explains how to find the limiting reagent when heating 10g of iron with 10g of sulphur. You will learn to calculate the mass of iron(II) sulphide produced and determine the exact amount of the excess reactant left over. Solved: Example 2: If 10.0g of iron is heated with 10.0g of sulphur, how much FeS? What will remain unreacted? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1023/vbyU6FrHIEEf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tdrWdUhMMHup</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/1023/tdrWdUhMMHup.jpg</video:thumbnail_loc>

            <video:title>Limiting reagents (3)</video:title>

            <video:description><![CDATA[
This lesson explains how to find the percentage of lead in an organic salt by reacting it with excess potassium chromate. You will learn to use the mass of the lead(II) chromate precipitate to calculate the initial lead content and determine the purity of the organic sample. Solved: 5g of a mixture of \text{CaCO}_3 and sand is treated with excess hydrochloric acid, 1.32g of \text{CO}_2 were produced. What is the percent \text{CaCO}_3 in the mixture? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/1023/tdrWdUhMMHup.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GWt6zcOvFRCk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Thumbnails/845/GWt6zcOvFRCk.jpg</video:thumbnail_loc>

            <video:title>Assigning oxidation numbers</video:title>

            <video:description><![CDATA[
This walkthrough applies the priority rules to find oxidation numbers for atoms in neutral compounds and polyatomic ions. You will learn to use known values for oxygen, hydrogen, and halogens to calculate the state of unknown central atoms like manganese or chromium. Solved: Assign oxidation number to all the atoms in each of the following: (i) (NH_4)_2HPO_4, (ii) K_4Fe(CN)_6 (iii) Na_2S_2O_3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LZj9JE98CL/Previews/845/GWt6zcOvFRCk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uhiXRsAZeaf4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/855/uhiXRsAZeaf4.jpg</video:thumbnail_loc>

            <video:title>Common-ion effect (1)</video:title>

            <video:description><![CDATA[
This lesson solves for the molar solubility of silver chloride in a potassium chloride solution. You will learn to apply the common-ion effect by using the chloride concentration to determine how much less salt dissolves compared to pure water. Solved: What is the molar solubility of AgCl in a 0.0001 M KCl solution? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/855/uhiXRsAZeaf4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6gsaumbcw0TC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/1022/6gsaumbcw0TC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
This walkthrough explains how to predict precipitate formation by calculating the ion product after mixing solutions. You will learn to adjust concentrations for dilution and compare the reaction quotient with the solubility product constant. Solved: Question 1 Does a precipitate of barium fluoride form when 100 mL of 1.0 \times 10^{-3} MBa(NO_3)_2 is mixed with 200 mL of 1.0 \times 10^{-3} MKF (ignore possible protonation of F^-)? Note that K_{sp} of BaF_2 = 1.7 \times 10^{-6} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/1022/6gsaumbcw0TC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VhGDkK67PumI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/1022/VhGDkK67PumI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
This lesson covers advanced calculations for predicting precipitation and finding the specific pH where solids start to form. You will learn to solve for ion products in complex mixtures and use solubility constants to determine the conditions needed for solid separation. Solved: Determine the pH at which precipitation ofFe(OH)_3 begins when a solution initially contains 0.020 M Fe(NO_3)_3. Given: K_{sp}(Fe(OH)_3) = 2.8 \times 10^{-39} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/1022/VhGDkK67PumI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7o1tQrwKBz5o</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/1022/7o1tQrwKBz5o.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
This lesson solves problems on predicting precipitate formation when mixing solutions of known molarity and volume. You will learn to calculate final concentrations after dilution and compare the ion product to the solubility product constant to determine if a solid settles. Solved: (a) 5.0 mL of 0.10 M K_2CO_3(aq) and 1.00 L of 0.010 M AgNO_3(aq); K_{sp}(Ag_2CO_3) = 6.2 \times 10^{-12}(b) 3.3 mL of 1.0 M HCl(aq), 4.9 mL of 0.0030 M AgNO_3(aq), and enough water to dilute the solution to 50.0 mL. K_{sp}(AgCl) = 1.6 \times 10^{-10} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/1022/7o1tQrwKBz5o.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/frEcMQFm4TM3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/frEcMQFm4TM3.jpg</video:thumbnail_loc>

            <video:title>Product derivative</video:title>

            <video:description><![CDATA[
Spot a function multiplied by its own derivative. Why use full substitution when the power rule applies directly to the base? This lesson shows you how to integrate these products by sight.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/frEcMQFm4TM3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BGe8X2_7HB6j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/919/BGe8X2_7HB6j.jpg</video:thumbnail_loc>

            <video:title>Assymetric suspension</video:title>

            <video:description><![CDATA[
Resolve tensions for a load suspended at unequal angles. Use free-body diagrams and equilibrium equations to calculate force magnitudes and check against cable breaking points. This walkthrough provides the standard mathematical method for solving asymmetric suspension systems. Solved: 1. A heavy shop sign of mass 30.0\text{ kg} hangs motionless from a horizontal support beam. It is held by two steel cables attached to a single ring ("the knot") above the sign as shown below, with \theta_1 = 40^\circ and \theta_2 = 50^\circ. Both cables can withstand a maximum tension of 200\text{ N}. If the tension in either cable exceed this limit, it will break. Determine the tension in each cable and assess whether or not the system will fail. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/919/BGe8X2_7HB6j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UEPtwfclR4Fh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/UEPtwfclR4Fh.jpg</video:thumbnail_loc>

            <video:title>Horizontal circle</video:title>

            <video:description><![CDATA[
Calculate the tension in a string required to keep a ball moving in a horizontal circle at a constant speed. You will apply the formula for centripetal force to relate mass, velocity, and radius to the pulling force. This walkthrough demonstrates circular dynamics on a flat plane.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/UEPtwfclR4Fh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HAQzcy0g3BCc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/93/HAQzcy0g3BCc.jpg</video:thumbnail_loc>

            <video:title>Angle between two lines</video:title>

            <video:description><![CDATA[
Calculating the angle between two lines in a two-dimensional Cartesian coordinates system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/93/HAQzcy0g3BCc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hNJtvx8VP87B</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/hNJtvx8VP87B.jpg</video:thumbnail_loc>

            <video:title>Smooth ramp</video:title>

            <video:description><![CDATA[
Learn how to calculate the acceleration of a block sliding down a frictionless inclined plane. You will resolve the weight vector into components parallel and perpendicular to the ramp to find the net driving force. This walkthrough applies Newton's second law to motion on a slope. Solved: 2. A block of mass 5.00\text{ kg} is released from rest on a frictionless plane inclined at an angle of 30.0^{\circ} to the horizontal. Calculate the acceleration of the block as it slides down the plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/hNJtvx8VP87B.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sOetROUgrlwP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/sOetROUgrlwP.jpg</video:thumbnail_loc>

            <video:title>Rough ramp</video:title>

            <video:description><![CDATA[
Calculate acceleration on a rough incline by resolving weight and accounting for kinetic friction. You will find the net force by subtracting the friction force from the downward weight component. This lesson shows how friction affects motion on a slope. Solved: 3. A 10.0\text{-kg} block is placed on a rough incline tilted at 37.0^{\circ} to the horizontal. If the coefficient of kinetic friction is 0.25, determine the acceleration of the block down the incline. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/sOetROUgrlwP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/18MmFqgAEDKa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/18MmFqgAEDKa.jpg</video:thumbnail_loc>

            <video:title>Stopping distance</video:title>

            <video:description><![CDATA[
Calculate how far a sled travels before stopping by finding deceleration from kinetic friction. You will use Newton's second law to determine the resisting force and apply kinematic equations to solve for the displacement. This walkthrough links dynamics with motion analysis. Solved: 7. A 40.0-kg sled is sliding along a horizontal surface with an initial velocity of 4.00 m/s. If the coefficient of friction is \mu_k = 0.050, calculate the distance the sled travels before it stops. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/18MmFqgAEDKa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EOJ3O_uep_EQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/EOJ3O_uep_EQ.jpg</video:thumbnail_loc>

            <video:title>Banked road</video:title>

            <video:description><![CDATA[
Calculate the ideal banking angle for a curved road to allow a car to turn safely without relying on friction. You will resolve the normal force into horizontal and vertical components to provide the necessary centripetal force. This lesson covers the design principles for high-speed track safety.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/EOJ3O_uep_EQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/A1AfDd7YNiyh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/986/A1AfDd7YNiyh.jpg</video:thumbnail_loc>

            <video:title>Ramp-pulley system</video:title>

            <video:description><![CDATA[
Calculate the acceleration of a system featuring a block on a rough incline connected to a hanging mass. You will resolve the inclined weight components and account for kinetic friction to set up the governing equations of motion. This walkthrough demonstrates solving for acceleration in coupled systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/986/A1AfDd7YNiyh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U5sW5QwEulQj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/666/U5sW5QwEulQj.jpg</video:thumbnail_loc>

            <video:title>The integrated terminal</video:title>

            <video:description><![CDATA[
The integrated terminal brings the power of the command line directly into your VS Code workspace, allowing you to run commands and edit code in one place. This lesson shows you how to use this feature to build a seamless and efficient workflow.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/666/U5sW5QwEulQj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RvBn7UywfZCp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/RvBn7UywfZCp.jpg</video:thumbnail_loc>

            <video:title>Polynomials and rational functions</video:title>

            <video:description><![CDATA[
Evaluation of limits at infinity for polynomials and rational functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/RvBn7UywfZCp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aXbTYhjCC7Qo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/aXbTYhjCC7Qo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the components of a force. Solved: The hydraulic cylinder BC exerts on a member AB a force P directed along line BC. Knowing that P must have a 600-N component perpendicular to member AB, determine: (a) the magnitude of the force P,(b) its component along line AB. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/aXbTYhjCC7Qo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739467566593.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/KLa-HMpTVCiO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/84/KLa-HMpTVCiO.jpg</video:thumbnail_loc>

            <video:title>Newton's method</video:title>

            <video:description><![CDATA[
Newton's method of solution of equations in one variable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/84/KLa-HMpTVCiO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BUyAFc6tsy-I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/649/BUyAFc6tsy-I.jpg</video:thumbnail_loc>

            <video:title>Overview</video:title>

            <video:description><![CDATA[
Meaning, types and need for vector products.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/649/BUyAFc6tsy-I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VZAfkxkBYOBe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/VZAfkxkBYOBe.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the components of a force. Solved: Members BC exerts on member AC a force P directed along line BC. Knowing that P must have a 325-lb horizontal component, determine(a) the magnitude of the force P,(b) its vertical component. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/VZAfkxkBYOBe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739468488331.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gTPcWtHVXhGu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/112/gTPcWtHVXhGu.jpg</video:thumbnail_loc>

            <video:title>Elementary matrices</video:title>

            <video:description><![CDATA[
Meaning, notations and examples of elementary matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/112/gTPcWtHVXhGu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b6b4_HNkp5VN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/62/b6b4_HNkp5VN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the derivative of a function over an interval. Solved: Show that the derivative of f(x)=Inx is f^1(x)=\frac{1}{x}, V x\in I,I={X\in IR|X>0} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/62/b6b4_HNkp5VN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Xb0HuDR9xAQM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/Xb0HuDR9xAQM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on implicit differentiation of functions of several variables using partial derivatives and Jacobian determinants. Solved: If u^2 -v = 3x + y and u - 2v^2 = x - 2y. Find \frac {\partial u} {\partial x} and \frac {\partial v} {\partial y}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/Xb0HuDR9xAQM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5e81kGKGebmq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/106/5e81kGKGebmq.jpg</video:thumbnail_loc>

            <video:title>Properties</video:title>

            <video:description><![CDATA[
Properties of the gradient.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/106/5e81kGKGebmq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OsPXVaIGwYOS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/666/OsPXVaIGwYOS.jpg</video:thumbnail_loc>

            <video:title>What is a code editor?</video:title>

            <video:description><![CDATA[
A professional does not write code in a word processor. This lesson defines a code editor as a purpose-built tool for developers, explaining how features like syntax highlighting and code completion make it fundamentally different from a simple text editor.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/666/OsPXVaIGwYOS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/CN1y7BjWCmoX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/63/CN1y7BjWCmoX.jpg</video:thumbnail_loc>

            <video:title>Rolle's theorem</video:title>

            <video:description><![CDATA[
The Rolle's theorem and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/63/CN1y7BjWCmoX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FOPrX1oNduWp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/63/FOPrX1oNduWp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the Rolle's and mean-value theorems. Solved: Verify Rolle's theorem for the following cases, and obtain the point(s) no that satisfies it.(a) f(x)=x^2-8x+5;[3,5] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/63/FOPrX1oNduWp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Pqj1PQja82L_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/104/Pqj1PQja82L_.jpg</video:thumbnail_loc>

            <video:title>Vector products (2)</video:title>

            <video:description><![CDATA[
Vector product of two vectors - using sign notations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/104/Pqj1PQja82L_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6tw0W16_c0vT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/707AP7eKHp/Thumbnails/1204/6tw0W16_c0vT.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Learn to sync UniDrills modules with your university management science lectures for maximum efficiency. This lesson explains how to use digital resources alongside school notes to cover the NUC CCMAS syllabus and ensure total exam success.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/707AP7eKHp/Previews/1204/6tw0W16_c0vT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Mls01G7hXjX3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/Mls01G7hXjX3.jpg</video:thumbnail_loc>

            <video:title>Hyperbolic functions</video:title>

            <video:description><![CDATA[
Hyperbolic functions describe hanging cables and heat flow. Why does the derivative of sinh look like cosh? Watch how exponential definitions make these rates easy to find.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/Mls01G7hXjX3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FgusZW-EkCCs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/FgusZW-EkCCs.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: The slider of mass m = 0.5 kg moves along the parabolic guide rod ABC, propelled by the horizontal force F(t). The kinetic coefficient of friction between the slider and the guide rod is \mu = 0.2. The position of the slider is given by x = b sin (\frac {2\pi t} {t_o})y = \frac b 4 (1 + cos \frac {4\pi t} {t_o} )where t_o = 0.8 s and b = 1.2 m. Assuming that ABC lies in the vertical plane, determine the force F when the slider is at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/FgusZW-EkCCs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744388828115.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xDpdGRNRePEy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/xDpdGRNRePEy.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: (a) The coordinates in meters of the 360-kg sport plane's center of mass relative to an earth-fixed reference frame during an interval of time are x = 20t - 1.63t^2,y = 35t - 0.15t^3,and z = -20t - 1.38t^2.where t is the time in seconds. The y axis points upward. The forces exerted on the plane are its weight, the thrust vector T exerted by its engine, its lift force vector L, and the drag force vector D. At t = 4 s, determine T + L + D.(b) The force in newtons exerted on the 360-kg sport plane in (a) by its engine, its lift force and the drag force during an interval of time is T + L + D = (-1000 + 280t)i + (4000 - 430t)j + (700 + 200t)k,where t is the time in seconds. If the coordinates of the plane's center of mass is (0, 0, 0) and its velocity is 20i + 35j - 20k (m/s) at t = 0, what are the coordinates of the center of mass at t = 4 s? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/xDpdGRNRePEy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1744046927207.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/TgA-zb71QKld</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/323/TgA-zb71QKld.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the analysis of machines. Solved: If a force of F=350Nis applied to the handle of the toggle clamp, determine the resulting clamping force at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/323/TgA-zb71QKld.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739363854524.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/63ZY2FK_Seco</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/134/63ZY2FK_Seco.jpg</video:thumbnail_loc>

            <video:title>Eigenvalues and eigenvectors</video:title>

            <video:description><![CDATA[
An overview of eigenvalues and eigenvectors of matrices.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/134/63ZY2FK_Seco.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1bnXKwlB7Xpu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/1bnXKwlB7Xpu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: (a) A 40-Ib suitcase slides from rest 20ft down the smooth ramp. Determine the point where it strikes the ground at C. How long does it take to go from A to C?(b) Solve (a) if the suitcase has an initial velocity down the ramp of V_A = 10ft/s and the coefficient of kinetic friction along AB is\mu_k=0.2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/1bnXKwlB7Xpu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744533319012.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/pHjPvVA8EuSB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/156/pHjPvVA8EuSB.jpg</video:thumbnail_loc>

            <video:title>Units of force</video:title>

            <video:description><![CDATA[
Units of measurement of mass, length, time and their relation to force in different systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/156/pHjPvVA8EuSB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4KfQ4ueJIdS8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Thumbnails/82/4KfQ4ueJIdS8.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Numerical methods are algorithmic procedures that approximate solutions when closed-form answers are unavailable. They convert continuous problems into discrete computations. This lesson defines their scope and purpose.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mUjjajbMzQ/Previews/82/4KfQ4ueJIdS8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7eMMrXiwzdIS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/7eMMrXiwzdIS.jpg</video:thumbnail_loc>

            <video:title>Solutions</video:title>

            <video:description><![CDATA[
Meaning and kinds of solutions of systems of linear equations; meaning of consistency of systems of linear equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/7eMMrXiwzdIS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iDmfZtsG5kRF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/61/iDmfZtsG5kRF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More examples on the determination of the derivative of a function at a given point. Solved: Investigate the differentiability of the following functions at x=0:(i) f(x)=|x|,x\in IR(ii) f(x)=\begin{cases} x ^2\cos(\frac{1}{x}),x\ne0\\ 0,x=0,x\in IR \end{cases} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/61/iDmfZtsG5kRF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/k0ZYLBMh4Hcm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/k0ZYLBMh4Hcm.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Meaning of homogeneous and non-homogeneous linear differential equations.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/k0ZYLBMh4Hcm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SCcPolpUgpA-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/SCcPolpUgpA-.jpg</video:thumbnail_loc>

            <video:title>Consistency</video:title>

            <video:description><![CDATA[
How to detect inconsistency in systems of linear equations using elementary row operations - how the ranks of coefficient and augmented matrices tell inconsistency.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/SCcPolpUgpA-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Httk_1s-QK6D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/288/Httk_1s-QK6D.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of curvilinear motion of particles in rectangular coordinates. Solved: (a) A steel sphere in a tank of oil is given an initial velocity v=2i(m/s) at the origin of the coordinate system shown. The radius of the sphere is 15mm. The density of the steel is 8000kg/m^3 and the density of the oil is 980kg/m^3. If V is the sphere's volume, the (upward) buoyancy force on the sphere is equal to the weight of the volume V of oil. The magnitude of the hydrodynamic drag force D on the sphere as it falls is |D|=16|v|N , where |v| is the magnitude of the sphere's velocity in m/s. What are the x and y components of the sphere's velocity at t=0.1s?(b) In problem (a), what are the x and y coordinates of the sphere at t=0.1s? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/288/Httk_1s-QK6D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wzgm7c44oGYd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/Wzgm7c44oGYd.jpg</video:thumbnail_loc>

            <video:title>Radial and transverse components</video:title>

            <video:description><![CDATA[
Position, displacement, velocity and acceleration of a particle in curvilinear motion, using radial and transverse (polar) components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/Wzgm7c44oGYd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W9oAPxa2jev9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/W9oAPxa2jev9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: Determine the moment about the origin O of the force F=4i+10j+6k that acts at a point A. Assume that the position vector of A is (a) r=2i-3j+4k, (b) r=2i+6j+3k, (c) r=2i+5j+6k. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/W9oAPxa2jev9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yOqC39NFgSIc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/yOqC39NFgSIc.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the components of a force. Solved: Determine the design angle \phi ( 0^{\circ} \le \phi \le 90^{\circ}) between members AB and AC so that the 400-lb horizontal force has a component of 600-lb which acts up to the right, in the direction from B towards A. Also, calculate the magnitude of the force component along AC. Take \theta = 30^{\circ}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/yOqC39NFgSIc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739468227748.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ny8deWDtolo_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/svBWhkklVn/Thumbnails/697/ny8deWDtolo_.jpg</video:thumbnail_loc>

            <video:title>Worked Examples</video:title>

            <video:description><![CDATA[
This lesson provides a series of worked examples for number base division. You'll learn the step-by-step process for long division in other bases, preparing you to solve any division problem.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/svBWhkklVn/Previews/697/ny8deWDtolo_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RqCI7JH071eD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1090/RqCI7JH071eD.jpg</video:thumbnail_loc>

            <video:title>Combustion</video:title>

            <video:description><![CDATA[
Combustion Data reveals the formula of an unknown hydrocarbon. How do you deduce molecular structure from volume changes and potassium hydroxide absorption? We solve this eudiometry problem step by step.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1090/RqCI7JH071eD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m9Sa5md9v9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1118/m9Sa5md9v9.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
You have the rules. Can you pick the right one for a messy function? Watch to tie it all together.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1118/m9Sa5md9v9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2-e90_OOSE-D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/100/2-e90_OOSE-D.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluation of double integrals - involving change of variables. Solved: Evaluate \iint_V \\(x^2+y^2) \,dx\,dy , where R is the square below, defined by the transformation,x + y = u, x - y = v, 0\leq u \leq 2, 0 \leq v \leq 2 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/100/2-e90_OOSE-D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747318713214.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/aDSzGIBxuQay</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/75/aDSzGIBxuQay.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating limits of two-variable real-valued functions. Solved: Evaluate \lim_{(x,y) \to (1,1)} f(x,y) iff(x,y) = \begin{cases} \frac {y^2 - x^2} {xy - 1}, (x, y) \ne (1, 1) \\ 2, (x, y) = (1, 1) \end {cases} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/75/aDSzGIBxuQay.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aC0MxpeiLEBj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/202/aC0MxpeiLEBj.jpg</video:thumbnail_loc>

            <video:title>Principal argument</video:title>

            <video:description><![CDATA[
Principal argument of a complex number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/202/aC0MxpeiLEBj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3h_qQWPzjec7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/295/3h_qQWPzjec7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the components of a force. Solved: A force F of magnitude 800-lb is applied to point C of the bar AB as shown. Determine both the x-y and n-t components of F. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/295/3h_qQWPzjec7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739469023465.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/RT6ne6zof2Nw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/RT6ne6zof2Nw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: Three smooth homogeneous cylinders A, B, and C are stacked in a V-shaped trough as shown below. Each cylinder has a diameter of 500 mm and a mass of 100kg. Determine the forces exerted on cylinder A by the inclined surfaces. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/RT6ne6zof2Nw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739782608180.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/qdmVI0cmmk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/qdmVI0cmmk.jpg</video:thumbnail_loc>

            <video:title>Inverse-trig product</video:title>

            <video:description><![CDATA[
Products of algebraic and inverse trig functions need care. How do you combine the product rule with the derivative of arctan? Watch the step-by-step application of both rules. Solved: Find the derivative of the function y = x \tan^{-1} x with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/qdmVI0cmmk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UKcP_jXEzA6c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/UKcP_jXEzA6c.jpg</video:thumbnail_loc>

            <video:title>Denominator Power</video:title>

            <video:description><![CDATA[
Spot a fraction with a powered denominator. Why use the log rule when the power is not one? This walkthrough shows you how to apply the functional power pattern instead. Solved: Determine \int \frac{x}{(x^{2} + 1)^{2}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/UKcP_jXEzA6c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fU69zva74DsU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FQr3njbcDJ/Thumbnails/1203/fU69zva74DsU.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Learn to sync UniDrills modules with your university physics lectures for maximum efficiency. This lesson explains how to use digital resources alongside school notes to cover the NUC CCMAS syllabus and ensure total exam success.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FQr3njbcDJ/Previews/1203/fU69zva74DsU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fuqiaifmXq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/fuqiaifmXq.jpg</video:thumbnail_loc>

            <video:title>Parametric differentiation</video:title>

            <video:description><![CDATA[
Parametric equations define motion. How do you calculate the second derivative of y with respect to x when both depend on time? Watch the solution for this mechanical component. Solved: A mechanical component moves such that x = \frac{4+t}{1+3t} and y = \frac{2+t}{t}. Find the value of the acceleration-related term \frac{d^2y}{dx^2} at the instant when x=0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/fuqiaifmXq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JRtoTBeYWttb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/JRtoTBeYWttb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on rectilinear relative motion analysis. Solved: Two rockets are launched at a fire works display. Rocket A is launched with an initial velocity v_0=100m/s and rocket B is launched t_1 seconds later with the same velocity. The two rockets are timed to explode simultaneously at a height of 300m as A is falling and B is rising. Assuming a constant acceleration g=9.81m/s^2, determine (a) the time t_1 (b) the velocity of B relative to A at the time of explosion. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/JRtoTBeYWttb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742047115972.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-m6Ew9rEacdB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Thumbnails/224/-m6Ew9rEacdB.jpg</video:thumbnail_loc>

            <video:title>Direction and one point</video:title>

            <video:description><![CDATA[
Vector equation of a straight line through a given point in a given direction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qYiZNj7yuI/Previews/224/-m6Ew9rEacdB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hOTDta5rYh4c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/104/hOTDta5rYh4c.jpg</video:thumbnail_loc>

            <video:title>Scalar products (1)</video:title>

            <video:description><![CDATA[
Scalar product of two vectors - using their magnitudes and angle, and using their Cartesian components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/104/hOTDta5rYh4c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e0VjE5EuSZyO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/323/e0VjE5EuSZyO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the analysis of machines. Solved: Determine the compressive force exerted on the stone by a vertical load of 50N applied to the toggle press. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/323/e0VjE5EuSZyO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739363659759.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/8iyOy4IlqAtV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/8iyOy4IlqAtV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on rectilinear relative motion analysis. Solved: A man can swim at 4ft is in still water. He wishes to cross the 40ft wide river to point B, 30ft downstream. If the river flow with a velocity of 2ft/s,determine the speed of the man and the time needed to make the crossing. Note: while in the water he must not direct himself toward point B to reach this point. Why? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/8iyOy4IlqAtV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742047553802.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/e-Oij-u8MMpq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/296/e-Oij-u8MMpq.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components. Solved: Determine(a) the required tension in cable AC knowing that the resultant of the three forces exerted at point C of boom BC must be directed along BC,(b) the corresponding magnitude of the resultant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/296/e-Oij-u8MMpq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739470114738.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/8gOjxK3OmtL0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/156/8gOjxK3OmtL0.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome and overview of course outline.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/156/8gOjxK3OmtL0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lbjUM7LrBsr5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/lbjUM7LrBsr5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: The structure shown supports a force F=20kN. Use the vector approach with the position vectors cited below to determine the moment of the force about point A.(a) Use the position vector from point A to point D, namely \vec{r}_AD(b) Use the position vector from point A to point E, namely \vec{r}_AE 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/lbjUM7LrBsr5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738679815164.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/pnZbw5BOkKT2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/pnZbw5BOkKT2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: Determine the moment of force F about point O. The force has a magnitude of 800 N and coorrdinate direction angles of \alpha=60^\circ, \beta=120^\circ, \gamma=45^\circ. Express the result as a Cartesian vector. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/pnZbw5BOkKT2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738680527690.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/rVqISL2MHRWC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/274/rVqISL2MHRWC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on implicit differentiation of functions of several variables using partial derivatives and Jacobian determinants. Solved: Given that x^2 + y^2 + z^2 = 1 where z(x, y), obtain \frac {\partial z} {\partial x} and \frac {\partial z} {\partial y}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/274/rVqISL2MHRWC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yTvQgcCq8IaY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/78/yTvQgcCq8IaY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating first partial derivatives from the first principles. Solved: Let the function f : \mathbb{R}^2 \rightarrow \mathbb{R} be defined by f(x,y) = \begin {cases} \frac {y^2 - x^2} {xy - 1}, (x, y) \ne (1, 1) \\ 2, (x,y) = (1, 1) \end {cases}.Find \frac {\partial y} {\partial x} at the point (1, 1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/78/yTvQgcCq8IaY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3vSul_J0_rdz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/296/3vSul_J0_rdz.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components. Solved: If the resultant force acting on the bracket is required to be a minimum, determine the magnitudes of F_1 and the resultant force. Set \phi = 30^{\circ}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/296/3vSul_J0_rdz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739469542922.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/jWwXJrMvYNx_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/jWwXJrMvYNx_.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A 110-N force acting in a vertical plane parallel to the yz plane is applied to the 220-mm-long horizontal handle AB of a socket wrench. Replace the force with an equivalent force-couple system at the origin O of the coordinate system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/jWwXJrMvYNx_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739185744106.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/SMMOuNULm3_S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/SMMOuNULm3_S.jpg</video:thumbnail_loc>

            <video:title>Log of a log</video:title>

            <video:description><![CDATA[
Spot a fraction where the denominator hides its own derivative. Why miss the log jump when the top is just one over x? This walkthrough shows you how to solve nested logs by sight. Solved: Determine the integral \int \frac{1}{x \ln x} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/SMMOuNULm3_S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mcKWX2RPDIuO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/mcKWX2RPDIuO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on dependent motion analysis with aligned cables. Solved: The motor draws in the cable at C with a constant velocity of v_C=4m/s. The motor draws in the cable at D with a constant acceleration of a_D=8m/s^2. If v_D=0 when t=0, determine (a) the time needed for block A to rise 3m and (b) the relative velocity of block A with respect to block B when this occurs. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/mcKWX2RPDIuO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742049465042.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/XD8BxTnVJ20i</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/XD8BxTnVJ20i.jpg</video:thumbnail_loc>

            <video:title>Equations of motion</video:title>

            <video:description><![CDATA[
Equations of motion and procedure for force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/XD8BxTnVJ20i.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yZEsmMR3ftJJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/rfniqbE772/Thumbnails/91/yZEsmMR3ftJJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on solving homogeneous linear ordinary differential equations with constant coefficients. Solved: Solve the initial value problem\ddot x + 2\dot x + 5x = 0; x(0) = 1; \dot x(0) = 0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/rfniqbE772/Previews/91/yZEsmMR3ftJJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wy18HWvA7o3K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/Wy18HWvA7o3K.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: If the motor turns gear A with an angular acceleration of \alpha _A=3rad/s^2 when the angular velocity is \omega_A=60rad/s, determine the angular acceleration and angular velocity of gear D. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/Wy18HWvA7o3K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743852795798.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/VLhpfLfqEasW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/206/VLhpfLfqEasW.jpg</video:thumbnail_loc>

            <video:title>Expressions (1)</video:title>

            <video:description><![CDATA[
Expressions for Sine and Cosine functions and their powers using complex numbers in polar and exponential forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/206/VLhpfLfqEasW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8KZogKgWpeVn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/8KZogKgWpeVn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components. Solved: Pin B weighs 4 oz and is free to slide in a horizontal plane along the rotating arm OC and along the fixed circular slot DE of radius b=20 in. Neglecting friction and assuming that \theta=15rad/s and \theta=250rad/s^2 for the position \theta=20^0, determine for that position (a) the radial and transverse components of the resultants forces exerted on pin B (b) the forces P and Q on pin B , respectively by rod OC and the wall of slot DE 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/8KZogKgWpeVn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1746110602636.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/IHkhfs5eUW6z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/IHkhfs5eUW6z.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: The 50-mm-radius pulley A of the clothes dryer rotates with an angular acceleration of \alpha_A= {(27 \theta_A^\frac{1}{2})} rad\s^2, where \theta_A is in radians. Determine its angular acceleration when t=1s , starting from rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/IHkhfs5eUW6z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743766347449.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/yoyVOug3ockz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/yoyVOug3ockz.jpg</video:thumbnail_loc>

            <video:title>Applications</video:title>

            <video:description><![CDATA[
Applications of the motion of a point on a rigid body undergoing rotation about a fixed axis - gears, pulleys and their connections.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/yoyVOug3ockz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/co49mcmhgtiF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/co49mcmhgtiF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: The paint spraying robot is programmed to paint a production line of curved surfaces A (seen on edge). The length of the telescoping arm is controlled according to b = 0.3 sin (\frac \pi 2), where b is in meters and t is in seconds. Simultaneously, the arm is programmed to rotate according to \theta = \frac \pi 4 + (\frac \pi 8) sin (\frac \pi 2) radians. Calculate the magnitude v of the velocity of the nozzle N and the magnitude \alpha of the acceleration of N for t = 1 s and t = 2 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/co49mcmhgtiF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742220561598.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0d_yUg7r3gZS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/0d_yUg7r3gZS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: The pin is free to slide along the circular slot DE and along the rotating rod OC. Assuming that the rod OC rotate at a constant rate \dot \theta,(a) show that the acceleration of pin B is of constant magnitude(b) determine the direction of the acceleration of pin B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/0d_yUg7r3gZS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742221477870.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/iPuqocaONPm3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/aNaQYVEiEu/Thumbnails/165/iPuqocaONPm3.jpg</video:thumbnail_loc>

            <video:title>Units of a force</video:title>

            <video:description><![CDATA[
Units of force in the S. I. system and U. S. customary units.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/aNaQYVEiEu/Previews/165/iPuqocaONPm3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MmsQU5cEub4b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/12/MmsQU5cEub4b.jpg</video:thumbnail_loc>

            <video:title>Centroid</video:title>

            <video:description><![CDATA[
Meaning and analysis of the centroid of a number of points.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/12/MmsQU5cEub4b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GCbv2GjK6xqX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/GCbv2GjK6xqX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: The mass center G of the car has a velocity of 40mi\hr at position A and 1.52 seconds later at B has a velocity of 50mi\hr. The radius of curvature of the road at B is 180ft. Calculate the angular velocity \omega of the car at B and the average angular velocity \omega_{av} of the car between A and B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/GCbv2GjK6xqX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743770712658.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/any6XbwVA6dJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cW9hj6hg0X/Thumbnails/1202/any6XbwVA6dJ.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson explains the MTH 102 course structure and its alignment with the NUC CCMAS syllabus. You will learn the order of modules needed to cover the entire calculus curriculum for your exams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cW9hj6hg0X/Previews/1202/any6XbwVA6dJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kJC_pQr5kF8f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/kJC_pQr5kF8f.jpg</video:thumbnail_loc>

            <video:title>Exponential base</video:title>

            <video:description><![CDATA[
Spot an exponential fraction with a powered denominator. Why use the log rule when the power is not one? This walkthrough shows you how to apply the functional power pattern by sight. Solved: Find the integral \int \frac{e^{x}}{(e^{x} + 1)^{2}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/kJC_pQr5kF8f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AxeRQIQ5RwdW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Thumbnails/1397/AxeRQIQ5RwdW.jpg</video:thumbnail_loc>

            <video:title>Zaitsev's rule</video:title>

            <video:description><![CDATA[
Elimination reactions often yield multiple alkene products from a single substrate. How do you predict which isomer dominates when hydrogen can be removed from more than one adjacent carbon? This lesson states Zaitsev's rule and links product stability to substitution level precisely.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/MVabJ1KDOv/Previews/1397/AxeRQIQ5RwdW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DrrkZuYxGg0s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/DrrkZuYxGg0s.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on curvilinear motion in rectangular coordinates. Solved: A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. The motion of the car is defined by the position vector r = (2 + 2t^2)i + (6 + t^3)j, where r and t are expressed in meters and seconds, respectively. Determine(a) the distance between the car and the girl when t=2 s,(b) the distance the car travelled in the interval from t=0 s to t=2 s,(c) the speed and the direction of the car's velocity at t=2 s,(d) the magnitude of the car's acceleration at t=2 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/DrrkZuYxGg0s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742211258165.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/AQsXXmLz689m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/665/AQsXXmLz689m.jpg</video:thumbnail_loc>

            <video:title>What and why?</video:title>

            <video:description><![CDATA[
This lesson defines the command-line interface and answers the critical question: why use it? We explain how the CLI provides the speed, control, and automation that graphical interfaces lack, making it an indispensable tool for any serious developer.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/665/AQsXXmLz689m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dd7nrAx9LXiU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/dd7nrAx9LXiU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: A motor gives gear A an angular acceleration of \alpha_A= {(2t^3)}rad/s^2 , where t is in seconds. If this gear is initially turning at \omega_A=15rad\s, determine the angular velocity of gear B when t=3s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/dd7nrAx9LXiU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743852032178.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sLtyewXGod92</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/sLtyewXGod92.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 2-kg collar is at rest in position A when the constant force P is applied as shown. Determine the speed of the collar as it passes position B if (a)P=25N and (b)P=40N . The curved rod lies in a vertical plane, and friction is negligible. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/sLtyewXGod92.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746784241087.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JtexyP8Wa9Vw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/297/JtexyP8Wa9Vw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of a particle in two dimensions. Solved: The slider A is in equilibrium and the bar is smooth. What is the mass of the slider? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/297/JtexyP8Wa9Vw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739782722906.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/eMm_jgfTvJ6k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/eMm_jgfTvJ6k.jpg</video:thumbnail_loc>

            <video:title>Direct product jump</video:title>

            <video:description><![CDATA[
Spot a function multiplied by its own derivative. Why expand brackets when the power rule applies directly to the base? This walkthrough shows you how to integrate by sight. Solved: Determine \int (x^{2} + 12x + 2)(2x + 12) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/eMm_jgfTvJ6k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1I37ZBwFMM4e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Thumbnails/94/1I37ZBwFMM4e.jpg</video:thumbnail_loc>

            <video:title>Hyperbola</video:title>

            <video:description><![CDATA[
Equation of a hyperbola.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/uYz3YfA6bZ/Previews/94/1I37ZBwFMM4e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4MqPdW7AUNyb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/4MqPdW7AUNyb.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: The mechanism of a machine is constructed so that the roller at A follows the surface of the cam described by the equation r = (0.3 + 0.2 cos \theta) m. If \dot \theta = 0.5 rad/s and \ddot \theta = 0, determine the magnitudes of the roller's velocity and acceleration when \theta = 30^\circ. Neglect the size of the roller. Also determine the velocity components (v_A)_x and (v_A)_y of the roller at this instant. The rod to which the roller is attached remains vertical and can slide up and down along the guides while the guides translate horizontally to the left. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/4MqPdW7AUNyb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742222966245.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/63FzCppmBXcV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/63FzCppmBXcV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems of the second kind. Solved: The motion of a peg sliding within a rectilinear guide is controlled by an actuator in such a way that the peg's acceleration takes on the formx=a_0(2\cos 2\omega t -\beta\sin\omega t) , where t is time, a_0=3.5m/s, \omega=0.5m/s, and \beta=1.5 a) Determine the expressions for the velocity and the position of the peg as functions of time if x(0)=0m/s and x(0)=0mb) Determine the total distance travelled by the peg during the time interval 0s\le t\le 5s if x(0)=a_0\beta /\omega 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/63FzCppmBXcV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1741948212960.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/BlWKprW0Ir6h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/212/BlWKprW0Ir6h.jpg</video:thumbnail_loc>

            <video:title>Definition</video:title>

            <video:description><![CDATA[
Meaning of linear dependence and independence of vectors in a vector space.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/212/BlWKprW0Ir6h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LM5CBcM4Ccg0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/LM5CBcM4Ccg0.jpg</video:thumbnail_loc>

            <video:title>Creating your first repository</video:title>

            <video:description><![CDATA[
A repository is the foundation of a version-controlled project. This lesson covers the first practical command, `git init`, which creates a new repository and instructs Git to begin tracking changes within a folder.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/LM5CBcM4Ccg0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q-toqw7IqltZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/Q-toqw7IqltZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
Worked examples on curvilinear motion in rectangular coordinates involving algebraic relations. Solved: A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y^2 = [120(10^3)x] m. If the x component of the acceleration is a_x = (\frac 1 4 t^2) m/s^2, where t is in seconds, determine the magnitudes of the rocket's velocity and acceleration when t=10 s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/Q-toqw7IqltZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/r5ubaVV11ael</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/r5ubaVV11ael.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
Worked examples on particle rectilinear motion problems of the 4th kind. Solved: Starting from x=0 with no initial velocity, a particle is given an acceleration a=0.8\sqrt{v^2+49} where a and v are expressed in ft/s^2 and ft/s , respectively. Determine (a) the position of the particle when v=24ft/s (b) the speed and acceleration of the particle when x=40ft 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/r5ubaVV11ael.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GFFn7330i-UK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/GFFn7330i-UK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: The motor applies a constant download force F=550 lb to the cable connected to the 4000-lb elevator E shown in the figure. The counterweight has a weight of W=3000 lb. Knowing that the elevator starts from rest, determine the time when the velocity of the elevator will be 3ft/s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/GFFn7330i-UK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748267789317.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/woJauPHZWYyU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/woJauPHZWYyU.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components. Solved: The robot is programmed so that the 0.4-kg part A describes the partr=1-0.5 \cos2 \pi tm\theta=0.5-0.2\sin 2 \pi tradDetermine the polar components of force exerted on A by the robot's jaw at t = 2s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/woJauPHZWYyU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745935881445.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/YITe9Zjzbm8a</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/209/YITe9Zjzbm8a.jpg</video:thumbnail_loc>

            <video:title>Polynomials</video:title>

            <video:description><![CDATA[
Examples of vector spaces - space of polynomials and its operators.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/209/YITe9Zjzbm8a.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Qc8ZvzB4P3Vu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/789/Qc8ZvzB4P3Vu.jpg</video:thumbnail_loc>

            <video:title>The form element</video:title>

            <video:description><![CDATA[
This lesson introduces the <form> element, the essential container for all input fields. We will discuss its role and important attributes like 'action' and 'method'.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/789/Qc8ZvzB4P3Vu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3x2sIGler6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/3x2sIGler6.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Integration reverses differentiation to find totals. How do you master the core methods for solving complex problems? This course outlines the essential techniques for your technical journey.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/3x2sIGler6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0IZL6Ha8XC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/0IZL6Ha8XC.jpg</video:thumbnail_loc>

            <video:title>Fundamental theorem (1)</video:title>

            <video:description><![CDATA[
Integration and differentiation are inverse operations. How do you differentiate an integral with a variable upper limit? We prove the First Fundamental Theorem and recover the original integrand.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/0IZL6Ha8XC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M5UMbotRurJd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/M5UMbotRurJd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems. Solved: On its takeoff roll, the airplane starts from rest and accelerates according to a=a_0-kv^2 , where a_0 is the constant acceleration resulting from the engine thrust and -kv^2 is the acceleration due to aerodynamic drag. If a_0=2m/s, k=0.00004m^{-1}, and v is in meters per second , determine the design length of runway required for the airplane to reach the takeoff speed of 250km/h if the drag term is (a) excluded and (b) included. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/M5UMbotRurJd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746264806996.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gox6wBR3p1UP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/gox6wBR3p1UP.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: The 70-m microwave transmission tower is steadied by three guy cables as shown. Cable AB carries a tension of 12kN. Express the corresponding force on point B as a vector. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/gox6wBR3p1UP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739795383425.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/HK47ir_Hj7cS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/279/HK47ir_Hj7cS.jpg</video:thumbnail_loc>

            <video:title>Method</video:title>

            <video:description><![CDATA[
The method of Lagrange multiplier for examining stationary points of a function of two variables subject to a constraint.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/279/HK47ir_Hj7cS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2bR4qo3nm2Ka</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/157/2bR4qo3nm2Ka.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of particles. Solved: A 60-kg woman holds a 9-kg package as she stands within an elevator which briefly accelerates upward at a rate of g/4. Determine the force R which the elevator floor exerts on her feet and the lifting force L which she exerts on the package during the acceleration interval. If the elevator support cables suddenly and completely fail, what values would R and L acquire? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/157/2bR4qo3nm2Ka.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742298265469.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/C57hSQJ3in</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/C57hSQJ3in.jpg</video:thumbnail_loc>

            <video:title>Reciprocal trigonometric functions</video:title>

            <video:description><![CDATA[
Reciprocal trigonometric integrals often trap students with sign errors. How do you handle cotangent, secant, cosecant, and their common product forms correctly? This lesson clarifies the standard results for these functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/C57hSQJ3in.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/P8PpBQYnVo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/P8PpBQYnVo.jpg</video:thumbnail_loc>

            <video:title>Primary trigonometric functions</video:title>

            <video:description><![CDATA[
Trigonometric integrals form the backbone of oscillation models. How do you integrate sine, cosine, and tangent without error? This lesson locks in the standard forms for immediate recall.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/P8PpBQYnVo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QfiGdPhqU8tZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/QfiGdPhqU8tZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components. Solved: The collar, which has a weight of 30 lb, slides along a smooth rod lying in the horizontal plane and having the shape of a parabola r=[4/1-(\cos\theta)]ft. Where \theta is in radians. If the collar's angular rate is constant and equals \theta=4rad/s, determine the tangential force P needed to cause the motion and the normal force components that the collar exerts on the rod at the instant \theta=90^0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/QfiGdPhqU8tZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/c2eLh88ew9-T</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/618/c2eLh88ew9-T.jpg</video:thumbnail_loc>

            <video:title>Special limits</video:title>

            <video:description><![CDATA[
Evaluating limits of functions by use of known special limits.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/618/c2eLh88ew9-T.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ptJYl-xj4Qil</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/ptJYl-xj4Qil.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: During a hammer thrower's practice swings, the 7.1kg head A of the hammer revolves at a constant speed in a horizontal circle as shown. Knowing that the speed of the hammer is 2.5m/s and \theta =60^{\circ}, determine (a) the tension in wire BC, (b) the radius of the circle, p. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/ptJYl-xj4Qil.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745925591003.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/7ZarMkf30OZV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/7ZarMkf30OZV.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: The motion of an oscillating flywheel is defined by the relation\theta =\theta_0e^{-3\pi t} \cos 4\pi t , where \theta is expressed in radians and t in seconds. Knowing that \theta_0=0.5rad , determine the angular coordinate, the angular velocity, and the angular acceleration of the flywheel when (a) t=0, (b) t=0.125s 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/7ZarMkf30OZV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743765431155.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/uPI-NNemmhhm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/148/uPI-NNemmhhm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on acceleration analysis of the motion of a rigid body undergoing general plane motion using the acceleration of a point relative to another point on the same rigid body. Solved: The center O of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of A and the acceleration of B for the instant represented. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/148/uPI-NNemmhhm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744987467712.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xKQRRLBHN8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/xKQRRLBHN8.jpg</video:thumbnail_loc>

            <video:title>Rationalising substitutions</video:title>

            <video:description><![CDATA[
Standard substitution fails when orphaned variables remain. How do you clear mixed radicals and express stray x terms in u? We use algebraic inversion and LCM powers to rationalise the integrand.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/xKQRRLBHN8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dCa5xiHOo8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/dCa5xiHOo8.jpg</video:thumbnail_loc>

            <video:title>Inverse trigonometric functions</video:title>

            <video:description><![CDATA[
Inverse trigonometric functions act as both integrands and integration results. How do you integrate arcsine itself versus spotting the algebraic fraction that yields arctan? We cover both roles with precise standard forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/dCa5xiHOo8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s4EBZBxSGf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/s4EBZBxSGf.jpg</video:thumbnail_loc>

            <video:title>Exponential functions</video:title>

            <video:description><![CDATA[
Exponential integrals drive growth and decay models. How do you handle base e and general base a forms? This lesson fixes the standard rules for both cases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/s4EBZBxSGf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0VyOFXhZv_Rx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/0VyOFXhZv_Rx.jpg</video:thumbnail_loc>

            <video:title>Rated voltage</video:title>

            <video:description><![CDATA[
Dielectric strength sets the voltage limit. How do you calculate rated voltage and maximum charge before breakdown? We apply field limits to find the safe operating boundary. Solved: A parallel-plate capacitor is designed for a school laboratory project using a dielectric material with a dielectric constant of 5.00 and a dielectric strength of 20.0\text{ kV/mm}. The plates have an area of 8.00\text{ cm}^2 and are separated by a gap of 3.00\text{ mm} which is completely filled by the dielectric. Determine (i) the maximum safe operating voltage (rated voltage) for this capacitor and (ii) the absolute limit of charge it can store before the material fails. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/0VyOFXhZv_Rx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zFwOHwCMRR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/zFwOHwCMRR.jpg</video:thumbnail_loc>

            <video:title>The LIATE rule</video:title>

            <video:description><![CDATA[
Integration by parts requires correct term selection. How do you systematically choose u to avoid complex integrals? This lesson establishes the LIATE priority hierarchy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/zFwOHwCMRR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NDOLsayka2RG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/674/NDOLsayka2RG.jpg</video:thumbnail_loc>

            <video:title>The meta tag</video:title>

            <video:description><![CDATA[
The <meta> tag provides structured data about your document to browsers and search engines. This lesson covers the most important meta tags, including the description for SEO and the viewport for mobile responsiveness. Getting these right is a professional requirement.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/674/NDOLsayka2RG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ComlMgFSsa-6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/ComlMgFSsa-6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 20-N object at B moves in a circular, horizontal path under the action of a cord AB and a rigid bar BC, which can be considered weightless. At the instant B has a speed 2m/s, what are the forces in the cord AB and the bar BC? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/ComlMgFSsa-6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745332704577.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/y1xt9sqEyXin</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/789/y1xt9sqEyXin.jpg</video:thumbnail_loc>

            <video:title>The input and label elements</video:title>

            <video:description><![CDATA[
We will learn how to create text fields using the <input> element and how to properly associate them with a <label> for accessibility, which is a non-negotiable professional standard.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/789/y1xt9sqEyXin.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uX2gr91bGW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1129/uX2gr91bGW.jpg</video:thumbnail_loc>

            <video:title>Back-substitution</video:title>

            <video:description><![CDATA[
Radicals trap extra powers of x outside the root. How do you express stray terms in u when the differential is incomplete? This walkthrough uses algebraic inversion to clear the integrand. Solved: Evaluate \int x^{5} \sqrt{x^{3} + 1} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1129/uX2gr91bGW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/56YgQYjfasXi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/56YgQYjfasXi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: Calculate the moment of 250-N force on the handle of the monkey wrench about the center of the bolt. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/56YgQYjfasXi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688004712.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nV4dc61nDU6H</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/nV4dc61nDU6H.jpg</video:thumbnail_loc>

            <video:title>Mechanics</video:title>

            <video:description><![CDATA[
Meaning of mechanics and engineering mechanics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/nV4dc61nDU6H.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Q34dFE1S4TgH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/Q34dFE1S4TgH.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on dependent motion analysis with aligned cables. Solved: Slider block A moves to the right with a constant velocity of 300m/s. Determine (a) the velocity of slider block A (b) the velocity of portion C of the cable (c) the velocity of portion D of the cable (d) the relative velocity of portion C of the cable with respect to slider block A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/Q34dFE1S4TgH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742048531883.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/6rTS2IJcgbAh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/148/6rTS2IJcgbAh.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on acceleration analysis of the motion of a rigid body undergoing general plane motion using the acceleration of a point relative to another point on the same rigid body. Solved: The deployment mechanism for the spacecraft magnetometer boom of 5-9 is shown again here. The driving link OB has a constant clockwise angular velocity \omega_{OB} of 0.5rad\sec as it crosses the vertical position. Determine the angular acceleration \alpha_{CA} of the boom for the position shown where tan\theta=\frac{4}{3} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/148/6rTS2IJcgbAh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1747301474409.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Gx_Eg_9-h81c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/Gx_Eg_9-h81c.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: (i) A 300-N force is applied at A as shown. Determine (a) the the moment of the 300-N force about D, (b) the smallest force applied at B that creates the same moment about D.(ii) A 300-N force is applied at A as shown. Determine (a) the moment of the 300-N force about D, (b) the magnitude and sense of the horizontal force applied at C that creates the same moment about C, (c) the smallest force applied at C that creates the same moment about D. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/Gx_Eg_9-h81c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688263538.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/UYQ2zTYKE7FT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/aNaQYVEiEu/Thumbnails/165/UYQ2zTYKE7FT.jpg</video:thumbnail_loc>

            <video:title>Forces and reactions (1)</video:title>

            <video:description><![CDATA[
How to obtain different forces and reactions in a given system, for use in free-body diagrams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/aNaQYVEiEu/Previews/165/UYQ2zTYKE7FT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pfwOAUP52A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/pfwOAUP52A.jpg</video:thumbnail_loc>

            <video:title>Product with one</video:title>

            <video:description><![CDATA[
Lone transcendental functions resist direct integration. How does the product with one trick enable evaluation by parts? This walkthrough applies the method to find the antiderivative. Solved: Find \int \ln x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/pfwOAUP52A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9NL0kdRQgLCZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/152/9NL0kdRQgLCZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on dependent motion analysis with unaligned cables. Solved: The block B suspended from a cable that is attached to the block at E, wraps around three pulleys and is tied to back of a truck. If the truck starts from rest when x_D is zero, and moves forward with a constant acceleration of a_D=0.5m/s^2, determine the speed of the block at the instant x_D=2m. neglect the size of the pulleys in the calculation. when x_D=0,y_C=5m, so that point C and D are the same elevation. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/152/9NL0kdRQgLCZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742050617350.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/F9u3zsujLHvN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/F9u3zsujLHvN.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: If the tension in the belt is 52 lb, determine the moment of each of the forces about the pin at A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/F9u3zsujLHvN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688638788.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sEGdGLkmR_Rp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/310/sEGdGLkmR_Rp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for two dimensional cases. Solved: The bar BC exerts a force at C that points from C toward B. The hydraulic cylinder DH exerts a 1550-N force at D that points from D toward H. The sum of the moments of these two forces about K is zero. What is the magnitude of the force that bar BC exerts at C? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/310/sEGdGLkmR_Rp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688823168.JPEG</image:loc>
            </image:image>
            
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738688908337.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/29fUorV1l2VD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/29fUorV1l2VD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: A container of weight W is suspended from ring A, to which cables AC and AE are attached. A force P is applied at the end F of a third cable that passes over a pulley at B and through ring A and that is attached to a support at D. Knowing that W = 1000 N, determine the magnitude of P. ( The tension is the same in all portions of cables FBAD.) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/29fUorV1l2VD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740072492075.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JNBOSHrxWMVk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/JNBOSHrxWMVk.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on simplifying systems of forces on rigid bodies. Solved: Replace the force and couple moment system acting on the beam by an equivalent resultant force and couple moment at point O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/JNBOSHrxWMVk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740077114754.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/MwFM_P1hXRNc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/155/MwFM_P1hXRNc.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on particle curvilinear motion problems using radial and transverse (polar) components. Solved: The rotation of rod OA about O is defined by the relation \theta = \pi(4t^2 - 8t), where \theta and t are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance from O is r = 10 + 6 sin \pi t where r and t are expressed in inches and seconds, respectively. When t= 1 s, determine(a) the velocity of the collar(b) the acceleration of the collar (c) the acceleration of the collar relative to the rod. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/155/MwFM_P1hXRNc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742219899224.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/rQS88K_CHec7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/293/rQS88K_CHec7.jpg</video:thumbnail_loc>

            <video:title>Systems of units (2)</video:title>

            <video:description><![CDATA[
Conversion from one system of unit to another.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/293/rQS88K_CHec7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GoC2VOkWvjV6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/GoC2VOkWvjV6.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: Determine the magnitude of F so that resultant couple moment is 450 lb . ft, counterclockwise. Where on the beam does the resultant couple moment act? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/GoC2VOkWvjV6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738863877630.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/e4XdATe4ybYt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/e4XdATe4ybYt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 2-Ib block slides down the smooth parabolic surface, such that when it is at A it has a speed of 10ft/s . Determine the magnitudes of the block's velocity and acceleration when it reaches point B, and the maximum height y_{max} reached by the block. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/e4XdATe4ybYt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746786334825.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/khF6k-8oxVhk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/137/khF6k-8oxVhk.jpg</video:thumbnail_loc>

            <video:title>More worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on solutions of general systems of linear equations. Solved: Solve-2x+4y+2z-8s+4t=-83x-6y-2z+11s-7t=13x-2y-5z+8s+t=-3 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/137/khF6k-8oxVhk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HxWOvsm2ckYo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/HxWOvsm2ckYo.jpg</video:thumbnail_loc>

            <video:title>Flat horizontal road</video:title>

            <video:description><![CDATA[
Calculate the maximum speed a car can maintain on a flat circular track without skidding. You will equate static friction to the required centripetal force to find the safe velocity limit. This walkthrough applies Newton's laws to vehicle stability on unbanked curves.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/HxWOvsm2ckYo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J0xRlYjev3nv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/65/J0xRlYjev3nv.jpg</video:thumbnail_loc>

            <video:title>Harmonic progressions</video:title>

            <video:description><![CDATA[
Meaning, examples, and descriptions of harmonic progressions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/65/J0xRlYjev3nv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dWMEYO14g8vh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/666/dWMEYO14g8vh.jpg</video:thumbnail_loc>

            <video:title>Code formatters</video:title>

            <video:description><![CDATA[
Arguments over code style are unproductive and a waste of time. This lesson introduces code formatters, tools that automatically enforce a consistent style across your project, ensuring your code is always readable and professional.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/666/dWMEYO14g8vh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B9p3-Ay80YHi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/B9p3-Ay80YHi.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: The rubber mallet is used to drive a cylindrical plug into the wood member. If the impact force varies with time as shown in the plot, determine the magnitude of the linear impulse derived by the mallet to the plug. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/B9p3-Ay80YHi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748265301048.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/CrDf_WVunFT9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/CrDf_WVunFT9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: The 200-kg crate rest on the ground for which the coefficients of static and kinetic friction are u_s =0.5 and u_k=0.4, respectively. The winch delivers a horizontal towing force T to its cable at A which varies as shown in the graph. Determine the speed of the crate when t=4s. Originally the tension in the cable is zero. Hint: First determine the force needed to begin moving the crate. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/CrDf_WVunFT9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748267437020.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dVYRb0PAoi_4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/dVYRb0PAoi_4.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: A boat trailer is subjected to the forces shown where the forces at point A-E are vertical and the forces at points F and G lies on the y z plane. Determine(a) an equivalent force system at point O,(b) an equivalent force system consisting of a single force, specifying the x and y coordinates of the point where the force's line of action intersects the x y plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/dVYRb0PAoi_4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740078265829.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/9SPUN_uDSJ6V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/9SPUN_uDSJ6V.jpg</video:thumbnail_loc>

            <video:title>Vertical circle (1)</video:title>

            <video:description><![CDATA[
Calculate the varying tension in a string as a mass moves in a vertical circle. You will resolve weight and centripetal force at the top and bottom positions to find the minimum and maximum tension. This walkthrough demonstrates how gravity affects non-uniform circular motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/9SPUN_uDSJ6V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AKeXlg5lL4VC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/789/AKeXlg5lL4VC.jpg</video:thumbnail_loc>

            <video:title>The submit button</video:title>

            <video:description><![CDATA[
Use <button> or <input type="submit"> to send form data. Learn their differences, key attributes, and how to place the submit button correctly in a contact form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/789/AKeXlg5lL4VC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1jmqzQXFT-t2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yequYBiBiU/Thumbnails/206/1jmqzQXFT-t2.jpg</video:thumbnail_loc>

            <video:title>Expressions (2)</video:title>

            <video:description><![CDATA[
Expressions for Sine and Cosine functions and their powers using complex numbers in polar and exponential forms.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yequYBiBiU/Previews/206/1jmqzQXFT-t2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/-enoxrUE0UIZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/163/-enoxrUE0UIZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it. Solved: The 90-kg man dives from the 40-kg canoe. The velocity indicated in the figure is that of the man relative to the canoe just after loss of contact. If the man, woman, and canoe are initially at rest, determine the horizontal component of the absolute velocity of the canoe just after separation. Neglect drag on the canoe, and assume that the 60-kg woman remains motionless relative to the canoe. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/163/-enoxrUE0UIZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1748268139075.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/tlL5bMLKBt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/tlL5bMLKBt.jpg</video:thumbnail_loc>

            <video:title>Null field location</video:title>

            <video:description><![CDATA[
Opposing fields cancel out. How do you calculate the exact coordinate where the net electric field is zero? Watch to solve this null point problem step by step. Solved: Two point charges, q_1 = +25.0 \mu\text{C} and q_2 = +9.00 \mu\text{C}, are fixed at x = 10.0\text{ cm} and x = 90.0\text{ cm} respectively. Find the coordinate on the x-axis where the net electric field is zero. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/tlL5bMLKBt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lDxLmjb8DdBS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/987/lDxLmjb8DdBS.jpg</video:thumbnail_loc>

            <video:title>Vertical circle (2)</video:title>

            <video:description><![CDATA[
Calculate the minimum speed required to maintain a vertical circular path without the string going slack. You will analyze forces at the highest point to determine the critical velocity where tension becomes zero. This example covers the threshold for complete circular motion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/987/lDxLmjb8DdBS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NfWZ3HlgbB8n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/NfWZ3HlgbB8n.jpg</video:thumbnail_loc>

            <video:title>Conservative forces</video:title>

            <video:description><![CDATA[
Gravity saves your work; electric force does the same. Why does this similarity prove the field is conservative? See the link that builds potential energy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/NfWZ3HlgbB8n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sy4IRh1fU6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1060/Sy4IRh1fU6.jpg</video:thumbnail_loc>

            <video:title>Uniqueness of carbon</video:title>

            <video:description><![CDATA[
Out of all elements in the universe, why does only one form the basis of every living thing? What makes carbon so special that life cannot exist without it? The answer lies in properties you will discover in this lesson.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1060/Sy4IRh1fU6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6OqCIRNQloep</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/6OqCIRNQloep.jpg</video:thumbnail_loc>

            <video:title>Composite product</video:title>

            <video:description><![CDATA[
Products of composite functions demand two rules at once. How do you apply the product rule while chaining the inner derivatives correctly? Watch the step-by-step breakdown to see the logic unfold. Solved: Find the derivative of the function h(z) = (z^2 + 4)^2 \sin(5z) with respect to z. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/6OqCIRNQloep.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a_KaEvcXf9KX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/a_KaEvcXf9KX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components. Solved: A 2kg mass rests on a flat horizontal bar. The bar begins rotating in the vertical plane about O with a constant angular acceleration of 1rad/s^2. The mass is observed to slip relative to the bar when the bar is 30^0 above the horizontal. What is the static coefficient of friction between the mass and the bar? Does the mass slip toward or away from O? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/a_KaEvcXf9KX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1746105068356.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/totwS4umwOMn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/totwS4umwOMn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 300-lb car is travelling at 60 mi/hr on the straight portion of the road, and then its speed is reduced uniformly from A to C, at which point it comes to rest. Compute the magnitude F of the total friction force exerted by the road on the car (a) just before it passes point B, (b) just after it passes point B, and (c) just before it stops at point C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/totwS4umwOMn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745331553230.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/QqcBk_K0TArC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/789/QqcBk_K0TArC.jpg</video:thumbnail_loc>

            <video:title>Grouping inputs</video:title>

            <video:description><![CDATA[
Use <fieldset> and <legend> to group related inputs. Learn how grouping improves clarity, accessibility, and structure in a professional contact form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/789/QqcBk_K0TArC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/X_hydS0gK0t8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/922/X_hydS0gK0t8.jpg</video:thumbnail_loc>

            <video:title>Work of spring and weight</video:title>

            <video:description><![CDATA[
Calculate work done by gravity on falling objects and by springs during extension or compression. Use the weight formula for vertical movement and Hooke's law for variable spring forces. These calculations are required for applying the work-energy theorem to mechanical systems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/922/X_hydS0gK0t8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C48uEYuuyMpS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/C48uEYuuyMpS.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: Two bolts at A and B are tightened by applying the forces and couples shown. Replace the two wrenches with a single equivalent wrench and determine (a) the resultant R (b) the pitch of the single equivalent wrench (c) the point where the axis of the wrench intersects the xz plane. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/C48uEYuuyMpS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740300513778.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/_zYIpra6JLJ1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/_zYIpra6JLJ1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The maximum allowable value for each of the reactions is 180N. Neglecting the weight of the beam, determine the range of the distance d for which the beam is safe. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/_zYIpra6JLJ1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736623777014.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/M0KDoecm8of_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/789/M0KDoecm8of_.jpg</video:thumbnail_loc>

            <video:title>Setting options</video:title>

            <video:description><![CDATA[
Use <select>, <option>, checkboxes, and radios to capture choices. Learn when each fits, how to structure them, and how to apply them in a contact form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/789/M0KDoecm8of_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bM8sKlvFCI23</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/bM8sKlvFCI23.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: Calculate the constant speed of the cars on the amusement-park ride if it is observed that the cables are directed at 30^\circ from the vertical. Each car, including its passengers, has a mass of 550kg . Also, what are the components of force on the n, t, and z directions which a 60-kg passenger exerts on the car during the motion? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/bM8sKlvFCI23.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745663482677.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5teeSO69ZyHo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/5teeSO69ZyHo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: A girl having a mass of 25kg sits at the edge of the merry-go-round so her center of mass G is at a distance of 1.5m from the axis of rotattion. If the angular motion of the platform is slowly increased so that the girl's tangential componenets of acceleration can be neglected, determine the maximum speed which she can have before she begins to slip off the merry-go-round. The coefficient of static friction between the girl and the merry-go-round is \mu_s=0.3 . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/5teeSO69ZyHo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745667690545.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-06hQU3WtGTC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/-06hQU3WtGTC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: For the beam and loading shown, determine the range of the distance a for which the reaction at B does not exceed 100 lb downward or 200 lb upward. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/-06hQU3WtGTC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736694881884.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/K-rLGMBVZmRb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/55/K-rLGMBVZmRb.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of piecewise-defined functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/55/K-rLGMBVZmRb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GUXdeyOAYMkT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/54/GUXdeyOAYMkT.jpg</video:thumbnail_loc>

            <video:title>Range of functions</video:title>

            <video:description><![CDATA[
Meaning of the range of functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/54/GUXdeyOAYMkT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3s4stjBH5e6g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/3s4stjBH5e6g.jpg</video:thumbnail_loc>

            <video:title>Worked examples (16)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The "egg beater" wind turbine is stopped by using spoilers which consists of 20lb blocks that slide out along the blades when the blades are turning. As the spoilers travel along the blades, the create a drag on the blade that slows and eventually stops the blade. If it is observed that the spoilers reach point A on the blades, determine the required minimum speed of the spoilers needed to maintain this position, and also the normal force they exert on the blade when in this position. The blade has the shape of a parabola, as shown in the figure. The coefficient of static friction between the spoilers and the blade is \mu_s=0.3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/3s4stjBH5e6g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1746107150901.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/2aY3s_8Hni</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/2aY3s_8Hni.jpg</video:thumbnail_loc>

            <video:title>Medical defibrillator</video:title>

            <video:description><![CDATA[
Capacitors deliver life-saving power. How do you find the charging voltage and average discharge power for a defibrillator? We solve this critical medical physics problem. Solved: A medical defibrillator unit at a clinic uses an 80.0 \text{-}\mu\text{F} capacitor. To treat a patient, the capacitor is charged until it stores 400 \text{ J} of electrical potential energy. During the procedure, 25.0\% of this stored energy is discharged through the patient's chest in a pulse lasting 4.00 \text{ ms}.(a) Calculate the potential difference (voltage) required to store the 400 \text{ J} in the capacitor.(b) Determine the average power delivered to the patient during the discharge pulse. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/2aY3s_8Hni.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Yuv35oSIYh8I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/62/Yuv35oSIYh8I.jpg</video:thumbnail_loc>

            <video:title>Differentiability on an interval</video:title>

            <video:description><![CDATA[
Derivative of a function over an interval.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/62/Yuv35oSIYh8I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mkgGb5Tm1JAj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/mkgGb5Tm1JAj.jpg</video:thumbnail_loc>

            <video:title>Intervals and boundary points</video:title>

            <video:description><![CDATA[
Master the use of open and closed intervals to define solution sets for inequalities. You will learn to distinguish between inclusive and exclusive boundary points using brackets, parentheses, and circles on the real number line. This notation is critical for representing range-based data sets.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/mkgGb5Tm1JAj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/q9HEb-KcZEtd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Thumbnails/619/q9HEb-KcZEtd.jpg</video:thumbnail_loc>

            <video:title>Rationalization</video:title>

            <video:description><![CDATA[
Evaluation of the limits of functions with rationalizable radicals at infinity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/7Q3ZqzeqmE/Previews/619/q9HEb-KcZEtd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3O_2WYSkpuH0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/3O_2WYSkpuH0.jpg</video:thumbnail_loc>

            <video:title>Potential energy curves</video:title>

            <video:description><![CDATA[
Potential energy curves reveal force and identify equilibrium states. Classify these states as stable, unstable, or neutral by observing the peaks and valleys of the curve. This visual analysis is essential for predicting system stability.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/3O_2WYSkpuH0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sjtvXu_X9LIf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/sjtvXu_X9LIf.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: If the roller at A and the pin at B can support a load up to 4 kN and 8 kN, respectively, determine the maximum intensity of the distributed load w, measured in kN/m, so that failure of the supports does not occur. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/sjtvXu_X9LIf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736823481550.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/hOdLsc8-xp2t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/616/hOdLsc8-xp2t.jpg</video:thumbnail_loc>

            <video:title>Exponential and logarithmic functions</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of exponential and logarithmic functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/616/hOdLsc8-xp2t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7AKVrGtz2Sbo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/7AKVrGtz2Sbo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The collar has a mass of 5kg and is confined to move along the smooth circular rod which lies in the horizontal plane. The attached spring has an unstretched length of 200mm . If at the instant \theta=30^\circ the collar has a speed v=2m/s , determine the magnitudes of the normal force of the rod on the collar and the collar's acceleration. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/7AKVrGtz2Sbo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745668387585.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xY8bA1mRGZIw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/xY8bA1mRGZIw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: A small box of mass m is given a speed of v=\sqrt{\frac{1}{4}gr} at the top of the smooth half cylinder. Determine the angle \theta at ehich the box leaves the surface. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/xY8bA1mRGZIw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746786641610.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-MDJry1vWeCQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/98/-MDJry1vWeCQ.jpg</video:thumbnail_loc>

            <video:title>Techniques of integration (2)</video:title>

            <video:description><![CDATA[
A review of the techniques of integration of single-variable real-valued functions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/98/-MDJry1vWeCQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_FBfAJ1o21oz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/_FBfAJ1o21oz.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: Three loads are applied as shown to a light beam supported by cables attached at B and D. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P=0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/_FBfAJ1o21oz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736823260701.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/PTlDV5hQ9hBY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/924/PTlDV5hQ9hBY.jpg</video:thumbnail_loc>

            <video:title>The impulse-momentum theorem</video:title>

            <video:description><![CDATA[
The impulse-momentum theorem states that the impulse applied to an object equals its change in momentum. This lesson explains how force acting over time changes an object's velocity, helping you calculate impact forces during collisions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/924/PTlDV5hQ9hBY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/121oQp93stRq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/121oQp93stRq.jpg</video:thumbnail_loc>

            <video:title>Viewing your Project's history</video:title>

            <video:description><![CDATA[
A version control system is useless without a way to view its history. This lesson covers the essential `git log` command, which displays a chronological list of all project commits, allowing you to understand how your code has evolved.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/121oQp93stRq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kqFu4wrEp5Cv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/kqFu4wrEp5Cv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The weight W_1= 1000 lb. Neglect the weight of the bar AB. The cable goes over a pulley at C. Determine the weight W_2 and the reactions at the pin support A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/kqFu4wrEp5Cv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736824239256.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gXRyFIJCh1UM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/gXRyFIJCh1UM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (15)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: The ladder AB, of length L and weight W, can be raised by cable BC. Determine the tension T required to raise end B just off the floor (a) in terms of W and \theta, (b) if h=8ft, and W=35lb. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/gXRyFIJCh1UM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736864129996.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0_8wT16gofqI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/0_8wT16gofqI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 5-Ib cylinder is falling from A with a speed v_A=10ft/s onto the platform. Determine the maximum displacement of the platform, caused by the collision. The spring has an unstretched length of 1.75tft and is originally kept in compression by the 1-ft-long cables attached to the platform. Neglect the mass of the platform and spring and any energy lost during the collision. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/0_8wT16gofqI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746787771452.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/7qetsicvKDYA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/315/7qetsicvKDYA.jpg</video:thumbnail_loc>

            <video:title>Worked examples (24)</video:title>

            <video:description><![CDATA[
More worked examples on the equilibrium of rigid bodies under the action of co-planar forces. Solved: It is desired that a person be able to begin closing the van hatch from the open position shown with a 10-lb vertical force P. As a design exercise, determine the necessary force in each of the two hydraulic struts AB. The center of the gravity of the 90-lb door is 1.5 in. directly below point A. Treat the problem as two-dimensional. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/315/7qetsicvKDYA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1736940130055.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/roDaauSNBAS1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cW9hj6hg0X/Thumbnails/1202/roDaauSNBAS1.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Learn to sync UniDrills modules with your university calculus lectures for maximum efficiency. This lesson shows you how to use digital tools alongside school notes to ensure you cover the NUC CCMAS syllabus and pass your exams.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cW9hj6hg0X/Previews/1202/roDaauSNBAS1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QbGAvEq3GXO1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/961/QbGAvEq3GXO1.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a formal welcome to the CSS course. We will review the unstyled HTML project and outline our goal of transforming it into the professional design we generated with AI.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/961/QbGAvEq3GXO1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/n6tQ89py2Bdt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/n6tQ89py2Bdt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (13)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: If P = 0 in the figure, replace the two remaining couples with a single equivalent couple, specifying its magnitude and the direction of its axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/n6tQ89py2Bdt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738866656223.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dA1y7eG_56Lr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/dA1y7eG_56Lr.jpg</video:thumbnail_loc>

            <video:title>Worked examples (16)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: Determine the magnitudes of the couple moments M_1, M_2, and M_3 so that the resultant couple moment is zero. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/dA1y7eG_56Lr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738866933868.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/v7Dlb3ogCh6A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/159/v7Dlb3ogCh6A.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using normal and tangential components. Solved: The 2-lb collar is released from rest at A and slides down along the smooth rod. If the attached spring has a stiffness k=2 lb/ft, determine its unstretched length so that it does not allow the collar to leave contact with the top surface of the rod until \theta =60^{\circ}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/159/v7Dlb3ogCh6A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1745931138516.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/lHmCUYJd4Qt3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/lHmCUYJd4Qt3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (15)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: Shafts A and B connects the gear box to the real assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lies in the vertical y z plane, while shaft C is directed along the x axis. Replace the couples applied to the shafts by a single equivalent couple, specifying its magnitude and the direction of its axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/lHmCUYJd4Qt3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738867666136.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/gQSt2H5mML5E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/217/gQSt2H5mML5E.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on proof of linearity of maps. Solved: Let D be the differential operator D:F\to{J} defined by D(f)=f^1. Show that D is a linear map. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/217/gQSt2H5mML5E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1JbFeoVPxISJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/1JbFeoVPxISJ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (10)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A 46-lb force F and a 2120-lb-in. couple M are applied to corner A of the block shown. Replace the given force-couple system with an equivalent force-couple system at corner H. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/1JbFeoVPxISJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740076878154.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/k_AhZ_BYVthb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/k_AhZ_BYVthb.jpg</video:thumbnail_loc>

            <video:title>Pushing your code to GitHub</video:title>

            <video:description><![CDATA[
Your work is not finished until it is on the remote server. This lesson shows you how to connect your local repository to GitHub and use the `git push` command to upload your commit history, making your code secure and ready for collaboration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/k_AhZ_BYVthb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SMSDXxjaoePZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/SMSDXxjaoePZ.jpg</video:thumbnail_loc>

            <video:title>Integrating an acceleration vector (1)</video:title>

            <video:description><![CDATA[
This lesson demonstrates the reverse process. Given an acceleration vector as a function of time, a(t), and a set of initial conditions, we will apply integration twice to determine the object's velocity and final position. Solved: 7. A body has an acceleration \vec{a} = (4.0t)\underline{j} m/s2. At t = 0, the body starts from the origin with an initial velocity \vec{v}_0 = (10\underline{i}) \text{ m/s}. Find its(a) velocity \vec{v}(t) and(b) position \vec{r}(t)at any time t. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/SMSDXxjaoePZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1utbZ4PqnjWI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/965/1utbZ4PqnjWI.jpg</video:thumbnail_loc>

            <video:title>Styling project cards</video:title>

            <video:description><![CDATA[
This lesson transforms the raw project list items into professional card components. We will apply backgrounds, padding, and a box-shadow to create a clean, self-contained layout for each project, a fundamental skill for organising content in modern web design.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/965/1utbZ4PqnjWI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tIKovZaLk35v</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/971/tIKovZaLk35v.jpg</video:thumbnail_loc>

            <video:title>Time</video:title>

            <video:description><![CDATA[
This lesson defines time as the measure of the interval between events. It establishes the second (s) as the SI base unit and covers the practical use of timing instruments, like the stopwatch, for experimental work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/971/tIKovZaLk35v.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1EvMHkuWlQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/1EvMHkuWlQ.jpg</video:thumbnail_loc>

            <video:title>Conductors and insulators</video:title>

            <video:description><![CDATA[
Materials differ in their ability to allow the flow of internal charges. Learn why metals conduct electricity while plastics and wood act as barriers to charge movement.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/1EvMHkuWlQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NylrP2dxpPuI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/NylrP2dxpPuI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using parameters measured relative to a reference frame in rotation. Solved: The disk rolls without slipping on the horizontal surface, and at the instant represented, the center O has the velocity and acceleration shown in the figure. For this instant, the particle A has the indicated speed u and the time rate of change of speed \dot{u} , both relative to the disk. Determine the absolute velocity and acceleration of particle A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/NylrP2dxpPuI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1745156028556.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/8YQy8_I8hqns</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/8YQy8_I8hqns.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using parameters measured relative to a reference frame in rotation. Solved: The motion of pin P is guided by slots cut in rods AE and BD. Knowing that the rods rotate with the constant angular velocities \omega _A=4rad/s clockwise and \omega_B=5rad/s clockwise, determine the velocity of pin P for the position shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/8YQy8_I8hqns.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1745661822186.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/etVPvRrqLnkx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/etVPvRrqLnkx.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: Rotation of the robotic arm occurs due to linear movement of the hydraulic cylinders A and B. If this motion causes the gear at D to rotate clockwise at 5rad/s, determine the magnitudes of velocity and acceleration of the part C held by the grips of arm. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/etVPvRrqLnkx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743850130927.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/88v195Ze9-UC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/88v195Ze9-UC.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: When an electric motor is turned on at t=0, its angular acceleration is \alpha=10e^{-0.5t} rad/s, where t is the time in seconds. What is the terminal angular velocity of the motor? How many revolutions are required for the motor to reach half of its terminal angular velocity? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/88v195Ze9-UC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tKZ4DLE1Nh1M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/299/tKZ4DLE1Nh1M.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on addition of vectors in three dimensions. Solved: Determine the position (x, y, o) for fixing cable BA so that the resultant force exerted on the pole is directed along its axis, from B toward O. Also, what is the magnitude of the resultant force? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/299/tKZ4DLE1Nh1M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739873579605.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Mafpn5tiILJ9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/391/Mafpn5tiILJ9.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying distributed loads on rigid bodies. Solved: Replace the loading by an equivalent resultant force and couple moment acting at point O. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/391/Mafpn5tiILJ9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740301192062.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ADvtTH_Eva63</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/661/ADvtTH_Eva63.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Meet your instructor, get the course structure, and understand how professionals approach web development. This is the foundation for everything that follows.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/661/ADvtTH_Eva63.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yN1P-Z5gO02F</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/160/yN1P-Z5gO02F.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of the curvilinear motion of a particle using radial and transverse components.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/160/yN1P-Z5gO02F.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/We0DcDm57gRn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/321/We0DcDm57gRn.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of planar trusses by the method of sections. Solved: Determine the force in members DG and EG of the truss shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/321/We0DcDm57gRn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1739014160401.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/4tZdjNauB1eL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/322/4tZdjNauB1eL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on the analysis of frames. Solved: Knowing that each pulley has a radius of 250nm, determine the components of the reactions at D and E. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/322/4tZdjNauB1eL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739271947442.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/cvbciflp_tBj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/151/cvbciflp_tBj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on uniform motion problems. Solved: A small packet is released from rest at A and moves along the skate wheel conveyor ABCD. the package has a uniform acceleration of 4.8m/s^2 as it moves down section AB and CD, and its velocity is constant between B and C. If the velocity of the package at D is 7.2m/s, determine (a) the distance C and D (b) the time required for the package to reach D. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/151/cvbciflp_tBj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742042416873.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/hPdmvLjltZXM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Thumbnails/388/hPdmvLjltZXM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating limits of real sequences. Solved: Determine whether or not the following sequences converge. If they do, find the limit.{\frac{n-1}{n} } 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/YVYij6A3MY/Previews/388/hPdmvLjltZXM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/v5IqNmOueQUc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/873/v5IqNmOueQUc.jpg</video:thumbnail_loc>

            <video:title>Other forms of radiation</video:title>

            <video:description><![CDATA[
You know alpha, beta, and gamma rays. But are they the only particles released during radioactive decay? This lesson exposes the lesser-known radiation types that complete the full picture of nuclear disintegration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/873/v5IqNmOueQUc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K20HpEk8hP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1140/K20HpEk8hP.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Stationary charges exert measurable forces across empty space. What precise role does the Coulomb constant play alongside the permittivity of free space in the inverse square relationship? Watch the video to see how these terms combine in real problems.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1140/K20HpEk8hP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gm_DRV26VOss</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/gm_DRV26VOss.jpg</video:thumbnail_loc>

            <video:title>Nitrogen estimation (2)</video:title>

            <video:description><![CDATA[
Dumas nitrogen estimation requires correcting for water vapour pressure. How do you calculate the percentage of nitrogen from gas collected over water? Watch this worked example to master the correction and calculation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/gm_DRV26VOss.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i-3kZsj6So4V</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/339/i-3kZsj6So4V.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of frictional forces (rolling resistance) on wheels. Solved: The lawn roller has a mass of 80kg . If the arm is held at an angle of 30^\circ from the horizontal and the coefficient of rolling resistance for the roller is 25mm , determine the force P needed to push the roller at constant speed. Neglect friction developed at the axle, A, and assume that the resultant force P acting on the handle is applied along arm BA . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/339/i-3kZsj6So4V.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746871683483.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/On7VxCp2iDuL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Thumbnails/210/On7VxCp2iDuL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on linear vector subspaces. Solved: let V be the vector space of real valued functions over the field IR. Show that W is a subspace of V if W consists of all bounded functions; i.eW=\{f:IR\to IR:\exists M \in IR,|f(x)|\le M\forall x\in IR\} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/mFibUjy3MF/Previews/210/On7VxCp2iDuL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FOXqfsFyKLf7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/334/FOXqfsFyKLf7.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of frictional forces on wedges. Solved: If the coefficient of static friction between the axe and the wood is \mu_s = 0.2, determine the smallest angle \theta of the blade which will cause the axe to be self-locking. Neglect the weight of the axe. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/334/FOXqfsFyKLf7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741110151419.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/MKU7bC6ihm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/MKU7bC6ihm.jpg</video:thumbnail_loc>

            <video:title>2D superposition</video:title>

            <video:description><![CDATA[
Charges off-axis create angled electric fields. How do you resolve and sum these vectors to find the net field at a point in 2D space? See the vector breakdown here. Solved: A point charge q_1 = +9.00 \mu\text{C} is at the origin, and a second charge q_2 = -6.00 \mu\text{C} is placed at x = 0.500\text{ m}. Calculate the magnitude and direction of the net electric field at a point P located at (0, 1.20)\text{ m}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/MKU7bC6ihm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PET0cB3XFg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/PET0cB3XFg.jpg</video:thumbnail_loc>

            <video:title>Point charge fields</video:title>

            <video:description><![CDATA[
A single charge creates a field. How do you calculate its strength and direction at any distance? Watch to master the formula for point charge fields.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/PET0cB3XFg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WhgS0Vxd47</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/WhgS0Vxd47.jpg</video:thumbnail_loc>

            <video:title>Electric field intensity</video:title>

            <video:description><![CDATA[
Charges push without touching. How do you measure the strength of this invisible field at any point in space? Watch to master the definition and calculation of electric field intensity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/WhgS0Vxd47.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9QZfjC1yW9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/9QZfjC1yW9.jpg</video:thumbnail_loc>

            <video:title>Motion in a uniform field</video:title>

            <video:description><![CDATA[
Charges accelerate in uniform fields. How do you predict the parabolic path of a particle moving through constant electric force? Watch to master the kinematics of charged particles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/9QZfjC1yW9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XX6yv6YToAEa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/336/XX6yv6YToAEa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of frictional forces on flat belts. Solved: A rope having a weight per unit length of 0.4Ib/ft is wound 2\frac{1}{2} times around a horizontal rod. Knowing that the coefficient of static friction between the rope and the rod is 0.30 , determine the minimum length of the rope that should be left hanging if a 100- Ib load is to be supported. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/336/XX6yv6YToAEa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746867981298.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/QbvDsDPVqt8E</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/QbvDsDPVqt8E.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: If the 50-kg crate is subject to a force of P=200N ,determine its speed when it has travelled 15m starting from rest. The coefficient of kinetic friction between the crate and the ground is \mu=0.3. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/QbvDsDPVqt8E.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1746451492840.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/QPVCIRtU5sdL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/413/QPVCIRtU5sdL.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on theorems on Jacobians. Solved: Given that F(u, v, w, x, y) = 0, G(u, v, w, x, y) = 0, H(u, v, w, x, y) = 0,find (a) \frac {\partial v} {\partial y}\bigg|_{x}(b) \frac {\partial x} {\partial v}\bigg|_{w}(c) \frac {\partial w} {\partial u}\bigg|_{y} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/413/QPVCIRtU5sdL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2TyNnzquKf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/2TyNnzquKf.jpg</video:thumbnail_loc>

            <video:title>Charge distributions</video:title>

            <video:description><![CDATA[
Real objects spread charge over lines, surfaces, or volumes. How do you convert linear, surface, and volume densities into the exact enclosed charge for Gauss's Law? Watch to master these conversions.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/2TyNnzquKf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nO9CgFuAbM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/nO9CgFuAbM.jpg</video:thumbnail_loc>

            <video:title>Planar symmetry</video:title>

            <video:description><![CDATA[
Calculate the uniform electric field produced by an infinite sheet of charge. Learn why the field strength remains constant regardless of the distance from the surface.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/nO9CgFuAbM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7opXRLK7Z1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/7opXRLK7Z1.jpg</video:thumbnail_loc>

            <video:title>Spherical symmetry</video:title>

            <video:description><![CDATA[
Use a spherical Gaussian surface to find the field of point charges and hollow shells. Understand why the field inside a uniformly charged conducting shell is always zero.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/7opXRLK7Z1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sTdudkCYSV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/sTdudkCYSV.jpg</video:thumbnail_loc>

            <video:title>Gauss's law</video:title>

            <video:description><![CDATA[
Net flux depends only on enclosed charge. Why do surface shape and external charges have zero effect on the total? Watch to grasp this powerful shortcut.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/sTdudkCYSV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/O94hlUVMXh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/O94hlUVMXh.jpg</video:thumbnail_loc>

            <video:title>Electric flux</video:title>

            <video:description><![CDATA[
Electric flux measures field lines piercing a surface. How does the angle of the area vector change this count? Watch to master the dot product rule.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/O94hlUVMXh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/T38b1XSInO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1142/T38b1XSInO.jpg</video:thumbnail_loc>

            <video:title>Cylindrical symmetry</video:title>

            <video:description><![CDATA[
Apply Gaussian principles to infinitely long wires and cylinders. Derive the relationship showing that the field decreases inversely with the distance from the central axis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1142/T38b1XSInO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Abppuf6LzAUd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UR7vNInezV/Thumbnails/681/Abppuf6LzAUd.jpg</video:thumbnail_loc>

            <video:title>Overview</video:title>

            <video:description><![CDATA[
Watch this just before you begin the [Beginner] Modern Web Development Foundations learning track.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UR7vNInezV/Previews/681/Abppuf6LzAUd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/euFY0U7pEc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1060/euFY0U7pEc.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson welcomes you to organic chemistry and sets the stage for what lies ahead. You will know what to expect from this course and why this knowledge matters for your career.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1060/euFY0U7pEc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jNN_35WKQiiM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nyhn0hHeuR/Thumbnails/1201/jNN_35WKQiiM.jpg</video:thumbnail_loc>

            <video:title>UniDrills smart learning method</video:title>

            <video:description><![CDATA[
Learn to combine UniDrills modules with your university lectures for maximum efficiency. This lesson shows you how to sync digital resources with your school notes to ensure total exam success.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nyhn0hHeuR/Previews/1201/jNN_35WKQiiM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iRNlLXGrck</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1060/iRNlLXGrck.jpg</video:thumbnail_loc>

            <video:title>History of organic chemistry</video:title>

            <video:description><![CDATA[
Scientists once believed living things could only come from a mysterious vital force. How did one experiment shatter this belief and change chemistry forever? This lesson reveals the surprising history behind organic chemistry and the discoveries that shaped modern science.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1060/iRNlLXGrck.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4Rb0gtGfzd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1141/4Rb0gtGfzd.jpg</video:thumbnail_loc>

            <video:title>1D superposition</video:title>

            <video:description><![CDATA[
Opposite charges create a combined electric field. How do you find the net vector at the centre point between them? Watch to see the superposition principle in action. Solved: Two point charges are fixed on an x-axis: charge q_1 = -5.00 \times 10^{-7}\text{ C} is at x = 5.00\text{ cm} and charge q_2 = +5.00 \times 10^{-7}\text{ C} is at x = 25.0\text{ cm}. Determine the net electric field vector at the midpoint between these two charges. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1141/4Rb0gtGfzd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5jblkD8z1weJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1060/5jblkD8z1weJ.jpg</video:thumbnail_loc>

            <video:title>Formation</video:title>

            <video:description><![CDATA[
Carbon atoms do not bond in their ground state. How do electrons jump to create four unpaired partners? Watch the energy shift that makes bonding possible.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1060/5jblkD8z1weJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Iei1KNXSDTHT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/Iei1KNXSDTHT.jpg</video:thumbnail_loc>

            <video:title>Multi-layer trig</video:title>

            <video:description><![CDATA[
Triple nesting traps many students in calculus. How do you peel back the power, the sine, and the angle without missing a single derivative? Watch the full breakdown to see the chain rule applied layer by layer. Solved: Find the derivative of the function y = \sin^3(4x^2) with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/Iei1KNXSDTHT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XO1DbaLQyK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1143/XO1DbaLQyK.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
Electrostatics rests on two pillars: Coulomb and Gauss. How do discrete forces merge into continuous fields? Watch to see the full picture click into place.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1143/XO1DbaLQyK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MVb3UXGikGFR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/MVb3UXGikGFR.jpg</video:thumbnail_loc>

            <video:title>Halogens estimation</video:title>

            <video:description><![CDATA[
Carius halogen estimation uses silver halide precipitate mass. How do you calculate the percentage of chlorine from the mass of silver chloride formed? Watch this worked example to master the stoichiometry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/MVb3UXGikGFR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a_eozDpQcuKt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/320/a_eozDpQcuKt.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of planar trusses by the method of joints. Solved: The portion of truss shown represents the upper part of a power transmission line tower. For the given loading, determine the force in each of the members located above HJ. State whether each member is in tension (T) or compression (C). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/320/a_eozDpQcuKt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1738921600999.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/VyOP2i_Lx3uJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/VyOP2i_Lx3uJ.jpg</video:thumbnail_loc>

            <video:title>Colours</video:title>

            <video:description><![CDATA[
We will explore the different ways to define colours in CSS. This lesson covers keywords, hexadecimal codes, and the RGB format for specifying colour values.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/VyOP2i_Lx3uJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uYrFDkbyFI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/uYrFDkbyFI.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This course maps the energy landscape of static charges. How do potential and capacitance govern the storage and flow of electricity in real circuits? Watch to grasp the full scope of the course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/uYrFDkbyFI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Brhgh40WlCIE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/415/Brhgh40WlCIE.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of space trusses - identifying zero-force members in space trusses. Solved: Determine the force in each member of the space truss and state if the members are in tension or compression. The truss is supported by a ball-and-socket joint at A and short links at B and C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/415/Brhgh40WlCIE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739270010455.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/auhGf4BojQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/auhGf4BojQ.jpg</video:thumbnail_loc>

            <video:title>Units and conversions</video:title>

            <video:description><![CDATA[
Joules are too big for single electrons. How do you switch between macroscopic energy and electron-volts without losing your head? Watch to master the conversion.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/auhGf4BojQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kehup8TPDs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/Kehup8TPDs.jpg</video:thumbnail_loc>

            <video:title>Electric potential energy</video:title>

            <video:description><![CDATA[
Work done against electric force stays stored. How do you calculate this energy from charge positions? Watch to master the formula.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/Kehup8TPDs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Uie_rMeqo5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/Uie_rMeqo5.jpg</video:thumbnail_loc>

            <video:title>Conservation of energy</video:title>

            <video:description><![CDATA[
Total Energy stays constant as charges move. How do you balance kinetic and potential terms to find speed at any point? Watch to apply conservation laws.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/Uie_rMeqo5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z5TrrFWgwdTp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/Z5TrrFWgwdTp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on the domain and range of a relation. Solved: 1 R=[{(1,3),(2,4),(3,1),(3,4)}] is a relation in N or Z^+.2 R=[(1,2.5),(2,5.9),(4,6.2)] is a relation from IN to Q.3 R=[(a,b)|a+2b=5,a,b\in IR] is a relation in IR.4 Set inclusion for a "class" of non-empty sets.5 The relation R from A=[2,3,4,5,6] to B= [2,4,6] such that aRb if and only if a< b. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/Z5TrrFWgwdTp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HW_7kHcCbxSl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/661/HW_7kHcCbxSl.jpg</video:thumbnail_loc>

            <video:title>The AI reality</video:title>

            <video:description><![CDATA[
AI is already part of development. Learn how it changes workflows, what it can and cannot do today, and why ignoring it is not an option.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/661/HW_7kHcCbxSl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lyHCNclUBjvo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/410/lyHCNclUBjvo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on gradients and directional derivatives. Solved: If f(x, y)=x e^y, find the rate of change of f at the point P (2, 0) and in the direction from P to Q (\frac12, 2). In what direction does the maximum rate of change of f occur? What is this maximum rate of change? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/410/lyHCNclUBjvo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6zWSE6naR0jt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/6zWSE6naR0jt.jpg</video:thumbnail_loc>

            <video:title>Linear equations</video:title>

            <video:description><![CDATA[
Execute the systematic isolation of unknowns through a practical walkthrough of linear equation solutions. You will master clearing denominators, expanding brackets, and grouping like terms to solve first-degree algebraic problems with absolute precision. Solved: 1. Solve the equation\frac{2x - 1}{3} - \frac{x + 2}{5} = \frac{3x + 1}{15} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/6zWSE6naR0jt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xpvZs_h6DT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/xpvZs_h6DT.jpg</video:thumbnail_loc>

            <video:title>Superposition principle</video:title>

            <video:description><![CDATA[
Electric potential is a scalar sum, not a vector. How do you combine positive and negative contributions without resolving angles? We show the algebraic method that makes this calculation trivial.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/xpvZs_h6DT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qao8lyRgOB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/qao8lyRgOB.jpg</video:thumbnail_loc>

            <video:title>Equipotential surfaces</video:title>

            <video:description><![CDATA[
Equipotential surfaces connect points of equal potential. Why must electric field lines cross these surfaces at right angles? We prove the perpendicular relationship and zero work property.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/qao8lyRgOB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SiA9xIja35</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1145/SiA9xIja35.jpg</video:thumbnail_loc>

            <video:title>System assembly energy</video:title>

            <video:description><![CDATA[
System Energy is the work to assemble charges from infinity. How do you sum pairwise interactions without double counting? We apply the pairwise rule to calculate total stored energy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1145/SiA9xIja35.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QAI_y7w6iEVY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/QAI_y7w6iEVY.jpg</video:thumbnail_loc>

            <video:title>Typography</video:title>

            <video:description><![CDATA[
This lesson covers the core properties for controlling the appearance of text. We will learn how to use font-family, font-size, and font-weight to style your typography.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/QAI_y7w6iEVY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d_KsbIuCESmj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/d_KsbIuCESmj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: A 500-N force is applied to a bent plate as shown. Determine (a) an equivalent force-couple system at B, (b) an equivalent system formed by a vertical force at A and a force at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/d_KsbIuCESmj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739180918398.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-oVBVahvafOW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/-oVBVahvafOW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: The shearing forces exerted on the cross section of a steel channel can be represented by a 900-N vertical force and two 250-N horizontal forces as shown. Replace this force and couple with a single force F applied at point C, and determine the distance x from C to line BD. (Point C is defined as the shear center of the section.) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/-oVBVahvafOW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739181711644.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/omPWY_RhOjBD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/392/omPWY_RhOjBD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force. Solved: Three control rods attached to a lever ABC exert on it the forces shown. (a) Replace the three forces with an equivalent force-couple system at B. (b) Determine the single force that is equivalent to the force-couple system obtained in part a, and specify its point of application on the lever. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/392/omPWY_RhOjBD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1739185281988.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sPidtYSd4XgF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/158/sPidtYSd4XgF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of rectilinear motion of connected bodies. Solved: A 20-kg block A rests on the 60-kg plate B in the position shown. Neglecting the mass of the rope and pulley, and using the coefficient of kinetic friction indicated, determine the time needed for block A to slide 0.5 m on the plate when the system is released from rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/158/sPidtYSd4XgF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742305357810.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/oWmzMpg6R3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1146/oWmzMpg6R3.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Two opposite charges create a dipole field. How do you calculate the potential at any point using superposition? We derive the exact formula and define the dipole moment vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1146/oWmzMpg6R3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yp_8w7YHp_X2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/822/yp_8w7YHp_X2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
This lesson tests the validity of quantum numbers through worked examples, showing which combinations are allowed and which are not. Solved: 1. Which of the following orbital designations are incorrect: 1s, 1p, 7d, 9s, 3f, 4f, 2d?2. Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect.a. n = 3, \ell = 3, m_\ell = 0, m_s = -\frac{1}{2}b. n = 4, \ell = 3, m_\ell = 2, m_s = -\frac{1}{2}c. n = 4, \ell = 1, m_\ell = 1, m_s = +\frac{1}{2}d. n = 2, \ell = 1, m_\ell = -1, m_s = -1e. n = 5, \ell = -4, m_\ell = 2, m_s = +\frac{1}{2}f. n = 3, \ell = 1, m_\ell = 2, m_s = -\frac{1}{2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/822/yp_8w7YHp_X2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uQW4O7UJwY5m</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/415/uQW4O7UJwY5m.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of space trusses - using method of sections for space trusses. Solved: The truss shown has a socket support at point L, a roller at point K, and a cylindrical roller at a point A that prevents motion in the X and Z directions. Use the method of sections to determine the force supported by member JG if P=Q=10KN 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/415/uQW4O7UJwY5m.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1747301099084.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0xGFeLONt4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/0xGFeLONt4.jpg</video:thumbnail_loc>

            <video:title>Parallel-plate capacitor</video:title>

            <video:description><![CDATA[
Capacitance depends on geometry. How do plate area and separation distance determine the storage capacity of parallel plates? We derive the formula linking these physical dimensions to charge storage.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/0xGFeLONt4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ifXFY5DnXG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/ifXFY5DnXG.jpg</video:thumbnail_loc>

            <video:title>Energy storage</video:title>

            <video:description><![CDATA[
Capacitors store energy in electric fields. How does the work done during charging translate to stored potential energy? We derive the energy formulas and link them to field density.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/ifXFY5DnXG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fJn6WvX0_w</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1147/fJn6WvX0_w.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Every charge distribution creates potential. But how do we quantify the ability of a system to store that charge? Capacitance defines this geometric limit independent of voltage.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1147/fJn6WvX0_w.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/QXxpBJTmqI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/QXxpBJTmqI.jpg</video:thumbnail_loc>

            <video:title>Series connections</video:title>

            <video:description><![CDATA[
Series capacitors share charge but split voltage. Why does the smallest component take the biggest hit? We explain the single-path rule and the weak link effect.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/QXxpBJTmqI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EIs2QLXkVs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/EIs2QLXkVs.jpg</video:thumbnail_loc>

            <video:title>Parallel connections</video:title>

            <video:description><![CDATA[
Parallel capacitors share voltage but split charge. How do you calculate total storage when branches add up? We show why equivalent capacitance always exceeds the largest component.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/EIs2QLXkVs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MxNN4JOZN4uj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Thumbnails/316/MxNN4JOZN4uj.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on the condition for the equilibrium of a rigid body under the action of only two or three co-planar forces. Solved: A slender rod with a length of L and weight W is attached to a collar at A and is fitted with a small wheel at B. Knowing that the wheel rolls freely along a cylindrical surface of radius R, and neglecting friction, derive an equation in \theta, L, and R that must be satisfied when the rod is in equilibrium. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/BzZ3AEaZyq/Previews/316/MxNN4JOZN4uj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1737326980563.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/j7uGMZY0XRSx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/314/j7uGMZY0XRSx.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on simplifying systems of forces on rigid bodies. Solved: The weight of two children sitting at ends A and B of a seesaw are 84 lb and 64 lb, respectively. Where should a third child sit so that the resultant of the weights of the three children will pass through C if she weighs(a) 60 lb,(b) 52 lb? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/314/j7uGMZY0XRSx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740077376388.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/IBxBodWd2_Nd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/IBxBodWd2_Nd.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: The 3-kg crate rests on the 10-kg cart where the coefficients of static and kinetic friction are \mu_s = 0.25 and \mu_k = 0.2, respectively. Determine the smallest constant force P needed to cause the crate to slip. How much time does it take for the crate to slip off the cart? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/IBxBodWd2_Nd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742300313698.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/-eDd9plvypR5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/-eDd9plvypR5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: Determine the range of applied force P over which the block of mass m_2 will not slip on the wedge-shaped block of mass m_1. Neglect friction associated with the wheels of the tapered block. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/-eDd9plvypR5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742302422918.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/MA8PhTuY0y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/MA8PhTuY0y.jpg</video:thumbnail_loc>

            <video:title>Dielectric constant</video:title>

            <video:description><![CDATA[
Dielectrics boost capacitance by a specific factor. How does the dielectric constant scale storage without changing geometry? We define this ratio and its link to permittivity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/MA8PhTuY0y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7OdsSWE4DC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/7OdsSWE4DC.jpg</video:thumbnail_loc>

            <video:title>Induced charge</video:title>

            <video:description><![CDATA[
Dielectrics generate bound surface charge when polarised. How much induced charge opposes the free plate charge? We derive the exact formula linking bound charge to the dielectric constant.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/7OdsSWE4DC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BbfwsZPLdn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/BbfwsZPLdn.jpg</video:thumbnail_loc>

            <video:title>Polarisation</video:title>

            <video:description><![CDATA[
Insulators do not conduct, yet they reshape electric fields. How does internal polarisation create an opposing field that weakens the net force? We expose the mechanism of bound charge and field reduction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/BbfwsZPLdn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JslLZ5QH1f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/JslLZ5QH1f.jpg</video:thumbnail_loc>

            <video:title>Battery state logic</video:title>

            <video:description><![CDATA[
Inserting a dielectric changes capacitance, but the outcome depends on the circuit state. Does charge stay fixed or does voltage remain constant? We distinguish isolated and connected scenarios to predict energy shifts.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/JslLZ5QH1f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/I8EU0Vxhko8I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Thumbnails/541/I8EU0Vxhko8I.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on problems involving derivation of the definition of a linear map from some known images. Solved: Let T: M_{22} \to \mathbb{R} be a linear transformation for which T\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix} = 1, T\begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix} = 2, T\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix} = 3 and T\begin{pmatrix} 1 & 1 \\ 1 & 4 \end{pmatrix} = 1. Find T\begin{pmatrix} 1& 3 \\ 4& 2 \end{pmatrix} and T\begin{pmatrix} a & b \\ c & d \end{pmatrix} . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/iJ7ZrmvJfI/Previews/541/I8EU0Vxhko8I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IxpzntDo_NRJ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/IxpzntDo_NRJ.jpg</video:thumbnail_loc>

            <video:title>Constant acceleration (1)</video:title>

            <video:description><![CDATA[
This example solves a 2D constant acceleration problem. We apply the standard kinematic equations independently to the x and y vector components. Master this component-based method. Solved: A particle starts from its origin with an initial velocity \vec{v}_o=(10i-4.0j)m/s. It moves with a constant acceleration \vec{a}=(2.0i+3.0j)m/s^2. What is the particle's velocity \vec{v} after 5.0s? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/IxpzntDo_NRJ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/u3HwC8B4JfFq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1005/u3HwC8B4JfFq.jpg</video:thumbnail_loc>

            <video:title>Mixed quadratic and rational systems (1)</video:title>

            <video:description><![CDATA[
Execute the systematic resolution of simultaneous systems where reciprocal terms intersect with the difference of two squares. You will master the mechanical substitution of linear factors into fractional equations to reduce the system into solvable linear forms and determine precise coordinate sets. Solved: 5. Solve the equationsx^2 - y^2 = 24\frac{1}{x+y} + \frac{3}{x-y} = \frac{11}{12} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1005/u3HwC8B4JfFq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qmpzs3Pmzm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/qmpzs3Pmzm.jpg</video:thumbnail_loc>

            <video:title>Carbon and hydrogen estimation</video:title>

            <video:description><![CDATA[
Combustion analysis determines carbon and hydrogen content. How do you convert masses of CO2 and H2O into element percentages? Watch this worked example to master the calculation. Solved: Combustion of 0.35 \text{ g} of an organic substance yielded 0.88 \text{ g} of CO_{2}. Calculate the percentage of carbon in the sample. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/qmpzs3Pmzm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AWFUzU4PQLTs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/1205/AWFUzU4PQLTs.jpg</video:thumbnail_loc>

            <video:title>Half-life</video:title>

            <video:description><![CDATA[
Knowing the definition of half-life is one thing; using it to solve real problems is another. What if you must find the age of an object or remaining mass with only partial data; do you know the exact steps to solve it accurately?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/1205/AWFUzU4PQLTs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xwlFDqEXDwqz</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/xwlFDqEXDwqz.jpg</video:thumbnail_loc>

            <video:title>Composite inverse trig</video:title>

            <video:description><![CDATA[
Inverse trig functions hide complex denominators. How do you apply the chain rule to arctan of a polynomial without messing up the fraction? Watch to see the derived formula in action. Solved: Find the derivative of the function f(x) = \tan^{-1}(2x^3) with respect to x. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/xwlFDqEXDwqz.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TPWrQQl1ztgx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1061/TPWrQQl1ztgx.jpg</video:thumbnail_loc>

            <video:title>CO2 structures</video:title>

            <video:description><![CDATA[
CO2 can have multiple Lewis structures. Which arrangement minimises formal charges and satisfies the octet rule? See why double bonds beat single bonds here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1061/TPWrQQl1ztgx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M1oCq6h5gK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1150/M1oCq6h5gK.jpg</video:thumbnail_loc>

            <video:title>Summary</video:title>

            <video:description><![CDATA[
Electric potential and capacitance define energy storage in circuits. How do series networks and dielectrics alter total capacity? This summary ties every concept together for real-world application.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1150/M1oCq6h5gK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jiFC3qV592LK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/jiFC3qV592LK.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on calculating power and efficiency of a machine by the principle of work and energy. Solved: An escalator handles a steady load of 30 people per minute in elevating them from the first to the second floor through a vertical rise of 24ft . The average person weighs 140\space Ib . If the motor which drives the unit delivers , calculate the mechanical efficiency e of the system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/jiFC3qV592LK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746955828525.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/ZOWaefmQaUN3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/ZOWaefmQaUN3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on calculating power and efficiency of a machine by the principle of work and energy. Solved: The elevator E has a weight of 6600Ib when fully loaded and is connected as shown to a counterweight W of weight of 2200 Ib . Determine the power in hp delivered by the motor (a) when the elevator is moving down at a constant speed of 1ft/s (b) when it has an upward velocity of 1ft/s and a deceleration of 0.18ft/s^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/ZOWaefmQaUN3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746957023999.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5Yri09qyrnR3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/512/5Yri09qyrnR3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating power and efficiency of a machine by the principle of work and energy. Solved: The sports car has a mass of 2.3Mg, and while it is traveling at 28m/s the driver causes it to accelerate at 5m/s^2 . If the drag resistance on the car due to the wind is F_0=(0.3v^2)N , where v is the velocity in m/s , determine the power supplied to the engine at this instant. The engine has a running efficiency of \varepsilon=0.68 . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/512/5Yri09qyrnR3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746956411156.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Vyk5PrYwTzGI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/161/Vyk5PrYwTzGI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles by relating the kinetic energy of the body with the work done by forces applied on them. Solved: The 25-Ib block has an initial speed of v_0=10ft/s when it is midway between springs A and B. After striking spring B, it rebounds and slides across the horizontal plane toward spring A, and continues to move back and forth. If the coefficient of kinetic friction between the plane and the block is \mu_k=0.4 , determine the total distance traveled by the block before it comes to rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/161/Vyk5PrYwTzGI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746788384037.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xBLj65TtsjSm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/666/xBLj65TtsjSm.jpg</video:thumbnail_loc>

            <video:title>AI assistants</video:title>

            <video:description><![CDATA[
This lesson covers two professional workflows for AI assistance. We explore the integrated suggestions of GitHub Copilot and the focused, external queries using Google Gemini. Your goal is to choose the method that best accelerates your work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/666/xBLj65TtsjSm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PgOCceNqrKvW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/62/PgOCceNqrKvW.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on the derivative of a function over an interval. Solved: Show that the derivative of the function f defined by f(x)=\sin x is f^1(x) =\cos x Vx\in IR. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/62/PgOCceNqrKvW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/E7PGql8GQzcy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/E7PGql8GQzcy.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: The ball B has a mass 10 kg and is attached to the end of the rod whose mass may be neglected. If the rod is subjected to a torque M=(3t^2+5t+2)N.m, where t is in seconds, determine the speed of the ball whent=2s. The ball has a speed v=2m/s when t=0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/E7PGql8GQzcy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749045457447.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/GPJBRMpTNhVi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/962/GPJBRMpTNhVi.jpg</video:thumbnail_loc>

            <video:title>Specificity</video:title>

            <video:description><![CDATA[
This lesson explains how a browser decides which CSS rule to apply when multiple rules target the same element. Understanding this hierarchy is essential for debugging styles.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/962/GPJBRMpTNhVi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UbYGcQybNXE1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/UbYGcQybNXE1.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of systems of particles under steady flow. Solved: The 8-oz ball is supported by the vertical stream of fresh water which issues from the 1/2-in,-diameter nozzle with a velocity of 35ft/sec. Calculate the height h of the ball above the nozzle. Assume that the stream remains intact and there is no energy lost in the jet stream. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/UbYGcQybNXE1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1752748150150.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/q2ofr-XYJb0W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/114/q2ofr-XYJb0W.jpg</video:thumbnail_loc>

            <video:title>Properties of adjoints</video:title>

            <video:description><![CDATA[
Properties of the adjoint of a matrix and their applications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/114/q2ofr-XYJb0W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/OzU-8AMJf0NQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/560/OzU-8AMJf0NQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on the inverse of relations. Solved: 1 R=[{(1,3),(2,4),(3,1),(3,4)}] is a relation in N or Z^+.2 R=[(1,2.5),(2,5.9),(4,6.2)] is a relation from IN to Q.3 R=[(a,b)|a+2b=5,a,b\in IR] is a relation in IR.4 Set inclusion for a "class" of non-empty sets.5 The relation R from A=[2,3,4,5,6] to B= [2,4,6] such that aRb if and only if a< b. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/560/OzU-8AMJf0NQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PYnXPQ6nTqby</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/667/PYnXPQ6nTqby.jpg</video:thumbnail_loc>

            <video:title>Installing and configuring git</video:title>

            <video:description><![CDATA[
This is a one-time setup lesson. We will install the Git software on your machine and then run the two essential configuration commands to set your identity. This step is mandatory before you can create your first commit.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/667/PYnXPQ6nTqby.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/sKLXiYo-S5C2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/563/sKLXiYo-S5C2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on identifying transitive relations. Solved: Which of the following relation of the set Z of integers is transitive?(a) aRb means that a\le b(b) aRb means that a(c) aRb means a=2b(d) aRb means a+b\ge 5(e) aRb means a and b has the same parity. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/563/sKLXiYo-S5C2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/H2fH8FRNhl0R</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/H2fH8FRNhl0R.jpg</video:thumbnail_loc>

            <video:title>Solution of weak acids (2)</video:title>

            <video:description><![CDATA[
This lesson covers advanced weak acid calculations, focusing on finding the percentage ionisation and the acid dissociation constant from pH data. You will practice rearranging equilibrium expressions to solve for unknown concentrations. Use these worked examples to sharpen your accuracy. Solved: Example 2: Given that the pH of a 0.50 M monoprotic carboxylic acid solution is 2.35. Calculate the K_a and the \text{p}K_a of the acid 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/H2fH8FRNhl0R.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cNItT8HTc0Vb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/huvAseFoMS/Thumbnails/854/cNItT8HTc0Vb.jpg</video:thumbnail_loc>

            <video:title>Hydrolysis of salts (1)</video:title>

            <video:description><![CDATA[
This lesson provides worked examples for calculating the pH of salt solutions using the hydrolysis constant, Kh. You will learn to derive Kh from Kw, Ka, or Kb to determine the final acidity or alkalinity. Follow these steps to master equilibrium calculations for salts in water. Solved: Determine the pH of 0.20 M \text{NH}_4\text{Cl} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/huvAseFoMS/Previews/854/cNItT8HTc0Vb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a0_ctTaziKPY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/a0_ctTaziKPY.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: An earth satellite of mass 700 kg is launched into a free-flight trajectory about the earth with an initial speed of v_A=10km/s when the distance from the center of the earth is r_A=15Mm. If the launch angle of this position is \phi_A=70^\circ, determine the speed of v_B of the satellite and its closest distance r_B from the center of the earth. The earth has a mass M_e=5.976(10^{24})kg.Hint : Under these conditions, the satellite is subjected only to the earth's gravitational force, F=GM_em_s/r^2. For part of the solution, use the conservation of energy. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/a0_ctTaziKPY.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749116510677.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/JtxDbH0Poq7L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Thumbnails/301/JtxDbH0Poq7L.jpg</video:thumbnail_loc>

            <video:title>Guide</video:title>

            <video:description><![CDATA[
How to navigate the MEE 205 learning track.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/jAaYqyFFNn/Previews/301/JtxDbH0Poq7L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YLGl1VCFHErK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/973/YLGl1VCFHErK.jpg</video:thumbnail_loc>

            <video:title>Calculating vector products (1)</video:title>

            <video:description><![CDATA[
This problem walkthrough covers the vector (cross) product. We calculate the resultant vector using the determinant and term-by-term expansion methods with components. Solved: 7. Given two vectors \vec{A} = 2\underline{i} + 3\underline{j} and \vec{B} = -\underline{i} + 2\underline{j}, find the vector product \vec{A} \times \vec{B}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/973/YLGl1VCFHErK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oyvsrVfIvbNe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/309/oyvsrVfIvbNe.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the course, overview of course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/309/oyvsrVfIvbNe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lZIrWEutuS05</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/543/lZIrWEutuS05.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on graphical solution of erratic motion problems. Solved: An accelerometer record for he motion of a given part of mechanism is approximated by an arc of a parabola for 0.2s and a straight line for the next 0.2s, as shown in the figure. Knowing that v=0 when t=0 and x=0.8ft when t=0.4s. (a) Construct the v-t curve for 0\le{t}\le{0.4s} (b) determine the position of the part at t=0.3s and t=0.2s. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/543/lZIrWEutuS05.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742047947804.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/2gPxKb4iq8W9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/662/2gPxKb4iq8W9.jpg</video:thumbnail_loc>

            <video:title>The internet and the web</video:title>

            <video:description><![CDATA[
Understand the difference between the internet and the web. Learn how they connect users, servers, and browsers to make websites work.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/662/2gPxKb4iq8W9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Yd7_o_nBFHav</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Thumbnails/1019/Yd7_o_nBFHav.jpg</video:thumbnail_loc>

            <video:title>2023/2024 (14)</video:title>

            <video:description><![CDATA[
Watch this step by step solutions of more questions in the 2023/2024 OAU CHM 101 exam paper. You will learn how to answer difficult questions quickly and use the right formulas to get full marks in your test.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kZaDNYB1Pu/Previews/1019/Yd7_o_nBFHav.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ErOIJ4Dramb0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/662/ErOIJ4Dramb0.jpg</video:thumbnail_loc>

            <video:title>What is a website?</video:title>

            <video:description><![CDATA[
Learn what a website really is, what it is made of, and how browsers turn code into visual pages. This is where practical understanding begins.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/662/ErOIJ4Dramb0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iGpCPPEaTdLI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/662/iGpCPPEaTdLI.jpg</video:thumbnail_loc>

            <video:title>HTTP and HTTPS</video:title>

            <video:description><![CDATA[
HTTP is the protocol governing communication between clients and servers. This lesson defines its request-response structure. We then explain how HTTPS adds a critical layer of security through encryption, a non-negotiable standard for the modern web.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/662/iGpCPPEaTdLI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/14XTfjl6qvCV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/665/14XTfjl6qvCV.jpg</video:thumbnail_loc>

            <video:title>Commands (1): whoami and pwd</video:title>

            <video:description><![CDATA[
Our first two commands establish your context within the terminal. The `whoami` command confirms your user identity, while `pwd` (print working directory) reveals your current location in the file system. Master these to orient yourself.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/665/14XTfjl6qvCV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7aeGtCMnyOaM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/aVNUVvA2ym/Thumbnails/765/7aeGtCMnyOaM.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson provides a high-level overview of the learning track. We will explain why the courses are arranged in this specific order and what you will achieve by the end of the term.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/aVNUVvA2ym/Previews/765/7aeGtCMnyOaM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Nb5B6HKTHFK3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/665/Nb5B6HKTHFK3.jpg</video:thumbnail_loc>

            <video:title>Commands (2): ls and cd</video:title>

            <video:description><![CDATA[
Viewing and moving are the core actions of navigation. This lesson covers the `ls` (list) command to see the contents of your current location, and the `cd` (change directory) command to move through the file system. These are your foundational navigation tools.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/665/Nb5B6HKTHFK3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7D6LpYK9n1Cb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Thumbnails/665/7D6LpYK9n1Cb.jpg</video:thumbnail_loc>

            <video:title>Commands (4): mv, cp, and rm</video:title>

            <video:description><![CDATA[
To manage a project, you must manage its files. This lesson covers the core tools for file manipulation: `mv` for moving and renaming, `cp` for copying, and the powerful `rm` command for permanent deletion. Mastery of these is fundamental.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/gP92fCRcuv/Previews/665/7D6LpYK9n1Cb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/LBQUnWZSiG0H</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/312/LBQUnWZSiG0H.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about an arbitrary axis. Solved: Determine the moment of each force acting on the handle of the wrench about the a axis. Take F_1 = { -2i + 4j - 8k } lb, F_2 = { 3i + 2j - 6k } lb. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/312/LBQUnWZSiG0H.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738695431628.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/RYPb1OeReTQn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/671/RYPb1OeReTQn.jpg</video:thumbnail_loc>

            <video:title>Creating your logo</video:title>

            <video:description><![CDATA[
This is a practical lesson on using a free tool like Canva. You will create a simple, professional text-based logo or wordmark for your personal portfolio project.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/671/RYPb1OeReTQn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nnHoLa_E8aBe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/669/nnHoLa_E8aBe.jpg</video:thumbnail_loc>

            <video:title>Getting your project ready</video:title>

            <video:description><![CDATA[
This lesson combines the command line and Git skills you learned in the first course to create a professional project structure. We will create the project folder, open it in VS Code, create the index.html file, and initialise a Git repository.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/669/nnHoLa_E8aBe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/psG4o3ecRN</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/psG4o3ecRN.jpg</video:thumbnail_loc>

            <video:title>Nitrogen estimation (1)</video:title>

            <video:description><![CDATA[
Kjeldahl nitrogen estimation uses back titration data. How do you calculate the percentage of nitrogen from excess acid neutralisation? Watch this worked example to master the stoichiometry. Solved: In a Kjeldahl estimation, ammonia from 0.75 \text{ g} of an organic compound neutralised 15.0 \text{ mL} of 0.5 \text{ M} H_{2}SO_{4}. Determine the percentage of nitrogen in the compound. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/psG4o3ecRN.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i6alyZFDURp0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/874/i6alyZFDURp0.jpg</video:thumbnail_loc>

            <video:title>Types</video:title>

            <video:description><![CDATA[
Nuclear reactions release massive energy, yet they do not all follow the same path. What determines if a nucleus breaks apart or combines, and how does this distinction govern atomic power?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/874/i6alyZFDURp0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UwEu3jNxO5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Thumbnails/1063/UwEu3jNxO5.jpg</video:thumbnail_loc>

            <video:title>Graphite</video:title>

            <video:description><![CDATA[
Pure carbon, yet soft and conductive. How do weak forces between sp2 layers allow sliding and electron flow? See the structure-property link.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/T81Uso3UiU/Previews/1063/UwEu3jNxO5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mi7iQZGQKBQ5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/mi7iQZGQKBQ5.jpg</video:thumbnail_loc>

            <video:title>Zero-order reactions</video:title>

            <video:description><![CDATA[
Calculate reaction time and half-life for zero-order reactions using the integrated rate law. This walkthrough solves problems on reactant decay and the decomposition of ammonia on platinum.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/mi7iQZGQKBQ5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KmXBQgNBGW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/KmXBQgNBGW.jpg</video:thumbnail_loc>

            <video:title>Exponential quotient</video:title>

            <video:description><![CDATA[
Dividing exponential growth by a polynomial creates a complex rate. How do you apply the quotient rule in this case? Watch the step-by-step simplification of this mixed function. Solved: Find the derivative of the function s = \frac{e^t}{t^2} with respect to t. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/KmXBQgNBGW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/U1VN3nXPoirW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/669/U1VN3nXPoirW.jpg</video:thumbnail_loc>

            <video:title>Your HTML5 workflow</video:title>

            <video:description><![CDATA[
This lesson establishes the core developer loop of writing code, saving, and previewing. We will introduce and set up the "Live Server" extension in VS Code to see our changes update in the browser instantly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/669/U1VN3nXPoirW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bVFc4Rgh5Vgd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/aVNUVvA2ym/Thumbnails/765/bVFc4Rgh5Vgd.jpg</video:thumbnail_loc>

            <video:title>How to study</video:title>

            <video:description><![CDATA[
This lesson explains the purpose of this introductory course. We will show you how to use the information here as a reference to build effective study habits for all your other courses.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/aVNUVvA2ym/Previews/765/bVFc4Rgh5Vgd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/GT6UTdbEzI2U</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/GT6UTdbEzI2U.jpg</video:thumbnail_loc>

            <video:title>Nitrogen estimation (2)</video:title>

            <video:description><![CDATA[
The Dumas method estimates nitrogen in all organic compounds. How does heating with CuO convert bound nitrogen into measurable N2 gas? Watch to learn this universal technique.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/GT6UTdbEzI2U.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WxXre6nbzhN0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/865/WxXre6nbzhN0.jpg</video:thumbnail_loc>

            <video:title>The collision model</video:title>

            <video:description><![CDATA[
Understand how molecules must collide with enough energy and the correct orientation for a reaction to occur. This model explains why increasing temperature and concentration speeds up chemical processes. Master these fundamental rules to predict reaction behaviour at the molecular level.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/865/WxXre6nbzhN0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AyVlg1L5Yh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/AyVlg1L5Yh.jpg</video:thumbnail_loc>

            <video:title>Logarithmic sum</video:title>

            <video:description><![CDATA[
Mixed functions combine logarithmic and polynomial terms. How do you differentiate each part separately and sum the results? Watch the application of standard derivative rules to this expression. Solved: Determine the gradient function for w = \ln \theta + 5\theta^2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/AyVlg1L5Yh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ANPTfsiKEjaH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/ANPTfsiKEjaH.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Neutral charge pairs create strong fields. How do we measure the strength and direction of this separation? Watch to grasp the dipole moment vector.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/ANPTfsiKEjaH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xgblgPEWMv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/xgblgPEWMv.jpg</video:thumbnail_loc>

            <video:title>Kinetic energy gain</video:title>

            <video:description><![CDATA[
Electric fields turn potential into speed. How do you link field strength and displacement to find final velocity? Watch the calculation unfold. Solved: A proton is released from rest at x = -4.00 cm in a constant electric field with magnitude 2.50 \times 10^3 N/C, pointing in the positive x-direction. Find the speed of the proton at x = 8.00 cm. (Take the mass of a proton as 1.67 \times 10^{-27} kg and its charge as 1.60 \times 10^{-19} C). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/xgblgPEWMv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4Duzv7Y0JIka</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/4Duzv7Y0JIka.jpg</video:thumbnail_loc>

            <video:title>Creating content</video:title>

            <video:description><![CDATA[
The `<body>` tag holds all visible content. This lesson covers the most essential content elements: headings (`<h1>` to `<h6>`) to create a document hierarchy, and paragraphs (`<p>`) for text blocks. All content starts here.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/4Duzv7Y0JIka.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UsSO7bRTkE89</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/787/UsSO7bRTkE89.jpg</video:thumbnail_loc>

            <video:title>Making links functional</video:title>

            <video:description><![CDATA[
This lesson covers the <a> (anchor) tag. We will make our navigation and social media links functional by adding their required href attributes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/787/UsSO7bRTkE89.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9K3hWsnqsWtT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/789/9K3hWsnqsWtT.jpg</video:thumbnail_loc>

            <video:title>The textarea element</video:title>

            <video:description><![CDATA[
Use <textarea> for multi-line input. Learn its key attributes, when to use it over <input>, and how to integrate it into a working contact form.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/789/9K3hWsnqsWtT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ab5kbDx5jHQk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/671/Ab5kbDx5jHQk.jpg</video:thumbnail_loc>

            <video:title>Structuring your project folder</video:title>

            <video:description><![CDATA[
We will create a clean, professional folder structure for our project. This lesson covers creating an 'assets' or 'public' directory to keep our images and logo organised from the start.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/671/Ab5kbDx5jHQk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FgBxL7BPyv8L</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/865/FgBxL7BPyv8L.jpg</video:thumbnail_loc>

            <video:title>Rate constants</video:title>

            <video:description><![CDATA[
Use the Arrhenius equation to calculate the ratio of rate constants at different temperatures. This walkthrough solves problems involving biological enzymes and high-temperature reactions to determine exactly how many times faster a process becomes when heated. Master these calculations to predict reaction sensitivity to thermal changes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/865/FgBxL7BPyv8L.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cmqyiLcXtbuH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/1205/cmqyiLcXtbuH.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Every radioactive element decays, but why do some take seconds while others take millions of years? What law governs this invisible clock inside every unstable nucleus? The answer unlocks the mathematics of radiation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/1205/cmqyiLcXtbuH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wxls1lI6259C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/Wxls1lI6259C.jpg</video:thumbnail_loc>

            <video:title>The core structure</video:title>

            <video:description><![CDATA[
We now build the mandatory structure of a valid HTML5 document. This includes the `<!DOCTYPE>` declaration, the root `<html>` element, and the `<head>` and `<body>` sections that separate a page's metadata from its visible content.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/Wxls1lI6259C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DilxQ7XmTOde</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/DilxQ7XmTOde.jpg</video:thumbnail_loc>

            <video:title>Formatting text</video:title>

            <video:description><![CDATA[
Formatting text is about adding meaning, not just changing its look. This lesson contrasts older, visual tags with semantic tags like `<strong>` for importance and `<em>` for emphasis. Using the correct tag is a Mark of a professional.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/DilxQ7XmTOde.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/m_GRJBJU53yC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Thumbnails/830/m_GRJBJU53yC.jpg</video:thumbnail_loc>

            <video:title>Dipole moment</video:title>

            <video:description><![CDATA[
This lesson defines the dipole moment as the vector sum of all bond dipoles in a molecule. We use 1,4-dichlorobenzene (C6H4Cl2) and 1,2-dichlorobenzene (C6H4Cl2) to show how molecular geometry determines if the net dipole is zero or non-zero. Master how symmetry impacts overall molecular polarity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Gl7YBnf0co/Previews/830/m_GRJBJU53yC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F8vQ_AYwLUkQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/874/F8vQ_AYwLUkQ.jpg</video:thumbnail_loc>

            <video:title>Mass-Energy relation</video:title>

            <video:description><![CDATA[
In nuclear reactions, does mass disappear when energy appears? How can matter vanish and create enough power to light a city? The answer lies in the hidden link between mass and energy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/874/F8vQ_AYwLUkQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SqQ_nFXw2jG8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/1162/SqQ_nFXw2jG8.jpg</video:thumbnail_loc>

            <video:title>Nature of reactants</video:title>

            <video:description><![CDATA[
This lesson explains how the chemical identity and physical state of a substance determine its reaction speed. You will compare the rates of ionic and covalent reactions while examining how surface area affects collisions in solids.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/1162/SqQ_nFXw2jG8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9nvw_s0_zrW6</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/9nvw_s0_zrW6.jpg</video:thumbnail_loc>

            <video:title>Linear charge</video:title>

            <video:description><![CDATA[
Charges often spread along a wire. How do you sum the field from every tiny segment to find the total strength? Watch to see the integral in action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/9nvw_s0_zrW6.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y0HmXjbska9l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/Y0HmXjbska9l.jpg</video:thumbnail_loc>

            <video:title>Surface charge</video:title>

            <video:description><![CDATA[
Charges spread across flat plates. How do you sum the field from every tiny area element to find the total strength? Watch to see the double integral in action.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/Y0HmXjbska9l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rCqKe9_21djE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/rCqKe9_21djE.jpg</video:thumbnail_loc>

            <video:title>Absolute-value product</video:title>

            <video:description><![CDATA[
Products with absolute values need careful handling. How do you combine the signum function with the product rule? Watch the derivative solved. Solved: Determine the derivative of y = |x| \tan x for all points where x \neq 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/rCqKe9_21djE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Erymcc_t5u5D</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/671/Erymcc_t5u5D.jpg</video:thumbnail_loc>

            <video:title>Asset copyright</video:title>

            <video:description><![CDATA[
This essential lesson covers the professional responsibility of using assets. We will explain the basics of copyright and why you cannot use just any image you find online. We will then discuss the importance of using royalty-free or self-generated assets for your portfolio.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/671/Erymcc_t5u5D.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZpKsidZgikFU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/671/ZpKsidZgikFU.jpg</video:thumbnail_loc>

            <video:title>Preparing your professional headshot</video:title>

            <video:description><![CDATA[
This lesson covers how to choose a good professional photo for your portfolio. We will then use a free online tool to easily remove the background, preparing it for our design.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/671/ZpKsidZgikFU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/PLz8o7kkdYbL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/PLz8o7kkdYbL.jpg</video:thumbnail_loc>

            <video:title>Axial field of a ring (2)</video:title>

            <video:description><![CDATA[
Apply the axial field formula to a charged ring. How do you handle unit conversions and vector direction? Watch the step-by-step solution. Solved: A thin ring of radius R = 5.00 \text{ cm} carries a uniform charge of Q = +20.0 \text{ }\mu\text{C}. Calculate the magnitude of the electric field at a point on the central axis 50.0 \text{ cm} away from the centre of the ring. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/PLz8o7kkdYbL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fOMJTvKOX44e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/1162/fOMJTvKOX44e.jpg</video:thumbnail_loc>

            <video:title>Catalysts</video:title>

            <video:description><![CDATA[
This lesson explains how catalysts speed up reactions by providing an alternative pathway with lower activation energy. You will learn to identify homogeneous and heterogeneous catalysts and understand why they remain chemically unchanged after the reaction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/1162/fOMJTvKOX44e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ivcgKOgMqA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/ivcgKOgMqA.jpg</video:thumbnail_loc>

            <video:title>Composite Power</video:title>

            <video:description><![CDATA[
Nested brackets conceal the true gradient at every stage. How do you strip the outer power and multiply by the inner rate without expanding? Follow the full calculation to see the exact steps. Solved: Determine the derivative of the function z = (4t^3 - 5)^6 with respect to t. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/ivcgKOgMqA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/D_TLC0M8a5Cv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Thumbnails/874/D_TLC0M8a5Cv.jpg</video:thumbnail_loc>

            <video:title>Energy change</video:title>

            <video:description><![CDATA[
Mass is lost during nuclear reactions. How do you calculate the exact energy released from this loss without making costly errors? We solve a complete problem step-by-step to show the correct method for accuracy.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/2nC90vtyaR/Previews/874/D_TLC0M8a5Cv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V67N02iuuw_S</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/672/V67N02iuuw_S.jpg</video:thumbnail_loc>

            <video:title>Header and footer</video:title>

            <video:description><![CDATA[
We will build the very top and very bottom of our page. This lesson covers the correct usage of the <header> and <footer> elements as main page landmarks.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/672/V67N02iuuw_S.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vazHZ5wTKmdS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/787/vazHZ5wTKmdS.jpg</video:thumbnail_loc>

            <video:title>Building the About Me section</video:title>

            <video:description><![CDATA[
This lesson focuses on creating the "About Me" section. We will add an <h2> for the section title and then write the professional summary inside <p> tags.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/787/vazHZ5wTKmdS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/i82hpG0ofxFs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/673/i82hpG0ofxFs.jpg</video:thumbnail_loc>

            <video:title>Adding expandable details</video:title>

            <video:description><![CDATA[
His lesson introduces the <details> and <summary> elements. We will use them to add an interactive, expandable section to our table for displaying detailed accomplishments.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/673/i82hpG0ofxFs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EnJQjlopEc2u</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/674/EnJQjlopEc2u.jpg</video:thumbnail_loc>

            <video:title>The head element revisited</video:title>

            <video:description><![CDATA[
The <head> contains all the non-visible, but critical, information for your page. This lesson covers the essential metadata within it, including the <title> for the browser tab and the various <meta> tags that control SEO and character encoding.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/674/EnJQjlopEc2u.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/b6F2_R7r6JTZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/868/b6F2_R7r6JTZ.jpg</video:thumbnail_loc>

            <video:title>Identifying components</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to identify anodes and cathodes from given half-reactions and construct their complete cell notation. You will work through practical examples to determine electron flow and represent galvanic cells correctly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/868/b6F2_R7r6JTZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/x7hqwYWuuOVi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/670/x7hqwYWuuOVi.jpg</video:thumbnail_loc>

            <video:title>Special characters</video:title>

            <video:description><![CDATA[
This lesson explains how to handle special characters that have a meaning in HTML, like the less-than sign. We will introduce character entities as the professional method for displaying these reserved characters correctly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/670/x7hqwYWuuOVi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_7UGGiEFcIEI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/672/_7UGGiEFcIEI.jpg</video:thumbnail_loc>

            <video:title>Navigation</video:title>

            <video:description><![CDATA[
This lesson covers building the navigation bar inside our header. We will introduce the <nav> element and explain why an unordered list (<ul>) is the correct semantic choice for a menu. You will then build the navigation structure using <ul>, <Li>, and <a> tags.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/672/_7UGGiEFcIEI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/msg6ywTuNPG-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/msg6ywTuNPG-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: The roller coaster has a mass of 700 kg, including its passengers. If it is released from rest at the top of the hill A, determine the minimum height h of the hill crest so that the car travels around both inside loops without leaving the track. Neglect friction, the mass of the wheels, and the size of the car. What is the normal reaction on the car when the car is at B and when it is at C? Take \rho_{B} = 7.5 m and \rho_C = 5m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/msg6ywTuNPG-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747310238455.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/1OCpVViAa7mu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/1OCpVViAa7mu.jpg</video:thumbnail_loc>

            <video:title>Infinite limits</video:title>

            <video:description><![CDATA[
Learn how functions increase or decrease without bound as they approach vertical asymptotes. You will identify conditions where the output tends toward positive or negative infinity and understand why these limits technically do not exist as finite numbers. This lesson clarifies graph behaviour at points of infinite growth.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/1OCpVViAa7mu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Kg8QuIprEiXx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/162/Kg8QuIprEiXx.jpg</video:thumbnail_loc>

            <video:title>Worked examples (9)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system. Solved: A force P is slowly attached to a plate that is attached to two springs and causes a deflection x_o. In each of the cases shown, derive an expression for the constant k_e, in terms of k_1 and k_2, of the single spring equivalent to the given system, that is, of the single spring which will undergo the same deflection x_o when subjected to the same force P. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/162/Kg8QuIprEiXx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1747310590279.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/_h8F8G0CrCrb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/_h8F8G0CrCrb.jpg</video:thumbnail_loc>

            <video:title>Gibb's free energy change</video:title>

            <video:description><![CDATA[
This lesson explains the thermodynamic relationship between cell potential and Gibbs free energy. You will learn to calculate the free energy change of a reaction using standard cell potential values.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/_h8F8G0CrCrb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eeVQg2f_FAmr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/787/eeVQg2f_FAmr.jpg</video:thumbnail_loc>

            <video:title>Building the hero section</video:title>

            <video:description><![CDATA[
We will bring the top of our portfolio to life. This lesson covers adding your name with an <h1> tag, your tagline with a <p> tag, and your professional headshot using the <img> element, including a discussion of its essential src and alt attributes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/787/eeVQg2f_FAmr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/V_bpxutmTF3r</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/V_bpxutmTF3r.jpg</video:thumbnail_loc>

            <video:title>Electron-volt scaling</video:title>

            <video:description><![CDATA[
Joules are clumsy for atomic scales. How do you convert field strength and distance directly into Mega-electron-volts? Watch to master the shortcut. Solved: In a linear accelerator used for cancer treatment, a proton is accelerated through a distance of 0.8 m. The accelerator maintains a uniform electric field of 2.2 \times 10^7 V/m along the path of the proton. Calculate the energy gained by the proton in Mega-electron-volts (MeV). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/V_bpxutmTF3r.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pGDBLdZl0A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/pGDBLdZl0A.jpg</video:thumbnail_loc>

            <video:title>Inverse gradient</video:title>

            <video:description><![CDATA[
Curves defined by x in terms of y need care. How do you find the gradient at the y-axis intercept when the equation is not solved for y? See the method here. Solved: A curve is defined by x = y^2 - 6y. Find the value of \frac{dy}{dx} at the points where the curve intersects the y-axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/pGDBLdZl0A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BG6gavG9N19q</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/BG6gavG9N19q.jpg</video:thumbnail_loc>

            <video:title>Nernst equation</video:title>

            <video:description><![CDATA[
This lesson explains the Nernst equation, which calculates cell potential under non-standard concentrations and temperatures. You will learn to use this formula to predict cell behaviour when conditions deviate from standard states.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/BG6gavG9N19q.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UY1VIw2olH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/UY1VIw2olH.jpg</video:thumbnail_loc>

            <video:title>One-sided limits</video:title>

            <video:description><![CDATA[
Solve a right-hand limit for a piecewise function by selecting the correct expression. You will learn to apply direct substitution to determine the output trend from the right side. This walkthrough ensures you can identify which function branch to use accurately. Solved: Given f(x) = \begin{cases} 15x - 8 & x > 4 \\ 3x + 10 & x < 4 \end{cases}, find \lim_{x \to 4^+} f(x). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/UY1VIw2olH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pz4f0DvMSN72</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/788/pz4f0DvMSN72.jpg</video:thumbnail_loc>

            <video:title>Structuring the project card</video:title>

            <video:description><![CDATA[
This lesson introduces the <div> element. We will then build the complete HTML structure for all three of our project cards, creating placeholders for the static image, the local video, and the embedded third-party video.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/788/pz4f0DvMSN72.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gzx8VzLCAWgW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Thumbnails/788/Gzx8VzLCAWgW.jpg</video:thumbnail_loc>

            <video:title>Project card (1)</video:title>

            <video:description><![CDATA[
This lesson introduces the <video> element. We will implement our placeholder video clip, learning about important attributes like 'controls' and 'autoplay'.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6EeN5J0oBB/Previews/788/Gzx8VzLCAWgW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BWualCSu66fh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/BWualCSu66fh.jpg</video:thumbnail_loc>

            <video:title>Regions and boundary lines</video:title>

            <video:description><![CDATA[
Identify valid regions by shading areas that satisfy linear inequalities on a Cartesian plane. You will use solid lines for inclusive boundaries and broken lines for exclusive ones to define feasible solution spaces. This method is the visual standard for solving system-based constraints.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/BWualCSu66fh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7UqctkgIgk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/7UqctkgIgk.jpg</video:thumbnail_loc>

            <video:title>Existence of limits</video:title>

            <video:description><![CDATA[
Learn to determine limit existence for an absolute value function by evaluating its left and right sides. You will identify how the jump discontinuity at the point of interest leads to different one-sided results. This walkthrough proves why a limit fails to exist when directions do not match. Solved: Investigate the existence of the limit \lim_{x\to2} \frac{|x-2|}{x-2}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/7UqctkgIgk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/M3MDOiQV0kup</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/867/M3MDOiQV0kup.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson introduces electrochemistry as the study of chemical reactions and electricity. You will learn the basic differences between galvanic cells that produce power and electrolytic cells that use it. It provides a simple roadmap for the topics and industrial applications ahead.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/867/M3MDOiQV0kup.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3qhEkWYsFZ5P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/3qhEkWYsFZ5P.jpg</video:thumbnail_loc>

            <video:title>Axial field of a disk (2)</video:title>

            <video:description><![CDATA[
Apply the disk field formula to find strength on the axis. How do you handle unit conversions for radius and charge density? Watch the calculation steps. Solved: A circular disk has a radius of 20.0 \text{ cm} and a surface charge density of \sigma = +4.50 \text{ }\mu\text{C/m}^2. Calculate the magnitude of the electric field at a point 10.0 \text{ cm} along its central axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/3qhEkWYsFZ5P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AT9L_dWyG4v4</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/AT9L_dWyG4v4.jpg</video:thumbnail_loc>

            <video:title>Side-by-side dielectrics</video:title>

            <video:description><![CDATA[
Side-by-side dielectrics split the plate area. How do you combine different materials sharing the same gap? We treat them as parallel capacitors to find total capacitance. Solved: A parallel-plate capacitor is used in a technical college workshop. It has a total plate area of 14.0\text{ cm}^2 and a plate separation of 3.00\text{ mm}. The space between the plates is filled by two different dielectric materials placed side-by-side, such that each material occupies exactly half of the total plate area and spans the full distance between the plates. The first material has a dielectric constant of \kappa_1 = 4.00, and the second has a dielectric constant of \kappa_2 = 6.00. Determine the capacitance of this arrangement. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/AT9L_dWyG4v4.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j5aYjOYS2sKH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/964/j5aYjOYS2sKH.jpg</video:thumbnail_loc>

            <video:title>Aligning flex items</video:title>

            <video:description><![CDATA[
We will learn how to control the position of items along both axes. This lesson covers justify-content for main-axis alignment and align-items for cross-axis alignment.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/964/j5aYjOYS2sKH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/24e6wIz52WTa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/132/24e6wIz52WTa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on Taylor and Maclaurin series expansion of differentiable functions. Solved: Show that the taylor series expansion of e^x and sin x at x = 0 (Maclaurin series) are:e^x = \sum_{k=0}^{\infty} \frac {x^k} {k!}sin x = \sum_{k=0}^{\infty} (-1)^k \frac {x^{(2k+1)}}{(2k+1)!} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/132/24e6wIz52WTa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_TSEKG6B4ntd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/964/_TSEKG6B4ntd.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
This lesson explains the 'why' behind Flexbox and introduces the core `display: flex` property. We will cover the main concepts of the main axis and the cross axis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/964/_TSEKG6B4ntd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Uy0DhdQJ6Tm_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/865/Uy0DhdQJ6Tm_.jpg</video:thumbnail_loc>

            <video:title>Activation Energy</video:title>

            <video:description><![CDATA[
Define activation energy as the minimum energy required for a chemical reaction to occur. You will learn to identify the energy barrier on reaction profile diagrams and understand how it controls reaction speed. This is a core concept for mastering the effect of temperature on kinetics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/865/Uy0DhdQJ6Tm_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/4DmyUcD_jfzG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/4DmyUcD_jfzG.jpg</video:thumbnail_loc>

            <video:title>The infinite sheet</video:title>

            <video:description><![CDATA[
Derive the field of an infinite sheet from the disk formula. How does the limit as radius goes to infinity remove distance dependence? Watch the proof. Solved: Using the axial field formula for a disk, prove that as the radius R approaches infinity, the electric field becomes uniform (independent of distance). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/4DmyUcD_jfzG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/inYm1M24BvGn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/inYm1M24BvGn.jpg</video:thumbnail_loc>

            <video:title>Variable base and power</video:title>

            <video:description><![CDATA[
Standard rules fail when the base and exponent both vary. How do you differentiate a function raised to a variable power? Learn the log trick to solve it. Solved: Find the derivative of the function y = (\cos x)^x for the interval 0 < x < \frac{\pi}{2}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/inYm1M24BvGn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7mGHbJ1KsofT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Thumbnails/864/7mGHbJ1KsofT.jpg</video:thumbnail_loc>

            <video:title>First-order reactions</video:title>

            <video:description><![CDATA[
Use the first-order integrated rate law to calculate concentration and time. This walkthrough solves problems on hydrogen peroxide decomposition and sucrose hydrolysis. Master these calculations to find the exact amount of reactant remaining.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/9tw7dOSoRb/Previews/864/7mGHbJ1KsofT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/W4DGXJy8U6zw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/154/W4DGXJy8U6zw.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on particle curvilinear motion problems using components normal and tangential to the trajectory of motion. Solved: In the design of a timing mechanism, the motion of pin P in the fixed circular slot is controlled by the guide A which is being elevated by its lead crew. Guide A starts from rest with pin P at the lowest point in the circular slot and accelerates upwards at a constant rate until it reaches a speed of 175 mm/s at the halfway point of its vertical displacement. The guide then decelerates at a constant rate and comes to a stop with pin P at the uppermost point in the circular slot. Determine the n- and t- components of the acceleration of pin P once the pin has travelled 30^\circ around the slot from the starting position. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/154/W4DGXJy8U6zw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742215626266.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/dROWGXwiPZR8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/964/dROWGXwiPZR8.jpg</video:thumbnail_loc>

            <video:title>Footer layout</video:title>

            <video:description><![CDATA[
Construct the portfolio's footer, integrating copyright information and social media icons. Learn to use Flexbox to create a responsive, cleanly aligned footer for both mobile and desktop views.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/964/dROWGXwiPZR8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eCGHNjd2tn9j</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/964/eCGHNjd2tn9j.jpg</video:thumbnail_loc>

            <video:title>Hero layout</video:title>

            <video:description><![CDATA[
We will use Flexbox to create the two-column layout for our hero section, placing the headshot on one side and the name and tagline on the other.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/964/eCGHNjd2tn9j.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tBKDVXpSc8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1116/tBKDVXpSc8.jpg</video:thumbnail_loc>

            <video:title>Implicit product</video:title>

            <video:description><![CDATA[
Implicit equations mix x and y terms. How do you apply the product rule when differentiating mixed variables to find a specific gradient? Watch the step-by-step solution. Solved: Determine the gradient of the tangent to the curve x^2 + xy + 5y^2 = 11 at the point (1, 1). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1116/tBKDVXpSc8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R2cmf_AoAnk_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/R2cmf_AoAnk_.jpg</video:thumbnail_loc>

            <video:title>Piecewise-defined functions</video:title>

            <video:description><![CDATA[
What if one rule suddenly changes at exact points on the axis? The line splits into separate parts and leaves clear gaps. Where does the true value actually sit across and within these breaks?  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/R2cmf_AoAnk_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VWekGpTKBf0t</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/964/VWekGpTKBf0t.jpg</video:thumbnail_loc>

            <video:title>Skills and projects grids</video:title>

            <video:description><![CDATA[
This lesson uses Flexbox with the flex-wrap property to create the responsive grid-like layout for our skills icons and project cards.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/964/VWekGpTKBf0t.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Sk2qwwXzqkK_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/969/Sk2qwwXzqkK_.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This lesson outlines the course objectives, structure, and assessment methods. It defines what is required for success and explains the critical importance of this material for any student of science or engineering.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/969/Sk2qwwXzqkK_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/tEPR0tM_Mn_h</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/965/tEPR0tM_Mn_h.jpg</video:thumbnail_loc>

            <video:title>Styling the form</video:title>

            <video:description><![CDATA[
This lesson tackles inconsistent browser default styles for forms. We will apply uniform styling to all inputs, create a clear call-to-action button, and implement :focus states to deliver a professional and user-friendly experience.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/965/tEPR0tM_Mn_h.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qIitANLZHARV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/qIitANLZHARV.jpg</video:thumbnail_loc>

            <video:title>Standard cell potential (2)</video:title>

            <video:description><![CDATA[
This lesson demonstrates how to calculate an unknown electrode potential from a given standard cell potential. You will work through examples using the relationship between individual half-cell potentials and the overall cell EMF.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/qIitANLZHARV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Va1bJG3b8sbg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1107/Va1bJG3b8sbg.jpg</video:thumbnail_loc>

            <video:title>Fundamental laws</video:title>

            <video:description><![CDATA[
Learn to apply the sum and power laws to evaluate the limit of a quadratic function. You will see how to break the expression into smaller parts and solve each step using direct substitution. This walkthrough demonstrates the precise algebraic method needed to handle multi-part limit problems. Solved: Evaluate \lim_{x \to 2} (6x^{2} + 5). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1107/Va1bJG3b8sbg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BFkcB9xFfNrG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/BFkcB9xFfNrG.jpg</video:thumbnail_loc>

            <video:title>Field of a semicircular arc (2)</video:title>

            <video:description><![CDATA[
Calculate the field at the centre of a charged semicircle. How do you apply the derived formula with correct units? See the solution steps. Solved: A plastic rod of length L = 20.0 \text{ cm} is bent into a semicircle and carries a uniform charge of Q = -5.00 \text{ }\mu\text{C}. Calculate the magnitude of the electric field at the centre of curvature. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/BFkcB9xFfNrG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/RvfsYH6qE7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/RvfsYH6qE7.jpg</video:thumbnail_loc>

            <video:title>Second-order derivatives</video:title>

            <video:description><![CDATA[
The gradient itself changes. How do you measure the rate of that change to find acceleration or curvature? Watch to master the notation and method for second-order derivatives.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/RvfsYH6qE7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JUrh93POiXUf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/965/JUrh93POiXUf.jpg</video:thumbnail_loc>

            <video:title>Styling the table</video:title>

            <video:description><![CDATA[
This lesson transforms the default HTML table to improve data clarity. We will use border-collapse, cell padding, and header styling to make the tabular data professional and easy to scan, a critical skill for presenting information effectively.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/965/JUrh93POiXUf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qglp_U7Gv_jj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/qglp_U7Gv_jj.jpg</video:thumbnail_loc>

            <video:title>Sponteneity</video:title>

            <video:description><![CDATA[
This lesson explains how to predict the spontaneity of a redox reaction by using the cell potential and Gibbs free energy. You will learn the mathematical relationship that determines if a chemical reaction will occur naturally.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/qglp_U7Gv_jj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/FSFrVp4283</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/FSFrVp4283.jpg</video:thumbnail_loc>

            <video:title>Implicit differentiation</video:title>

            <video:description><![CDATA[
Implicit equations hide the gradient. How do you find the second derivative when y is not isolated? See the calculation for a circular profile. Solved: For a circular pipe defined by the equation x^2 + y^2 = 13y, determine the numerical value of the second derivative \frac{d^2y}{dx^2} at the point (6, 4). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/FSFrVp4283.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/anEtSx_4UeNA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/anEtSx_4UeNA.jpg</video:thumbnail_loc>

            <video:title>Field of a semicircular arc (1)</video:title>

            <video:description><![CDATA[
Find the field of a charged semicircular arc. How do you set up the integral and use symmetry to cancel components? Watch the derivation. Solved: A plastic rod is bent into a semicircle of radius R and carries a total positive charge Q spread uniformly. Find a symbolic expression for the magnitude of the electric field at the centre of curvature. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/anEtSx_4UeNA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/iwnIw9IxfV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1072/iwnIw9IxfV.jpg</video:thumbnail_loc>

            <video:title>Empirical and molecular formula (1)</video:title>

            <video:description><![CDATA[
Percentage composition hides the true atomic ratio. How do you convert mass data into a valid empirical formula? Watch this walkthrough to master the calculation steps. Solved: A compound contains 52.2\% carbon, 13.0\% hydrogen, and 34.8\% oxygen by mass. Determine its empirical formula. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1072/iwnIw9IxfV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/79vvLmw__vHV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/79vvLmw__vHV.jpg</video:thumbnail_loc>

            <video:title>Factorisation (2)</video:title>

            <video:description><![CDATA[
Direct substitution yields 0/0 again—what's the next algebraic step? Watch how factorisation untangles the expression to reveal the true limit. Solved: Evaluate \lim_{x \to 2} \frac{x^3 - 8}{x^2 - 4}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/79vvLmw__vHV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oiFxaJCi75Nv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/oiFxaJCi75Nv.jpg</video:thumbnail_loc>

            <video:title>Energy shift</video:title>

            <video:description><![CDATA[
Inserting a dielectric into an isolated capacitor shifts stored energy. How does constant charge affect the final energy state? We calculate the drop using capacitance scaling. Solved: A parallel-plate capacitor with a capacitance of 20.0\text{ pF} is charged using a 10.0\text{-V} battery. The battery is then disconnected, leaving the capacitor isolated. A slab of dielectric material with a dielectric constant of 4.00 is then inserted, completely filling the gap between the plates. Determine (i) the electrical potential energy stored in the capacitor before the slab is inserted and (ii) the potential energy stored after the insertion. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/oiFxaJCi75Nv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/N_fn40aA_jp0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/966/N_fn40aA_jp0.jpg</video:thumbnail_loc>

            <video:title>Stacking context</video:title>

            <video:description><![CDATA[
This lesson tackles the creation of an overlay menu for mobile devices. You will use position: absolute to detach the menu from the document flow and the z-index property to control the stacking context it creates, ensuring it always appears on top of other content.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/966/N_fn40aA_jp0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/hTBti_Lhoblu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Thumbnails/869/hTBti_Lhoblu.jpg</video:thumbnail_loc>

            <video:title>Nernst equation (pH)</video:title>

            <video:description><![CDATA[
This lesson applies the Nernst equation to determine the pH of a solution within a galvanic cell. You will work through calculations to relate non-standard cell potentials to hydrogen ion concentration.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/LtVID3Be7w/Previews/869/hTBti_Lhoblu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fZDMn7z38Wq3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/NNgjcc721k/Thumbnails/1071/fZDMn7z38Wq3.jpg</video:thumbnail_loc>

            <video:title>Sulphur estimation</video:title>

            <video:description><![CDATA[
Carius sulphur estimation relies on barium sulphate precipitate mass. How do you calculate the percentage of sulphur from the mass of BaSO4 formed? Watch this worked example to master the stoichiometry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/NNgjcc721k/Previews/1071/fZDMn7z38Wq3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jmQJVGTb_s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/jmQJVGTb_s.jpg</video:thumbnail_loc>

            <video:title>Special trigonometric limits (3)</video:title>

            <video:description><![CDATA[
Shifted trigonometric limits away from zero fail direct substitution. How do you match angle identities with a variable shift to expose the limit form? Watch the substitution process resolve the block. Solved: Evaluate \lim_{x \to 1} \frac{3\sin \pi x - \sin 3\pi x}{(1-x)^3}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/jmQJVGTb_s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ptn_Epe_K6Mf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1207/Ptn_Epe_K6Mf.jpg</video:thumbnail_loc>

            <video:title>Axial field of a ring (1)</video:title>

            <video:description><![CDATA[
A charged ring creates a field along its axis. How do you sum the vector components from every point on the circle? Watch to see the integration trick that solves it. Solved: A thin plastic ring of radius R carries a total positive charge Q distributed uniformly along its circumference. Derive a general mathematical expression for the magnitude of the electric field at an arbitrary point P located on the central axis at a distance z from the centre of the ring. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1207/Ptn_Epe_K6Mf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Zoa_DKOsmEZ9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/Zoa_DKOsmEZ9.jpg</video:thumbnail_loc>

            <video:title>Power</video:title>

            <video:description><![CDATA[
Power functions form the basis of calculus. How do you reverse the power rule for any exponent? This lesson provides the universal formula for integrating powers.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/Zoa_DKOsmEZ9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NUhwhKFi9fyx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Thumbnails/966/NUhwhKFi9fyx.jpg</video:thumbnail_loc>

            <video:title>Positioning</video:title>

            <video:description><![CDATA[
This lesson focuses on creating a sticky header that remains visible during scroll. You will use the position: sticky property to achieve this, while also learning how it compares to other core positioning values like fixed and absolute.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/vBZR6u2zMQ/Previews/966/NUhwhKFi9fyx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JJ8ALSkspSCg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/296/JJ8ALSkspSCg.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components. Solved: Knowing that \alpha = 40^\circ, determine the resultant of the three forces shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/296/JJ8ALSkspSCg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739469795217.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/YIC_l4GWVamw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Thumbnails/821/YIC_l4GWVamw.jpg</video:thumbnail_loc>

            <video:title>Isotopy</video:title>

            <video:description><![CDATA[
This is a worked example covering the calculation of relative atomic mass. We will use the specific masses and natural abundances of an element's isotopes to determine its weighted average mass. Solved: 1. Five isotopes of Zn occur in nature {}^{64}_{30}\text{Zn} (48.6%) of atomic mass of 63.9291 amu, {}^{66}_{30}\text{Zn} (27.9%) with atomic mass of 65.9260 amu; {}^{67}_{30}\text{Zn} (4.1%) with atomic mass 66.9721 amu; {}^{68}_{30}\text{Zn} (18.8%) with atomic mass 67.9249 amu and {}^{70}_{30}\text{Zn} (0.6%) with atomic mass of 69.9253 amu. Calculate the atomic weight of Zn expressing your answer in three decimal places. [CHM 101, 2025, OAU]2. The element silver (Ag) has two naturally occurring isotopes: {}^{109}\text{Ag} and {}^{107}\text{Ag} with a mass of 106.905 u. Silver consists of 51.82% {}^{107}\text{Ag} and has an average atomic mass of 107.868 u. Calculate the mass of {}^{109}\text{Ag}.[QUESTION 25, CHAPTER 3 OF CHEMICAL PRINCIPLES BY ZUMDAHL AND DE-COSTE]3. The element europium exists in nature as two isotopes: {}^{151}\text{Eu} has a mass of 150.9196 u, and {}^{153}\text{Eu} has a mass of 152.9209 u. The average atomic mass of europium is 151.96 u. Calculate the relative abundance of the two europium isotopes.[QUESTION 26, CHAPTER 3 OF CHEMICAL PRINCIPLES BY ZUMDAHL AND DE-COSTE] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/tOVpJG1IG5/Previews/821/YIC_l4GWVamw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Qb3mLmS13KVQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/675/Qb3mLmS13KVQ.jpg</video:thumbnail_loc>

            <video:title>Basic debugging</video:title>

            <video:description><![CDATA[
This final project makes your portfolio dynamic. You will learn to host your project data online as a live API endpoint using a GitHub Gist, then use fetch to load this data and dynamically generate your project cards.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/675/Qb3mLmS13KVQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JhjAAQpv8hbj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/675/JhjAAQpv8hbj.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
This is the mission briefing. We will define our objective: to master the fundamentals of JavaScript for adding interactivity to websites. This lesson outlines the course structure and the project we will enhance.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/675/JhjAAQpv8hbj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IfV_oS_SyWwU</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/675/IfV_oS_SyWwU.jpg</video:thumbnail_loc>

            <video:title>Your JavaScript workflow</video:title>

            <video:description><![CDATA[
This lesson covers the first practical steps. We will create our first JavaScript file, connect it to our HTML document using the script tag, and use the console to verify that our setup is working correctly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/675/IfV_oS_SyWwU.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6a8FIhJ3_5lH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/676/6a8FIhJ3_5lH.jpg</video:thumbnail_loc>

            <video:title>Data types</video:title>

            <video:description><![CDATA[
All information in JavaScript has a type. This lesson introduces the three most common primitive data types: strings for text, numbers for mathematics, and booleans for true or false logic.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/676/6a8FIhJ3_5lH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aPTId_jGhri2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/333/aPTId_jGhri2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of problems involving dry friction - for particles. Solved: Determine whether the block shown is in equilibrium and find the magnitude and direction of the frictional force when \theta = 40^\circ and P = 400 N. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/333/aPTId_jGhri2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1741106845281.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/wL4T180ZHqLE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/676/wL4T180ZHqLE.jpg</video:thumbnail_loc>

            <video:title>Functions</video:title>

            <video:description><![CDATA[
Functions are reusable blocks of code that perform a specific task. This lesson covers how to define and call your own functions, a core principle for writing organized and efficient code.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/676/wL4T180ZHqLE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NiavUXZq2dGc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/676/NiavUXZq2dGc.jpg</video:thumbnail_loc>

            <video:title>Variables</video:title>

            <video:description><![CDATA[
This lesson introduces variables, the fundamental way JavaScript stores information. We will cover the let and const keywords and discuss the professional standard for when to use each.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/676/NiavUXZq2dGc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Z6MmyahGt_N8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/676/Z6MmyahGt_N8.jpg</video:thumbnail_loc>

            <video:title>Conditional statements</video:title>

            <video:description><![CDATA[
This lesson introduces conditional logic, the primary way a program makes decisions. You will learn to use if and else statements to execute different blocks of code based on a condition.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/676/Z6MmyahGt_N8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/czJgF12uIHo2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/czJgF12uIHo2.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: The amusement park ride consist of a 200-kg car and passenger that are travelling at 3 m/s along a circular path having a radius of 8m. If at t=0, the cable OA is pulled in toward O at 0.5 m/s, determine the speed of the car when t=4s. Also, determine the work done to pull in the cable. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/czJgF12uIHo2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749109996781.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/9bIjMAA6UDiy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Thumbnails/972/9bIjMAA6UDiy.jpg</video:thumbnail_loc>

            <video:title>Dimensional homogeneity (2)</video:title>

            <video:description><![CDATA[
A worked example applying the principle of dimensional homogeneity. We will test the dimensional validity of common physical formulae, identifying both correct and incorrect equations. This is the core application of dimensional analysis. Solved: 3. A certain variable x which has the dimension L is related to time t according to the equation x = at + \frac{1}{2}bt^{2}, where a and b are constants. What are the dimensions of a and b? [6] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/CpErfLAmOC/Previews/972/9bIjMAA6UDiy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Aw8f4PkrggWi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/677/Aw8f4PkrggWi.jpg</video:thumbnail_loc>

            <video:title>Accessing user inputs</video:title>

            <video:description><![CDATA[
This lesson covers how to retrieve data that a user has typed into a form. We will use the .value property to access the input from form fields, a key skill for interactive applications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/677/Aw8f4PkrggWi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Jy7DXtwNBOLy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/Jy7DXtwNBOLy.jpg</video:thumbnail_loc>

            <video:title>Pressure of gases</video:title>

            <video:description><![CDATA[
This lesson explains the origin of gas pressure using the kinetic theory of matter. We demonstrate how constant, random particle collisions against container walls exert the aggregate force that defines pressure.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/Jy7DXtwNBOLy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MNQoHwGRqW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/MNQoHwGRqW.jpg</video:thumbnail_loc>

            <video:title>Special trigonometric limits (1)</video:title>

            <video:description><![CDATA[
Sine over variable limits at zero obey a standard rule. How do you extract the coefficient ratio without altering the limit form? Watch the multiplier adjustment reveal the answer. Solved: Evaluate \lim_{x \to 0} \frac{\sin 12x}{5x}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/MNQoHwGRqW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fqRR2cMm_bW9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/fqRR2cMm_bW9.jpg</video:thumbnail_loc>

            <video:title>Nth derivative</video:title>

            <video:description><![CDATA[
Successive differentiation reveals patterns. How do you derive a general formula for the nth derivative of a reciprocal function? Watch to spot the sequence. Solved: Determine the general formula for the nth derivative f^{(n)}(z) of the function f(z) = \frac{5}{3+z}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/fqRR2cMm_bW9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9T431DS7WhmM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/677/9T431DS7WhmM.jpg</video:thumbnail_loc>

            <video:title>Selecting elements</video:title>

            <video:description><![CDATA[
To manipulate a webpage, you must first select the element you want to change. This lesson introduces the powerful document.querySelector() method for precisely targeting any HTML element on your page.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/677/9T431DS7WhmM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cm9CE4tBHDIw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/677/cm9CE4tBHDIw.jpg</video:thumbnail_loc>

            <video:title>Interactive mobile menu</video:title>

            <video:description><![CDATA[
This first project brings your CSS to life. You will use your knowledge of DOM selection and event listeners to make the mobile navigation menu fully functional, toggling its visibility when the user clicks the menu icon.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/677/cm9CE4tBHDIw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/K22r6V8Ih6Ch</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Thumbnails/111/K22r6V8Ih6Ch.jpg</video:thumbnail_loc>

            <video:title>More worked examples (1)</video:title>

            <video:description><![CDATA[
More worked examples on transposes and properties of matrix transposes. Solved: Determine whether or not each of the following matrices is symmetric or skew-symmetric:(a) \left[\begin{array}{ccc}5& -7&1\\-7&8&2\\ 1& 2&-4\end{array}\right](b) \left[\begin{array}{ccc}0& 4&-3\\-4&0&5\\ 3& -5&0\end{array}\right](c) \left[\begin{array}{ccc}0& 0\\ 0& 0\end{array}\right](d) \left[\begin{array}{ccc}1& 2&-3\\ -3& 2&1\end{array}\right] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Ai3Z3mUznz/Previews/111/K22r6V8Ih6Ch.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vjsi2J1QAY2P</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/vjsi2J1QAY2P.jpg</video:thumbnail_loc>

            <video:title>Analysis of the trajectory (2)</video:title>

            <video:description><![CDATA[
This lesson derives the three key relationships governing projectile motion: time of flight, maximum height, and range. We use the vertical kinematic equations to establish time and the horizontal equation to calculate range. Master these derivations for complete trajectory analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/vjsi2J1QAY2P.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6EEzE7rkZknh</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/81/6EEzE7rkZknh.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on homogeneous functions and Euler's theorem. Solved: Obtain x\frac{\partial f}{\partial x}+y\frac{\partial f}{\partial y} for each of the following:(a) f(x)=x^3+4xy^2-3y^3(b) f(x,y)=e^{xy}(c) f(x,y)=log_e\frac{y}{x} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/81/6EEzE7rkZknh.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/gSvvqehgd1Tg</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/677/gSvvqehgd1Tg.jpg</video:thumbnail_loc>

            <video:title>Listening for events</video:title>

            <video:description><![CDATA[
Interactivity begins when your code responds to the user. This lesson covers the addEventListener() method, showing you how to listen for user actions like clicks and run a function in response.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/677/gSvvqehgd1Tg.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZRpX9hvsOyqS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/677/ZRpX9hvsOyqS.jpg</video:thumbnail_loc>

            <video:title>Manipulating elements</video:title>

            <video:description><![CDATA[
Once an element is selected, you can change it. This lesson covers how to modify an element's text content, alter its inner HTML, and dynamically add or remove CSS classes to change its style.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/677/ZRpX9hvsOyqS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XEYcAPinASqi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/XEYcAPinASqi.jpg</video:thumbnail_loc>

            <video:title>Motion parameters (4)</video:title>

            <video:description><![CDATA[
This lesson uses vector products to analyse the relationship between the velocity, position vector, and acceleration vector in uniform circular motion. You will apply the dot product and the cross product to demonstrate their perpendicular and parallel vector characteristics. Mastering these products is essential for a complete vector description of curvilinear motion. Solved: 4. A particle is in uniform circular motion with radius r = 3.00 \text{ m}. At one instant, its acceleration \vec{a} = (6.00 \hat{i} - 4.00 \hat{j}) \text{ m/s}^{2}. At that instant, what are the values of(a) \vec{v} \cdot \vec{a}(b) \vec{r} \times \vec{a} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/XEYcAPinASqi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/nBkM3W_Mq0-M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/145/nBkM3W_Mq0-M.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of general plane motion of rigid bodies by relating the angular motion of a line to the motion of a point on the same rigid body or different rigid bodies with dependent motion. Solved: In the engine system shown, L= 160mm and b=60mm. Knowing that the crank AB rotates with a constant angular velocity of 1000rpm clockwise, determine the velocity of the piston P and the angular velocity of the connecting rod when (a)\theta=0 (b)\theta =90 . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/145/nBkM3W_Mq0-M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1743854664229.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/RbBw5M3d5C59</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/678/RbBw5M3d5C59.jpg</video:thumbnail_loc>

            <video:title>Introduction to arrays</video:title>

            <video:description><![CDATA[
This lesson introduces the array, JavaScript's fundamental tool for storing ordered lists of data. You will learn how to create an array, add items to it, and access specific items using their index number.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/678/RbBw5M3d5C59.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/KZPlKDClvF6s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/678/KZPlKDClvF6s.jpg</video:thumbnail_loc>

            <video:title>Transforming arrays</video:title>

            <video:description><![CDATA[
This lesson covers the powerful .map() and .filter() methods. You will learn how to transform each item in an array into something new and how to create a new array containing only the items that meet a specific condition.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/678/KZPlKDClvF6s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3uSv5L1Ky6GI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/678/3uSv5L1Ky6GI.jpg</video:thumbnail_loc>

            <video:title>Introduction to objects</video:title>

            <video:description><![CDATA[
This lesson covers JavaScript objects, the primary way to structure related data with key-value pairs. You will learn the syntax for creating an object and how to access its properties using dot notation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/678/3uSv5L1Ky6GI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9u6KFZ3NRSqH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/975/9u6KFZ3NRSqH.jpg</video:thumbnail_loc>

            <video:title>General projectiles (2)</video:title>

            <video:description><![CDATA[
This lesson covers an additional case of a projectile launched at an angle from an elevated position. As the motion is asymmetric, standard range formulas do not apply. We rigorously apply the component kinematic equations to determine the time of flight and impact parameters. Solved: 6. A tennis ball is struck at a height of 1.0\text{m} with a velocity of 25.0 \text{ m/s} at angle of 15^\circ. A net, 1.0\text{m} high, is located 12.0\text{m} away. Does the ball clear the net? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/975/9u6KFZ3NRSqH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MRcUChuD7_0g</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1006/MRcUChuD7_0g.jpg</video:thumbnail_loc>

            <video:title>Multiple linear inequalities (2)</video:title>

            <video:description><![CDATA[
Follow a secondary walkthrough on solving systems of linear inequalities to reinforce finding common solution sets. You will apply algebraic isolation and graphical intersection to identify the valid region that satisfies all given constraints simultaneously. This builds speed for complex exam problems. Solved: 4. Determine the valid solution set for the system: 3x - 1 > 8 \text{ and } 4 - x \ge -1 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1006/MRcUChuD7_0g.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MzYdebr2BAiL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Thumbnails/678/MzYdebr2BAiL.jpg</video:thumbnail_loc>

            <video:title>Dynamic skills list</video:title>

            <video:description><![CDATA[
This project combines the chapter's concepts to make your skills section dynamic. You will create an array of skill objects, then use the .map() method and template literals to automatically generate the HTML for your skills list.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/1wEYFoZkdY/Previews/678/MzYdebr2BAiL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yCySpGdboPZ3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/976/yCySpGdboPZ3.jpg</video:thumbnail_loc>

            <video:title>Motion parameters (5)</video:title>

            <video:description><![CDATA[
This worked example calculates the centripetal, or radial, acceleration for a familiar object: the tip of a clock's second hand. We will determine the period of rotation, calculate the constant tangential speed, and then find the corresponding acceleration magnitude. Solving this problem confirms your ability to calculate centripetal acceleration using the period. Solved: 5. A wall clock has a second hand 15.0 cm long. What is the radial acceleration of the tip of this hand? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/976/yCySpGdboPZ3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yuD6q4DZpt_y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/192/yuD6q4DZpt_y.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on the use of sign conventions for gradient, divergence, curl and Laplacian. Solved: Evaluate the following: i)\nabla^2r 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/192/yuD6q4DZpt_y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/d2axh7B4xiSM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Thumbnails/194/d2axh7B4xiSM.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples length and volume elements in orthogonal curvilinear coordinates. Solved: Given the parabolic cylindrical coordinate system (u,v,z) defined by the transformation equations x=\frac{1}{2}(u^2-v^2), y=uv,z=z 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ERzbjBNuzb/Previews/194/d2axh7B4xiSM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9yIndz8W7Fbb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J6iFnacodl/Thumbnails/923/9yIndz8W7Fbb.jpg</video:thumbnail_loc>

            <video:title>Force and potential energy</video:title>

            <video:description><![CDATA[
Determine the force acting on a particle by differentiating its potential energy function. This walkthrough applies the negative derivative relationship to find the exact force magnitude at a specific position. Solved: The potential energy of a particle in a force field is given by the function U(x) = 3x^3 - 7x^2 + 10, where x is in metres and U is in joules. Calculate the magnitude of the force acting on the particle when it is at position x = 3.0 \, m. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J6iFnacodl/Previews/923/9yIndz8W7Fbb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fV0VlBfcieM9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UITdok7tyr/Thumbnails/1004/fV0VlBfcieM9.jpg</video:thumbnail_loc>

            <video:title>Quadratic equations</video:title>

            <video:description><![CDATA[
Execute the systematic solution of second-degree equations using factorisation, completing the square, and the quadratic formula. You will master the mechanical application of these methods through a step-by-step calculation walkthrough of various quadratic forms. Solved: 2. Solve x^2 - 6x - 4 = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UITdok7tyr/Previews/1004/fV0VlBfcieM9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3lfhI9IpJXCK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/55/3lfhI9IpJXCK.jpg</video:thumbnail_loc>

            <video:title>Polynomials</video:title>

            <video:description><![CDATA[
Meaning, domain and examples of polynomials.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/55/3lfhI9IpJXCK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BgDhC95tpxIf</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/BgDhC95tpxIf.jpg</video:thumbnail_loc>

            <video:title>Charged rod</video:title>

            <video:description><![CDATA[
A rod lacks symmetry. How do you integrate when distance varies along the length? We set up coordinates to solve the variable distance integral.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/BgDhC95tpxIf.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5rvvevR8kgqk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1211/5rvvevR8kgqk.jpg</video:thumbnail_loc>

            <video:title>Spherical capacitance</video:title>

            <video:description><![CDATA[
Spherical capacitors store charge between concentric shells. How does one calculate capacitance when the field follows an inverse-square law? This lesson derives the formula for this curved geometry.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1211/5rvvevR8kgqk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/HO9dDlyUJjkA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/baSCjoC949/Thumbnails/936/HO9dDlyUJjkA.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
A direct statement of the learning track's purpose. This lesson provides a brief overview of the courses within the track and their importance as the foundation for physics and engineering.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/baSCjoC949/Previews/936/HO9dDlyUJjkA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/edEdMg1gndun</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/edEdMg1gndun.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Express F as a vector in terms of the unit vectors i, j, and k. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/edEdMg1gndun.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739793793768.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nkXtsP4DkEYm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Thumbnails/918/nkXtsP4DkEYm.jpg</video:thumbnail_loc>

            <video:title>Sliding friction decision tree</video:title>

            <video:description><![CDATA[
Execute the systematic selection between static and kinetic friction models using a rigorous decision tree walkthrough. You will master the mechanical comparison of applied force to the limiting friction threshold to determine the motion state and resulting resistive magnitude. Solved: 1. A heavy crate of mass m = 20\text{kg} rests on a horizontal floor. The coefficients of friction between the crate and the floor are \mu_s = 0.50 and \mu_k = 0.40. You push the crate horizontally with a force P. Determine the friction force and the acceleration of the crate when(a) P = 80\text{ N}(b) P = 110\text{ N} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VxoDxkZc1f/Previews/918/nkXtsP4DkEYm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/3qEu4ERSb4HO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/993/3qEu4ERSb4HO.jpg</video:thumbnail_loc>

            <video:title>Real numbers</video:title>

            <video:description><![CDATA[
Define the set of real numbers as the union of rational and irrational numbers, represented by the symbol R. You will map these values onto a continuous number line and establish the real number system as the primary domain for foundational calculus and analysis.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/993/3qEu4ERSb4HO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/G2vNHzNgjPn1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Thumbnails/995/G2vNHzNgjPn1.jpg</video:thumbnail_loc>

            <video:title>Associative laws</video:title>

            <video:description><![CDATA[
Define the associative laws for union and intersection, demonstrating that the grouping of sets does not alter the result of the operation. You will master the symbolic manipulation of three-set expressions, establishing the foundation for regrouping terms in complex set algebraic proofs.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6ZKKESvYoZ/Previews/995/G2vNHzNgjPn1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2BtO8mc6rmZ3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/80/2BtO8mc6rmZ3.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on partial derivatives of composite functions. Solved: Let z=e^{xy^2}, x=tcost, y=tsint. Find \frac{dz}{dt} at t=\frac{\pi}{2}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/80/2BtO8mc6rmZ3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/B1NmMF7lwc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/B1NmMF7lwc.jpg</video:thumbnail_loc>

            <video:title>Potential difference</video:title>

            <video:description><![CDATA[
Potential difference is the work per unit charge. Why does this ratio stay constant regardless of the test charge size? Watch to grasp the true meaning of voltage.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/B1NmMF7lwc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rQuwtoHclcCQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Thumbnails/64/rQuwtoHclcCQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
Worked examples on evaluation of higher-order derivatives. Solved: Mathematical inductionn \epsilon \mathbb{N} D^n{y} = F_n(i) Establish for n = n_o where n \epsilon \{0, 1, 2, ....\}(ii) Assume it is true for n = m:D^m{y} = F_m(iii) Establish that it is true for n = m + 1D^{m + 1}y = D(D^m{y}) = D(F_m)Then D^n{y} = F_n is true. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZUNuF2vYnV/Previews/64/rQuwtoHclcCQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aJ_M1in7aeO-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Thumbnails/12/aJ_M1in7aeO-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on centroids and weighted means of a number of points. Solved: Find the centroid of points A, B, C and D with position vectors 4\underline{i}-3\underline{j}-2\underline{k}, 5\underline{i}-4\underline{j}-3\underline{k}, 8\underline{i}+3\underline{j}-2\underline{k}, and-\underline{i}+6\underline{j}-5\underline{k} respectively. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/J3VYrIyIzB/Previews/12/aJ_M1in7aeO-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NBrGGY3vdW65</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/NBrGGY3vdW65.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on evaluating line integrals in two and three dimensions. Solved: Evaluate \int_c \vec{F}.\vec{dr} , where \vec{F}=z\vec{i}+x\vec{j}+y\vec{k} and c is the curve given by \vec{r}(t)=\cos t\vec{i} + \sin t\vec{j }+ 3t\vec{k} (0\le {t} \le {2\pi}) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/NBrGGY3vdW65.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/p6iSoyNKTQCm</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Thumbnails/99/p6iSoyNKTQCm.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on evaluating line integrals in two and three dimensions. Solved: Find the value of the line integral of the vector function \vec{F} = -y\vec{i}+ xy\vec{j},(a) over the circular arc from A to B(b) along the straight line from A to B 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/UeFIzNqYnF/Previews/99/p6iSoyNKTQCm.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1740479355578.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/SrRYOTchFPKa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/144/SrRYOTchFPKa.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the motion of a point on a rigid body undergoing rotation about a fixed axis and its applications. Solved: At the instant shown, the shaft and plate rotates with an angular velocity of \omega=14rad\s and angular acceleration of \alpha=7rad/s^2.Determine the velocity and acceleration of point D located on the corner of the plate at this instant. Express the result in Cartesian vector form. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/144/SrRYOTchFPKa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1747301306527.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/T31rIgYpZqtZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/T31rIgYpZqtZ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems of the first kind. Solved: The circular cam of radius R and eccentricity R/2 rotates clockwise with a constant angular speed w. The resulting vertical motion of the flat follower A can be shown to be x=R(1+\frac{1}{2}\cos wt)(a) Obtain the velocity and acceleration of the follower as a function of t. (b) If w were doubled, how would the maximum velocity and maximum acceleration of the follower be changed? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/T31rIgYpZqtZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1741603675684.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/EALpIRv-fGYx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/EALpIRv-fGYx.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: The magnitude of the absolute velocity of point A on the automobile tire is 12m/s when A is in the position shown. What are the corresponding velocity v_0 of the car and the angular velocity \omega of the wheel ? (The wheel rolls without slipping.) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/EALpIRv-fGYx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744973942981.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/MeQOK9-HeFLl</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/MeQOK9-HeFLl.jpg</video:thumbnail_loc>

            <video:title>Worked examples (7)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: For the instant represented, the rotating link D has an angular velocity w = 2 rad/s, and its slot is vertical. Also \theta = 60^\circ momentarily. Determine the velocity of end A of link AB for this instant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/MeQOK9-HeFLl.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744985941615.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/Fof7neDwiPSQ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/148/Fof7neDwiPSQ.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on acceleration analysis of the motion of a rigid body undergoing general plane motion using the acceleration of a point relative to another point on the same rigid body. Solved: In the engine system shown, l=160mm and b=60mm. Knowing that crank AB rotates with a constant angular velocity of 1000rpm clockwise , determine the acceleration of the piston P and the angular acceleration of the connecting rod when \theta=60^\circ 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/148/Fof7neDwiPSQ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1745154763612.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WmvtH9RrPUBX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/311/WmvtH9RrPUBX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on calculating the moment of a force about a point (about an axis perpendicular to its plane) for three-dimensional cases. Solved: Determine the smallest force F that must be applied along the rope in order to cause the curved rod, which has a radius of 5 ft, to fail at the support C. This requires a moment of M = 80 lb . ft to be developed at C. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/311/WmvtH9RrPUBX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1738690980445.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/QwGotfWUasOT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/151/QwGotfWUasOT.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on uniformly-accelerated motion problems. Solved: A girl rolls a ball up an incline and allows it to return to her. For the angle \theta and ball involved, the acceleration of the ball along the incline is constant at 0.25g, directed down the incline. If the ball is release with a speed of 4m/s, determine the distance s it moves up the incline before reversing its direction and the total time t required for the ball to return to the child's hand. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/151/QwGotfWUasOT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742039624864.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/PFUlLfu6Ochv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/151/PFUlLfu6Ochv.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on uniform motion problems. Solved: Car A starts from rest at t=0 and travels along a straight road with a constant acceleration of 6ft/s^2 until it reaches a speed of 80ft/s. Afterwards it maintains this speed. Also when t=0, car B locates 6000ft down the road is travelling towards A at a constant speed of 60ft. Determine the distance travelled by car A when they pass each other. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/151/PFUlLfu6Ochv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1742044085126.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/uKOg4K39Iz1-</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/uKOg4K39Iz1-.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: The two structural members, one of which is in tension, and the other in compression, exert the indicated forces on joint O. Determine the magnitude of the resultant R of the two forces and the angle \theta which R makes with the positive x-axis. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/uKOg4K39Iz1-.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739463531644.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/qnazlrO-qjby</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/294/qnazlrO-qjby.jpg</video:thumbnail_loc>

            <video:title>Worked examples (6)</video:title>

            <video:description><![CDATA[
More worked examples on resultant of forces in two dimensions. Solved: Two forces are applied to the construction bracket bracket as shown. Determine the angle \theta which makes the resultant of the two forces vertical. Determine the magnitude R of the resultant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/294/qnazlrO-qjby.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1739464739209.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/1nUVD46_FADP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/298/1nUVD46_FADP.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on resolution of a force in three dimensions into its components. Solved: Two cables BG and BH are attached to frame ACD as shown. Knowing that the tension in cable BG is 540 N, determine the components of the force exerted by cable BG on the frame at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/298/1nUVD46_FADP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ABz3ByaEqA/1739795201892.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/sRqtLnDbmJ9C</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Thumbnails/80/sRqtLnDbmJ9C.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on partial derivatives of composite functions. Solved: Given that u = x^2 y + \frac{1}{y} and y = \log_{e}x, find \frac{du}{dx} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/zF7I3qFBeJ/Previews/80/sRqtLnDbmJ9C.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6v8TvisPt81W</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/300/6v8TvisPt81W.jpg</video:thumbnail_loc>

            <video:title>Worked examples (11)</video:title>

            <video:description><![CDATA[
More worked examples on equilibrium of a particle in three dimensions. Solved: Determine the tension in cables OD and OB and the force in strut OC, required to support the 50-kg crate. The spring OA has an unstretched length of 0.8 m and a stiffness k_OA= 1.2 kN/m. The force in the strut acts along the axis of the strut. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/300/6v8TvisPt81W.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1740072126097.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/3yVx_Xn0S4pI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/3yVx_Xn0S4pI.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
Worked examples on particle rectilinear motion problems of the second kind. Solved: Many car companies are performing research on collision avoidance systems. A small prototype applies engine braking that decelerates the engine according to the relationship a=-k\sqrt{t}, where a and t are expressed in m/s^2 and seconds, respectively. The vehicle is travelling at 20 m/s when its radar sensor detect a stationary obstacle. Knowing that it takes the prototype vehicle 4 seconds to stop, determine (a) expression for its velocity and position as a function of time, (b) how far the vehicle travelled before it stopped. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/3yVx_Xn0S4pI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/IhfrwG_TgzDS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/IhfrwG_TgzDS.jpg</video:thumbnail_loc>

            <video:title>Rationalisation (2)</video:title>

            <video:description><![CDATA[
Radicals in denominators block direct substitution. How do you clear the root without changing the limit value? Watch rationalisation cancel the undefined term. Solved: Evaluate \lim_{x \to 16} \frac{x - 16}{\sqrt{x} - 4}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/IhfrwG_TgzDS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XEJnrQejhPgG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/XEJnrQejhPgG.jpg</video:thumbnail_loc>

            <video:title>Verifying differential equations</video:title>

            <video:description><![CDATA[
Engineers, economists and scientists model physical phenomena with differential equations. How do you prove that a function solves a second-order differential equation? Watch the verification steps. Solved: Verify that the vibration function y = C_1 \cos(6t) + C_2 \sin(6t) is a valid solution for the differential equation \frac{d^2y}{dt^2} + 36y = 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/XEJnrQejhPgG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/8DZBK_wYxM2f</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Thumbnails/313/8DZBK_wYxM2f.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on moments of couples and their resultants. Solved: The top view of a workpiece that fits loosely in a fixture for drilling is shown. The drill bit has two edges that apply in-plane cutting forces F to the workpiece.(a) If F=600N, determine the forces Q between the workpiece and fixture so that the resultant couple moment is zero when \alpha=30^\circ. (b) Does your answer for Q from Part (a) change if \alpha has a different value? If yes, then repeat Part (a) with \alpha=60^\circ. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/FiqNJEzQI6/Previews/313/8DZBK_wYxM2f.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1738752967656.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nUHYHPHa_lRX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/290/nUHYHPHa_lRX.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on kinematics of motion of a rigid body undergoing general plane motion using parameters measured relative to a reference frame in rotation. Solved: The slider block B, which is attached to a cord, moves along the slot of the horizontal circular disk. If the cord is pulled down through the central hole A is the disk at a constant rate of x=-3m/s , measured relative to the disk, determine the acceleration of the block at the instant x=0.1m . The disk has a constant angular velocity of \omega_D=2rad/s . 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/290/nUHYHPHa_lRX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1745155537296.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/7f5KBHaQwTzo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Thumbnails/299/7f5KBHaQwTzo.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on addition of vectors in three dimensions. Solved: The boom OA carries a load P and is supported by two cables as shown. Knowing that the tension in cable AB is 183lb and that the resultant of the load P and the forces exerted at A by the two cables must be directed along OA. Determine the tension in cable AC 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ZRJRfRqUnB/Previews/299/7f5KBHaQwTzo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739878010513.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/iHxCGjtNXuQE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/iHxCGjtNXuQE.jpg</video:thumbnail_loc>

            <video:title>Worked examples (12)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: The pilot of an airplane carrying a package of mail to a remote outpost wishes to release the package at the right moment to hit the recovery location A. What angle \theta with the horizontal should the pilot's line of sight to the target make at the instant of release ? The airplane is flying horizontally at an altitude of 100m with a velocity of 200km/h. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/iHxCGjtNXuQE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746267304686.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/GpkZDUkB5hfO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/338/GpkZDUkB5hfO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of frictional forces on journal bearings. Solved: The collar fits loosely around a fixed shaft that has a radius of 2 in . If the coefficient of kinetic friction between the shaft and the collar is \mu_k=0.3 , determine the force P on the horizontal segment of the belt so that the collar rotates clockwise with a constant angular velocity. Assume that the belt does not slip on the collar; rather, the collar slips on the shaft. Neglect the weight and thickness of the belt and collar. The radius, measured from the center of the collar to the mean thickness of the belt, is 2.25in. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/338/GpkZDUkB5hfO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746870822310.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/FdI2TDuTcb49</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Thumbnails/338/FdI2TDuTcb49.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on analysis of frictional forces on journal bearings. Solved: The radius of the pulley is 4 in. The pulley is rigidly attached to the horizontal shaft, which is supported by two journal bearings. The radius of the shaft is 1in, and the combined weight of the pulley and shaft is 20Ib. The coefficients of friction between the shaft and the bearings are \mu_s=0.30 and \mu_k=0.28 . Determine the largest weight W that can be suspended as shown without causing the stationary shaft to slip in the bearings. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/JNmMy2IiQY/Previews/338/FdI2TDuTcb49.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746869950664.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/WwyB8V2XvfDB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/153/WwyB8V2XvfDB.jpg</video:thumbnail_loc>

            <video:title>Worked examples (14)</video:title>

            <video:description><![CDATA[
More worked examples on curvilinear motion in rectangular coordinates involving projectiles. Solved: In the cathode - ray tube, electrons traveling horizontally from their source with the velocity v_0 are deflected by an electric field E due to the voltage gradient across the plates P. The deflecting force causes an acceleration in the vertical direction on the sketch equal to eE/m , where e is the electron charge and m is its mass. When clear of the plates, the electrons travel in straight lines. Determine the expression for the deflection \delta for the tube and plate dimensions shown. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/153/WwyB8V2XvfDB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1746268692917.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/nD-0QqbRTLkD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/nD-0QqbRTLkD.jpg</video:thumbnail_loc>

            <video:title>Worked examples (8)</video:title>

            <video:description><![CDATA[
More worked examples on particle rectilinear motion problems of the 4th kind. Solved: A projectile is fired downward with initial speed v_0 in an experimental fluid and experiences an acceleration a=\sigma-\eta v^2 , where \sigma and \eta are positive constants and v is the projectile speed. Determine the distance traveled by the projectile when its speed has been reduced to one-half of the initial speed v_0 . Also, determine the terminal velocity of the projectile. Evaluate for \sigma=0.7m/s^2, \eta=0.2m^-1, and v_0=4m/s 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/nD-0QqbRTLkD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pfPCcFM81_yO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/146/pfPCcFM81_yO.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on kinematics of motion of a rigid body undergoing general plane motion using the velocity of a point relative to another point on the same rigid body. Solved: The vertical rod has a downward velocity v=2.5ft/sec when link AB is in the 30^\circ position shown. Determine the corresponding angular velocity of AB and the speed of roller B if R=16in. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/146/pfPCcFM81_yO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1744974334181.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/U90lBgH_JPjF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/U90lBgH_JPjF.jpg</video:thumbnail_loc>

            <video:title>Rationalisation (3)</video:title>

            <video:description><![CDATA[
Dual radicals in fractions routinely block direct substitution. How do you clear the roots from both numerator and denominator without altering the limit value? Watch the stepwise rationalisation process resolve the indeterminate form. Solved: Evaluate \lim_{x \to 0} \frac{\sqrt{x + 11} - \sqrt{11}}{\sqrt{x + 6} - \sqrt{6}}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/U90lBgH_JPjF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qbM5vbEsrZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1117/qbM5vbEsrZ.jpg</video:thumbnail_loc>

            <video:title>Polynomials</video:title>

            <video:description><![CDATA[
Polynomials are easy to differentiate. How do you find the second derivative and evaluate it at a specific point? Watch the step-by-step calculation. Solved: A construction beam follows a profile defined by y = 5x^4 + 3x^3 - 6x^2 + 8x - 12. Calculate the expression for the second derivative \frac{d^2y}{dx^2} and evaluate its value when x=2. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1117/qbM5vbEsrZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SRlTDNQhJ8d1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/SRlTDNQhJ8d1.jpg</video:thumbnail_loc>

            <video:title>Product expansion</video:title>

            <video:description><![CDATA[
Product terms block direct integration. How do you expand brackets to create a standard polynomial? This walkthrough shows the multiplication and term-by-term calculation. Solved: Determine \int (x+2)(x-5) dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/SRlTDNQhJ8d1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/bfJD45KZEEIF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/415/bfJD45KZEEIF.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of space trusses - identifying zero-force members in space trusses. Solved: The truss shown consists of nine members and is supported by a ball-and-socket at B, a short link at C and two short links at D. (a) Check that this truss is a simple truss, that it is completely constrained, and that the reactions at its supports are statistically determinate (b) Determine 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/415/bfJD45KZEEIF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/IEnUYmEZZ7/1739269457764.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/zK1ql62rPYbp</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/nzyA26uII2/Thumbnails/289/zK1ql62rPYbp.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on force-acceleration analysis of absolute and relative motion of bodies in contact. Solved: Consider the system below in which a crate is placed on the flat bed of a moving truck(a) The coefficient of static friction between the 200-kg crate and the flat bed of the truck is \mu_s = 0.3. Determine the shortest time for the truck to reach a speed of 60 km/h, starting from rest with constant acceleration so that the crate does not slip. (b) The truck showing is travelling at v_o = 20 mph when the driver applies the brakes to come to a stop. The deceleration of the truck is constant, and the the truck comes to a complete stop after braking for a distance of 350 ft. Treat the crate as a.particle so that tipping can be neglected.(i) Determine the minimum coefficient of static friction between the crate A and the truck so that the crate does not slide relative to the truck.(ii) If the coefficient of kinetic friction between the crate A and the bed of the truck is 0.3 and the static friction is not sufficient to prevent slip, determine the minimum distance d between the crate and the truck B so that the crate never hits the truck at B.(iii) If the coefficient of kinetic friction between the crate A and the bed of the truck is 0.3, static friction is not sufficient to prevent slip, and the distance d from the front of the crate to the truck at B is 10 ft, determine the speed relative to the truck with which the crate strikes the truck at B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/nzyA26uII2/Previews/289/zK1ql62rPYbp.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/ry3uu6UurN/1742300491331.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/5OfDqcLMIt</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/5OfDqcLMIt.jpg</video:thumbnail_loc>

            <video:title>Primary trigonometric functions</video:title>

            <video:description><![CDATA[
Sine, cosine and tangent model periodic motion. How do their gradients shift between each other? Watch to see the standard derivatives derived from first principles and quotient rules.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/5OfDqcLMIt.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/AC5_yxBmes_7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/AC5_yxBmes_7.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity (2)</video:title>

            <video:description><![CDATA[
When the denominator degree exceeds the numerator, the limit at infinity is zero. How do you spot this without full expansion? Watch the leading term comparison give the answer. Solved: Evaluate \lim_{x \to \infty} \frac{2x + 5}{x^2 - 3x + 4}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/AC5_yxBmes_7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/mF7FkIX6g_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/mF7FkIX6g_.jpg</video:thumbnail_loc>

            <video:title>Electric charge</video:title>

            <video:description><![CDATA[
This lesson explains the nature of electric charge and its classification into positive and negative types. It also covers the Coulomb as the standard SI unit for measurement.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/mF7FkIX6g_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xEM28lRH8_An</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Thumbnails/150/xEM28lRH8_An.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
Worked examples on particle rectilinear motion problems of the third kind. Solved: Heavy rains cause a particular stretch of road to have a coefficient of friction that changes as a function of location . Specifically, measurements indicate that the friction coefficient has a 3% decrease per meter. Under these conditions the acceleration of a car skidding while trying to stop can be approximated by s= -(\mu k-cs)g (the 3% decrease in friction was used in deriving this equation for acceleration ), where \mu\kappa=0.5, c=0.015m^-1, v_0=45km/h, where v_0 is the initial velocity of the car. Determine the distance it will take the car to stop and the percentage of increase in stopping distance with respect to dry conditions , i.e., when c=0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ruNUeQjB7v/Previews/150/xEM28lRH8_An.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1741950639139.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/7AbgyYt01Udu</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Thumbnails/143/7AbgyYt01Udu.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on angular motion of a rigid body undergoing rotation about a fixed axis. Solved: The angular acceleration \alpha (rad\s^2) of the rotating disk is related to its angular velocity \omega(rad\s) by \alpha=4\sqrt{\omega}. When t=0 , the disk is at rest and the angular position coordinate of a line in the disk is \theta=8rad. Find expressions for the following:(a)\theta(\omega) ; (b)\omega(t) ;and (c)\theta(t) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/Y3F62FIUuF/Previews/143/7AbgyYt01Udu.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1747301383391.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/xtd7BZXFXYMD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/xtd7BZXFXYMD.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity (3)</video:title>

            <video:description><![CDATA[
When the numerator degree exceeds the denominator, the limit at infinity diverges. How do you confirm the sign of infinity without full computation? Watch the leading term analysis settle the behaviour. Solved: Evaluate \lim_{x \to \infty} \frac{x^3 + 1}{x^2 + 4}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/xtd7BZXFXYMD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ntn7avC3lZfi</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/Ntn7avC3lZfi.jpg</video:thumbnail_loc>

            <video:title>Conservation and quantisation</video:title>

            <video:description><![CDATA[
This lesson explains that electric charge exists only in discrete packets and cannot be created or destroyed. These fundamental rules provide the theoretical basis for all subsequent mathematical examples.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/Ntn7avC3lZfi.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EqFwtQQ3Zckn</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1210/EqFwtQQ3Zckn.jpg</video:thumbnail_loc>

            <video:title>Rod off-axis potential</video:title>

            <video:description><![CDATA[
A point sits above a rod. How do you handle variable distance using Pythagoras in the integral? We solve the perpendicular potential case step by step. Solved: During a laboratory experiment, a thin non-conducting strip of length L = 10.0 \text{ cm} is charged uniformly with a total positive charge Q = 5.00 \text{ nC}. Calculate the electric potential at a point P located at a perpendicular distance d = 12.0 \text{ cm} directly above the centre of the strip. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1210/EqFwtQQ3Zckn.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2mzRfq5x6gNK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/2mzRfq5x6gNK.jpg</video:thumbnail_loc>

            <video:title>Inverse trigonometric functions</video:title>

            <video:description><![CDATA[
Inverse trig functions find angles from ratios. How do their derivatives become simple algebraic fractions? Watch the inverse function rule turn trig terms into roots.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/2mzRfq5x6gNK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/yX9xNT9IkN26</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Thumbnails/514/yX9xNT9IkN26.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on angular impulse and momentum principle, and conservation of angular momentum. Solved: The particle of mass m is gently nudged from the equilibrium position A and subsequently slides along the smooth circular path which lies in a vertical plane. Determine the magnitude of its angular momentum about point O as it passes (a) point B and (b) point C. In each case, determine the time rate of change of H_o. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/ja2RnibNNa/Previews/514/yX9xNT9IkN26.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1749045079313.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/0mZBfmpiLA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1144/0mZBfmpiLA.jpg</video:thumbnail_loc>

            <video:title>Work and displacement</video:title>

            <video:description><![CDATA[
Work depends on charge sign and direction. How do you handle a negative charge moving against the potential gradient? Watch to get the signs right. Solved: A uniform electric field is directed along the negative x-axis. The potential difference between point A (at x = 0.30 m) and point B (at x = 0.70 m) is 150 V. Calculate the work done on a negative point charge q = -0.400 \mu C by the electric field as it is moved from B to A. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1144/0mZBfmpiLA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dbkhSHgdV0i5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1208/dbkhSHgdV0i5.jpg</video:thumbnail_loc>

            <video:title>Far-field axial approximation</video:title>

            <video:description><![CDATA[
Derive the far-field of a dipole on its axis. How does the approximation for large distance yield the one over r cubed law? Watch the mathematical proof. Solved: An electric dipole consists of charges +q and -q separated by distance d along the y-axis. For a point P on the positive y-axis at a distance z from the centre, derive the far-field expression for the electric field magnitude, specifically showing how the 1/z^3 relationship emerges when z \gg d. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1208/dbkhSHgdV0i5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Wf_btlpw_gOd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/Wf_btlpw_gOd.jpg</video:thumbnail_loc>

            <video:title>Logarithmic functions</video:title>

            <video:description><![CDATA[
Logarithms reverse exponential growth. How does the derivative of natural log become a simple fraction? Watch the link between exponentials and logs reveal the answer.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/Wf_btlpw_gOd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jPpuydXzaWSe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/jPpuydXzaWSe.jpg</video:thumbnail_loc>

            <video:title>Factorisation (4)</video:title>

            <video:description><![CDATA[
Fractional differences routinely trigger indeterminate infinity minus infinity forms. How do you unify separate denominators to expose the common factor? Watch the consolidation process resolve the undefined expression cleanly. Solved: Evaluate \lim_{x \to 2} \left( \frac{1}{x-2} - \frac{4}{x^2-4} \right). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/jPpuydXzaWSe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ODLlK8E50Olb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1211/ODLlK8E50Olb.jpg</video:thumbnail_loc>

            <video:title>Coaxial cable</video:title>

            <video:description><![CDATA[
Coaxial cables rely on cylindrical capacitance. How does one compute storage per unit length and the required charge density? This walkthrough solves the exact design parameters for a transmission line. Solved: A coaxial transmission cable used in a telecommunications project has an inner wire with a radius of a = 0.25 \text{ mm} and an outer cylindrical shield with an inner radius of b = 1.75 \text{ mm}. Assuming the space between the conductors is a vacuum, (a) calculate the capacitance per unit length (in \text{pF/m}) for this cable. (b) Determine the magnitude of the linear charge density (\lambda) required to establish a potential difference of 80.0 \text{ V} between the conductors. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1211/ODLlK8E50Olb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/uFmHYgv0D534</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/551/uFmHYgv0D534.jpg</video:thumbnail_loc>

            <video:title>Worked examples (2)</video:title>

            <video:description><![CDATA[
More worked examples on Newton's second law equation for a system of particles. Solved: The two sliders A and B of weight W_A=8lb and W_B=6lb, respectively, move with negligible friction in the slots shown, which lie in the vertical plane. They are connected by a rigid bar of negligible weight and length L=1.75ft. Slider A is also subjected to the force P=15lb. If, for y_B=1.0ft, the system is initially at rest, determine the acceleration of each slider and the force in the bar immediately after release. Hint: The force that the bar exert on each slider has the same direction as the bar itself. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/551/uFmHYgv0D534.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/7MzunAqAnQ/1750749711934.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/9CamFCmix1_b</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Thumbnails/556/9CamFCmix1_b.jpg</video:thumbnail_loc>

            <video:title>Worked examples (3)</video:title>

            <video:description><![CDATA[
More worked examples on analysis of systems of particles under steady flow. Solved: One of the most advanced methods for cutting metal plates uses a high-velocity water jet with carries an abrasive garnet powder. The jet issues from the 0.01-in,-diameter nozzle at A and follows the path shown through the thickness t of the plate. As the plate is slowly moved to the right, the jet makes a narrow precision slot in the plate. The water-abrasive mixture is used at the low rate of 1/2 gal/min and has a specific weight of 68ft/s^2. Water issues from the bottom of the plate with a velocity which is 60 percent of the impinging nozzle velocity. Calculate the horizontal force F required to hold the plate against the jet. (There are 231in.^3 in 1 gal) 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/AErEbQnRnE/Previews/556/9CamFCmix1_b.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/U3mb7by2QU/1752748703131.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/StI25o6bB0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/StI25o6bB0.jpg</video:thumbnail_loc>

            <video:title>Rationalisation (1)</video:title>

            <video:description><![CDATA[
Radicals in numerators routinely defeat direct substitution. How do you clear the undefined result without altering the limit value? Track the rationalisation steps to watch the messy terms cancel out. Solved: Evaluate \lim_{x \to 3} \frac{\sqrt{x^2 + 7} - 4}{x - 3}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/StI25o6bB0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/owpy82bzIAth</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/owpy82bzIAth.jpg</video:thumbnail_loc>

            <video:title>Polynomial expression</video:title>

            <video:description><![CDATA[
Polynomials require term-by-term integration. How do you apply the power rule to each component while keeping constants intact? This walkthrough shows the direct calculation for a standard polynomial expression. Solved: Determine the indefinite integral \int (4x^{3} + 9x^{2} - 10x + 7) dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/owpy82bzIAth.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L8M4AGqqAvuP</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/L8M4AGqqAvuP.jpg</video:thumbnail_loc>

            <video:title>Exponential functions</video:title>

            <video:description><![CDATA[
Exponential functions model rapid growth. Why does e to the x stay unchanged while other bases gain a constant? Watch to see the general rule for any base.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/L8M4AGqqAvuP.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dQRrWsOvxc</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/dQRrWsOvxc.jpg</video:thumbnail_loc>

            <video:title>Induction and conduction</video:title>

            <video:description><![CDATA[
Objects can be charged through direct physical contact or without touching via influence. Master the step-by-step processes of charging by conduction and electrostatic induction.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/dQRrWsOvxc.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2-Wv8zxMC08k</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Thumbnails/566/2-Wv8zxMC08k.jpg</video:thumbnail_loc>

            <video:title>Worked examples (4)</video:title>

            <video:description><![CDATA[
More worked examples on calculating equivalence classes and quotient sets. Solved: Let S=[{2,3,4,6]} . A relation R is defined on the set S by xRy\iff x . Corresponding to each element a\in S , we define a subset R(a) by R (a) =[{x\in S: xRa]}(a) Find the subset R(a) for each a\in S(b) Give an example of an element a\in S such that R(a)=\emptyset(c) Give an example of a pair of elements a,b \in S such that R(a) \space n\space R(b)\ne\emptyset (d) Is R an equivalence relation? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/eeyJerinNQ/Previews/566/2-Wv8zxMC08k.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WDcEZezeMgu5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Thumbnails/613/WDcEZezeMgu5.jpg</video:thumbnail_loc>

            <video:title>Worked examples (1)</video:title>

            <video:description><![CDATA[
Worked examples on continuity of functions. Solved: Find the values of x for which the following functions are discontinuous:(a) f(x) = 5x^3 -3x^2+5(b) f(x) = \sqrt[3]{x-8}(c) f(x) = \sqrt{x-8}(d) f(x) = \frac 5 x + \frac {2x} {x+4}(e) f(x) = \frac {1} {\sqrt{x}} + \frac {3x} {x-2} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/REu7Fqq3MF/Previews/613/WDcEZezeMgu5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZxOp52bFyk_l</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1108/ZxOp52bFyk_l.jpg</video:thumbnail_loc>

            <video:title>Limits at infinity (4)</video:title>

            <video:description><![CDATA[
Radical differences at infinity routinely trap direct substitution. How do you multiply by the conjugate to clear the indeterminate form? Watch the video to see the terms cancel and reveal the limit. Solved: Evaluate \lim_{x \to \infty} \left( \sqrt{x^2 + 10x} - x \right). 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1108/ZxOp52bFyk_l.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dfZJf_Pn4I</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/dfZJf_Pn4I.jpg</video:thumbnail_loc>

            <video:title>Net ionic charge</video:title>

            <video:description><![CDATA[
This lesson shows how to calculate the net electrical charge of magnesium and hydroxide ions in Coulombs. It applies the concept of charge quantisation to convert chemical valency into physical charge values. Solved: Determine the net charge of a magnesium ion (Mg^{2+}) and a hydroxide molecular ion (OH^{-}) in coulombs, expressed to three significant figures. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/dfZJf_Pn4I.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Uzoo5pKaZg0M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1115/Uzoo5pKaZg0M.jpg</video:thumbnail_loc>

            <video:title>Hyperbolic product</video:title>

            <video:description><![CDATA[
Hyperbolic and exponential functions often appear together. How do you apply the product rule when both terms change? Watch the differentiation. Solved: If x = e^u \sinh u, obtain an expression for \frac{dx}{du}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1115/Uzoo5pKaZg0M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/VcJ8A7CRRluv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Thumbnails/53/VcJ8A7CRRluv.jpg</video:thumbnail_loc>

            <video:title>Number Systems</video:title>

            <video:description><![CDATA[
This lesson defines the hierarchy of number systems, from natural numbers through to the real numbers. These classifications provide the essential vocabulary for discussing functions and their domains throughout this course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/3N6BIVZ2qV/Previews/53/VcJ8A7CRRluv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/kMqDDlWhJ-Ig</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Thumbnails/323/kMqDDlWhJ-Ig.jpg</video:thumbnail_loc>

            <video:title>Worked examples (5)</video:title>

            <video:description><![CDATA[
More worked examples on the analysis of machines. Solved: Rod CD is attached to the collar D and passes through a collar welded to end B of lever AB. Neglecting the effect of friction, determine the couple M required to hold the system in equilibrium \theta=30^0 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/6MZFQ6VfiQ/Previews/323/kMqDDlWhJ-Ig.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
            <image:image>
              <image:loc>https://media.unidrills.com/media/instructor/BvFIrMrVnM/1740304768821.JPEG</image:loc>
            </image:image>
            
        </url>
        <url>
          <loc>https://unidrills.com/video/UXQJNrhKY29s</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/912/UXQJNrhKY29s.jpg</video:thumbnail_loc>

            <video:title>Kinematics with calculus (1)</video:title>

            <video:description><![CDATA[
This worked example applies differentiation to 1D motion. We will differentiate a given position coordinate (x) with respect to time to find velocity (v). We then differentiate velocity to find acceleration (a). Solved: The position of a particle moving along the x-axis is described by the function x(t)=2t^3-9t^2+12t, where x is in meters and t is in seconds.(a) Find the particle's velocity at t=1s.(b) Find the particle's acceleration at t=1s.(c) At what time(s) is the particle momentarily at rest. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/912/UXQJNrhKY29s.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qxWsUqRrPX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/qxWsUqRrPX.jpg</video:thumbnail_loc>

            <video:title>Special trigonometric limits (2)</video:title>

            <video:description><![CDATA[
Trigonometric quotients at zero obey a predictable rule. How do you pull the coefficient ratio from sine and tangent terms? Watch the limit law do the heavy lifting. Solved: Evaluate \lim_{x \to 0} \frac{\sin 3x}{\tan 7x}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/qxWsUqRrPX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_wqagzE5fYec</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1211/_wqagzE5fYec.jpg</video:thumbnail_loc>

            <video:title>Cylindrical scaling</video:title>

            <video:description><![CDATA[
Optimising cylindrical capacitors requires precision. Does extending length or widening the inner radius yield better storage? This example compares both strategies to find the superior design choice. Solved: A cylindrical capacitor is designed for a signal filtering system with an inner radius a and an outer radius b = 2.50a. An engineer wants to optimize the design to increase its capacitance (C). Determine which of the following two modifications is more effective at increasing the capacitance: (1) increasing the length (L) of the capacitor by 20.0\% or (2) increasing the inner radius (a) by 20.0\% while keeping the length (L) and the outer radius (b) constant. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1211/_wqagzE5fYec.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/aKAVrT3gr8Q7</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/aKAVrT3gr8Q7.jpg</video:thumbnail_loc>

            <video:title>Negative power</video:title>

            <video:description><![CDATA[
Variables in the denominator block direct integration. How do you rewrite this fraction as a negative power for the standard rule? This calculation shows the conversion and final result. Solved: Find the indefinite integral \int \frac{6}{x^{5}} dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/aKAVrT3gr8Q7.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Gwj3xLP45Y</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/Gwj3xLP45Y.jpg</video:thumbnail_loc>

            <video:title>Composite radical</video:title>

            <video:description><![CDATA[
Roots hide inner functions. How do you differentiate a radical containing a polynomial without expanding it? Watch the chain rule in action. Solved: Determine the derivative of the function g(w) = \sqrt{5w^2 + 4} with respect to w. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/Gwj3xLP45Y.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_xoYXYiQzbgs</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Thumbnails/913/_xoYXYiQzbgs.jpg</video:thumbnail_loc>

            <video:title>Average velocity (1)</video:title>

            <video:description><![CDATA[
This example applies the definition of average velocity. Watch how to calculate the displacement vector by subtracting position vectors, then divide by the time interval to find the average velocity vector. Solved: 1. An ion's position vector is initially \vec{r}_i=(5.0i-6.0j+2.0k)m. 10s later, it's position is \vec{r}"f=(-2.0i+80j-2.0k)m. In unit vector notation what is its average velocity during the 10s? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/TZ9d8GX7rU/Previews/913/_xoYXYiQzbgs.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ALjAHBsPcQH8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Thumbnails/1139/ALjAHBsPcQH8.jpg</video:thumbnail_loc>

            <video:title>Charge conservation</video:title>

            <video:description><![CDATA[
This lesson calculates the final charge on a metal canister after a series of contacts with other charged bodies. It applies the law of conservation of charge to show how total charge is shared equally between identical conductors upon contact. Solved: Two identical metal canisters, A and B, carry charges of +8.0 \text{ } \mu \text{C} and -2.0 \text{ } \mu \text{C}, respectively. A third identical neutral canister, C, is touched to canister A, then touched to canister B, and finally removed. Calculate the final charge remaining on canister B. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/kBLIbd8HhK/Previews/1139/ALjAHBsPcQH8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/oC6wsGWuFiOZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Thumbnails/834/oC6wsGWuFiOZ.jpg</video:thumbnail_loc>

            <video:title>Boyle's law</video:title>

            <video:description><![CDATA[
This problem walkthrough demonstrates precise application of Boyle's Law to determine the change in gas volume or pressure under constant temperature. We detail the inverse proportionality relationship and required unit consistency. Master this fundamental pressure-volume calculation. Solved: A volume of a certain gas equals to 20.0 \text{ L} was collected at 23^\circ\text{C} and 1.00 atmospheric pressure. What would be the volume of the same gas if it were collected at 23^\circ\text{C} and 0.830 atmospheric pressure. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/DYQaSniPFy/Previews/834/oC6wsGWuFiOZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5MPXUK8OpTY8</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Thumbnails/1206/5MPXUK8OpTY8.jpg</video:thumbnail_loc>

            <video:title>The squeeze theorem (1)</video:title>

            <video:description><![CDATA[
Oscillating functions near zero resist standard limit methods. How do you bound the erratic term between two fixed functions to isolate the true value? Watch the squeeze theorem deliver the answer. Solved: Evaluate \lim_{x \to 0} x^2 \sin\left(\frac{1}{x}\right) using the Squeeze Theorem. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/qj26ocsTf1/Previews/1206/5MPXUK8OpTY8.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/5cHWggI3vj6K</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/5cHWggI3vj6K.jpg</video:thumbnail_loc>

            <video:title>Potential from field</video:title>

            <video:description><![CDATA[
Electric potential is the negative line integral of the field. Does moving perpendicular to field lines change the voltage? We prove path independence and show why sideways motion yields zero potential difference.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/5cHWggI3vj6K.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ah52qW1bFgVv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1114/ah52qW1bFgVv.jpg</video:thumbnail_loc>

            <video:title>Nested radicals</video:title>

            <video:description><![CDATA[
Nested roots trap variables. How do you peel back three layers of radicals using the chain rule? Watch the step-by-step unraveling. Solved: Differentiate the multi-layered root function y = \sqrt{x + \sqrt{x + \sqrt{x}}} with respect to x for the domain x > 0. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1114/ah52qW1bFgVv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/s8pPG85ba1Pk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/s8pPG85ba1Pk.jpg</video:thumbnail_loc>

            <video:title>Field from potential</video:title>

            <video:description><![CDATA[
The electric field is the negative gradient of potential. How do you extract vector components from a scalar voltage function? We derive E equals minus grad V and show why field lines always point down the steepest slope.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/s8pPG85ba1Pk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1f5u6HaZ_g61</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1211/1f5u6HaZ_g61.jpg</video:thumbnail_loc>

            <video:title>Spherical shells</video:title>

            <video:description><![CDATA[
Spherical capacitors store charge between concentric shells. How does one calculate capacitance and required charge for a specific voltage? This walkthrough solves the design parameters for a high-voltage system. Solved: A research laboratory is designing a spherical capacitor for a high-voltage experiment. The device consists of an inner conducting sphere with a radius of a = 15.0 \text{ cm} and a concentric outer conducting shell with an inner radius of b = 18.0 \text{ cm}. The space between the spheres is a vacuum. (a) Calculate the capacitance of this spherical system. (b) Determine the magnitude of the charge Q that must be placed on the spheres to establish a potential difference of 500 \text{ V} between them. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1211/1f5u6HaZ_g61.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7GyXmImEGhPb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/7GyXmImEGhPb.jpg</video:thumbnail_loc>

            <video:title>Parallel charge division</video:title>

            <video:description><![CDATA[
Parallel capacitors share the same voltage. How do you find the charge on just one branch? We use the capacitance value to isolate the specific storage. Solved: Two capacitors, C_1 = 8.00 \text{ }\mu\text{F} and C_2 = 12.0 \text{ }\mu\text{F}, are connected in parallel across a 15.0\text{-V} DC power source. Determine the magnitude of the charge stored on the 12.0 \text{-}\mu\text{F} capacitor. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/7GyXmImEGhPb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/dFviseHuY2zk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/dFviseHuY2zk.jpg</video:thumbnail_loc>

            <video:title>Field from spatial function</video:title>

            <video:description><![CDATA[
A linear potential function defines the voltage profile. How do you extract the electric field vector from this scalar relation? We apply E equals minus dV by dx to find the constant field magnitude and direction. Solved: In a certain region of space, the electric potential is distributed along the x-axis according to the linear function V = a + bx, where a = 15.0 \text{ V} and b = -4.00 \text{ V/m}. Determine the magnitude and the direction of the electric field at the following positions:(i) x = 0,(ii) x = 2.50 \text{ m}, and(iii) x = 5.00 \text{ m}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/dFviseHuY2zk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/80DUqR2Cat</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/80DUqR2Cat.jpg</video:thumbnail_loc>

            <video:title>Potential from spatial function</video:title>

            <video:description><![CDATA[
A linear potential function defines voltage along an axis. How do you extract specific values from this spatial relation? We substitute positions to map the potential drop. Solved: In a certain region of space, the electric potential is distributed along the x-axis according to the linear function V = a + bx, where a = 15.0 \text{ V} and b = -4.00 \text{ V/m}. Calculate the electric potential at the following positions: (i) x = 0, (ii) x = 2.50 \text{ m}, and (iii) x = 5.00 \text{ m}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/80DUqR2Cat.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/el0gIPP8_nQZ</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/el0gIPP8_nQZ.jpg</video:thumbnail_loc>

            <video:title>Field from radial gradient</video:title>

            <video:description><![CDATA[
A charged sphere has distinct potential zones. How does the gradient yield zero field inside but a radial field outside? We differentiate V with respect to r to resolve the field magnitude at any distance. Solved: A solid conducting metal sphere of radius R = 25.0 \text{ cm} carries a total charge Q. The electric potential at any point inside the sphere is constant at V_{in} = k_e Q/R, and the potential at any external point is V_{out} = k_e Q/r, where r is the distance from the centre. Using the gradient relationship between potential and field, calculate the magnitude of the electric field: (i) at a point 10.0 \text{ cm} from the centre, and (ii) at a point 50.0 \text{ cm} from the centre. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/el0gIPP8_nQZ.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/EX8ypcnZswEG</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/EX8ypcnZswEG.jpg</video:thumbnail_loc>

            <video:title>Charge distribution</video:title>

            <video:description><![CDATA[
Mixed networks split voltage and charge unevenly. How do you find the charge on one capacitor in a parallel branch? We trace the total charge to isolate the specific value. Solved: A network consists of three capacitors. Capacitors C_1 = 10.0 \text{ }\mu\text{F} and C_2 = 20.0 \text{ }\mu\text{F} are connected in parallel. This parallel pair is then connected in series with a third capacitor, C_3 = 15.0 \text{ }\mu\text{F}. If a potential difference of 45.0 \text{ V} is applied across the entire network, determine the magnitude of the charge stored on capacitor C_1. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/EX8ypcnZswEG.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eW38trBMLppI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/eW38trBMLppI.jpg</video:thumbnail_loc>

            <video:title>Multi-variable gradients</video:title>

            <video:description><![CDATA[
A complex potential function varies across three dimensions. How do you extract the full electric field vector from this scalar map? We compute partial derivatives to find the resultant field magnitude at a specific point. Solved: In a specific region of space, the electric potential is defined by the three-dimensional function V = 3.00xyz^2, where V is in volts and the coordinates are in metres. Determine the magnitude of the resultant electric field vector at the point (2.00, -2.00, 1.00) \text{ m}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/eW38trBMLppI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DjGvKmU6ku</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/DjGvKmU6ku.jpg</video:thumbnail_loc>

            <video:title>Series voltage division</video:title>

            <video:description><![CDATA[
Series capacitors split voltage by size. Why does the smallest component take the biggest hit? We calculate the exact potential difference across the weak link. Solved: A 100\text{-V} DC power source is connected to a series combination of a 5.00 \text{-}\mu\text{F} and a 20.0 \text{-}\mu\text{F} capacitor. Determine the potential difference across the 5.00 \text{-}\mu\text{F} capacitor. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/DjGvKmU6ku.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ProJv4rOecG2</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/ProJv4rOecG2.jpg</video:thumbnail_loc>

            <video:title>Graphical analysis</video:title>

            <video:description><![CDATA[
A potential graph maps voltage against position. How do you extract field strength from the slope of these lines? We calculate the negative gradient to find the electric field in rising and flat regions. Solved: The graph of electric potential V versus position x for a specific region of space is provided below. The potential rises linearly from 0 \text{ V} at x = 0 to 40.0 \text{ V} at x = 2.00 \text{ cm}, then falls linearly back to 0 \text{ V} at x = 4.00 \text{ cm}, and remains constant at 0 \text{ V} until x = 6.00 \text{ cm}. Calculate the magnitude and direction of the electric field in the following intervals:(i) 0 < x < 2.00 \text{ cm}, and(ii) 4.00 < x < 6.00 \text{ cm}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/ProJv4rOecG2.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ogTOiK3cPT</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1148/ogTOiK3cPT.jpg</video:thumbnail_loc>

            <video:title>Equivalent capacitance</video:title>

            <video:description><![CDATA[
Mixed networks combine series and parallel rules. How do you simplify a parallel block in series with another capacitor? We calculate the total equivalent capacitance step by step. Solved: Two capacitors, C_1 = 10.0 \text{ }\mu\text{F} and C_2 = 20.0 \text{ }\mu\text{F}, are connected in parallel. This parallel combination is then connected in series with a third capacitor, C_3 = 15.0 \text{ }\mu\text{F}. Determine the equivalent capacitance of this network. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1148/ogTOiK3cPT.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0KMQsKYzlRa3</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1209/0KMQsKYzlRa3.jpg</video:thumbnail_loc>

            <video:title>Uniform field design</video:title>

            <video:description><![CDATA[
High voltage risks dielectric breakdown in air. How do you calculate the minimum plate separation to prevent sparking? We use the uniform field relation to find the safe distance for a given potential difference. Solved: A student at a Nigerian University of Technology is designing a parallel-plate apparatus for a high-voltage experiment. The system is connected to a power supply maintaining a potential difference of 24.0 \text{ kV}. To avoid "dielectric breakdown" (creating a spark in the air), the electric field between the plates must not exceed the dielectric strength of dry air, which is 3.00 \times 10^6 \text{ V/m}. Calculate the minimum separation distance required between the plates to ensure the system operates safely without sparking. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1209/0KMQsKYzlRa3.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ti1_PKfS5Upe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/ti1_PKfS5Upe.jpg</video:thumbnail_loc>

            <video:title>Splitting boundaries</video:title>

            <video:description><![CDATA[
The Fundamental Theorem requires a constant lower limit. How do you differentiate when both boundaries are variables? We split the integral and apply the Chain Rule to each part. Solved: Determine the derivative \frac{dy}{dx} if the function is defined as y = \int_{x}^{x^{2}} \cos(t) dt. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/ti1_PKfS5Upe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fHsURzvqGJ0e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/fHsURzvqGJ0e.jpg</video:thumbnail_loc>

            <video:title>Iterative trig</video:title>

            <video:description><![CDATA[
Quadratic-trigonometric products require iterative reduction. How do you manage sign bookkeeping across multiple parts applications? This walkthrough executes the systematic elimination sequence. Solved: Find \int x^2 \sin x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/fHsURzvqGJ0e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1ix30yj82UpW</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/1ix30yj82UpW.jpg</video:thumbnail_loc>

            <video:title>Induced charge</video:title>

            <video:description><![CDATA[
Dielectrics develop bound charge on their surfaces. How do you calculate this induced charge from free charge and the dielectric constant? We derive the magnitude using polarisation principles. Solved: A parallel-plate capacitor has a capacitance of 150\text{ pF} when its gap is completely filled with a dielectric material having a dielectric constant of 4.00. If a potential difference of 60.0\text{ V} is applied across the plates, determine the magnitude of the induced charge that appears on the surfaces of the dielectric. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/1ix30yj82UpW.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/l5qw9MR9H6rv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1079/l5qw9MR9H6rv.jpg</video:thumbnail_loc>

            <video:title>Stereoisomerism</video:title>

            <video:description><![CDATA[
Stereoisomerism defines molecules with identical connections but different 3D arrangements. How do you distinguish geometric from optical types and separate conformational from configurational isomers? This overview maps the complete classification hierarchy clearly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1079/l5qw9MR9H6rv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/fJ82w2Zt0lGO</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/fJ82w2Zt0lGO.jpg</video:thumbnail_loc>

            <video:title>Algebraic simplification</video:title>

            <video:description><![CDATA[
Algebraic forms block direct integration. How do you convert roots, fractions, and products into standard power terms? We rewrite expressions to expose exponents for immediate rule application.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/fJ82w2Zt0lGO.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/_GVN1r5l88TS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/_GVN1r5l88TS.jpg</video:thumbnail_loc>

            <video:title>Functional limit</video:title>

            <video:description><![CDATA[
The First Fundamental Theorem handles simple limits. How do you differentiate when the upper limit is a function? We combine the theorem with the Chain Rule to solve this exact case. Solved: Calculate the derivative \frac{dy}{dx} if the function is defined as y = \int_{2}^{x^{3}} \sin(t^{2}) \, dt. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/_GVN1r5l88TS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/NfuXhoxaauDw</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1079/NfuXhoxaauDw.jpg</video:thumbnail_loc>

            <video:title>E and Z priority rule</video:title>

            <video:description><![CDATA[
When atoms directly attached to the double bond are identical, priority assignment requires a tie-breaker. How do you determine the higher priority group by comparing the next set of attached atoms? This lesson demonstrates the step-by-step comparison method using atomic number lists.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1079/NfuXhoxaauDw.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2ONFz052xHWo</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1126/2ONFz052xHWo.jpg</video:thumbnail_loc>

            <video:title>Verifying an antiderivative</video:title>

            <video:description><![CDATA[
Integration claims to reverse differentiation. How do you prove a proposed solution is actually correct? We differentiate the result to verify it matches the original function. Solved: Show that F(x) = \frac{x^{10}}{10} + C is a valid antiderivative of the function f(x) = x^{9}. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1126/2ONFz052xHWo.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/1GDTAQZ223YV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1261/1GDTAQZ223YV.jpg</video:thumbnail_loc>

            <video:title>Linearity</video:title>

            <video:description><![CDATA[
Complex sums look intimidating. How do you split a polynomial into simple parts for integration? This lesson applies linearity to handle constants and sums with ease.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1261/1GDTAQZ223YV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9flfjXvbRgIA</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/9flfjXvbRgIA.jpg</video:thumbnail_loc>

            <video:title>Introduction</video:title>

            <video:description><![CDATA[
Some molecules are mirror images yet cannot be superimposed. Why do identical formulas behave differently in the human body? This lesson defines chirality and explains non-superimposable mirror images using simple hand analogies.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/9flfjXvbRgIA.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/j_oe365bt4PX</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/j_oe365bt4PX.jpg</video:thumbnail_loc>

            <video:title>Composite parity</video:title>

            <video:description><![CDATA[
Spot a product of functions over a symmetric interval. Is the result zero or double? This walkthrough shows you how to determine parity by inspection. Solved: Evaluate the definite integral \int_{-1}^{1} x^{5} \cos (\pi x) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/j_oe365bt4PX.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Nz_uLshTM0aI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/locFFLBZbW/Thumbnails/1149/Nz_uLshTM0aI.jpg</video:thumbnail_loc>

            <video:title>Partially-filled gap</video:title>

            <video:description><![CDATA[
A partial dielectric splits the gap into series layers. How do you combine air and material sections to find total capacitance? We model the stack as two capacitors in series. Solved: A parallel-plate capacitor has a capacitance of C_0 = 120\text{ pF} when the space between its plates is filled with air. A dielectric slab with a dielectric constant of \kappa = 4.00 and a thickness equal to one-quarter of the total plate separation is inserted into the gap. By modelling this arrangement as two capacitors connected in series, determine the new total capacitance of the system. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/locFFLBZbW/Previews/1149/Nz_uLshTM0aI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/z6P2FhsRjD39</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Thumbnails/1080/z6P2FhsRjD39.jpg</video:thumbnail_loc>

            <video:title>R or S assignment (1)</video:title>

            <video:description><![CDATA[
R and S assignment becomes tricky with complex molecular structures. How do you handle priority ties and hidden chiral centres correctly? This lesson applies configuration rules to diverse enantiomer examples for mastery. Solved: \begin{array}{ccccccc} & \mathrm{OH} & & \vdots & & \mathrm{OH} & \\ & | & & \vdots & & | & \\ \mathrm{CH_3CH_2} - & \mathrm{C} & \cdots \mathrm{H} & \vdots & \mathrm{H} \cdots & \mathrm{C} & - \mathrm{CH_2CH_3} \\ & \boldsymbol{\blacktriangle} & & \vdots & & \boldsymbol{\blacktriangle} & \\ & \mathrm{CH_3} & & \vdots & & \mathrm{CH_3} & \end{array} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/duUf9iRNcT/Previews/1080/z6P2FhsRjD39.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/L0hj6wTTOTFa</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/L0hj6wTTOTFa.jpg</video:thumbnail_loc>

            <video:title>Average value</video:title>

            <video:description><![CDATA[
Spot an average value problem over a symmetric interval. Why integrate the whole function when odd parts vanish? This walkthrough shows you how to solve by parity inspection. Solved: Evaluate the average value of the function f(x) = 10 - \sin^5 x over the symmetric interval [-\pi, \pi]. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/L0hj6wTTOTFa.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Y7PebDuKNmYd</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1128/Y7PebDuKNmYd.jpg</video:thumbnail_loc>

            <video:title>Hyperbolic functions</video:title>

            <video:description><![CDATA[
Hyperbolic functions act as both integrands and integration results. How do you handle sinh and cosh versus the algebraic radicals that yield inverse hyperbolic forms? We map these patterns to their exact standard integrals.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1128/Y7PebDuKNmYd.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Cs1mrEQhvf1M</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1262/Cs1mrEQhvf1M.jpg</video:thumbnail_loc>

            <video:title>Fourier orthogonality</video:title>

            <video:description><![CDATA[
Spot a product of different trig harmonics over a full period. Why integrate when orthogonality forces the area to zero? This walkthrough shows you how to solve by inspection. Solved: Evaluate the definite integral \int_{-\pi}^{\pi} \sin (2x) \cos (3x) \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1262/Cs1mrEQhvf1M.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TGrRceiJTreq</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/TGrRceiJTreq.jpg</video:thumbnail_loc>

            <video:title>Drift speed</video:title>

            <video:description><![CDATA[
Current links directly to drift speed of charge carriers. How does this microscopic motion define current density? This lesson derives the exact relation.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/TGrRceiJTreq.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/6GSa4MgSZAM5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/6GSa4MgSZAM5.jpg</video:thumbnail_loc>

            <video:title>Current density</video:title>

            <video:description><![CDATA[
Total current hides flow intensity within a conductor. How does cross-section define current density? This lesson establishes the precise link.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/6GSa4MgSZAM5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/63CfE47sSvmI</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/63CfE47sSvmI.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Welcome to the Direct Current Circuits course. What must you master at each stage to progress from the definition of electric current to full multiloop circuit analysis? This overview maps every chapter so you always know where you are headed.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/63CfE47sSvmI.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/JfFJrf1ZQwvE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/JfFJrf1ZQwvE.jpg</video:thumbnail_loc>

            <video:title>Electron drift speed</video:title>

            <video:description><![CDATA[
A small but measurable current flows through a copper wire of known diameter and charge-carrier density. How do you determine both the current density and the electron drift speed from these quantities? This lesson applies the fundamental relationships step by step. Solved: A small but measurable current of 3.6 \times 10^{-10} \text{ } \mathrm{A} exists in a copper wire whose diameter is 1.5 \text{ } \mathrm{mm}. The number of charge carriers per unit volume is 8.49 \times 10^{28} \text{ } \mathrm{m^{-3}}. Assuming the current is uniform, calculate (a) the current density and (b) the electron drift speed. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/JfFJrf1ZQwvE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/DgMGEzuSFB7n</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/DgMGEzuSFB7n.jpg</video:thumbnail_loc>

            <video:title>Electric current</video:title>

            <video:description><![CDATA[
Electric current quantifies how much charge passes through a cross section of a conductor per unit time. How do you connect the microscopic motion of individual charge carriers to the macroscopic current you measure with an ammeter? This lesson establishes the precise definition and SI unit you will use throughout the course.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/DgMGEzuSFB7n.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/F8kRhfC_lp3z</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Thumbnails/1083/F8kRhfC_lp3z.jpg</video:thumbnail_loc>

            <video:title>Curved arrow notation (1)</video:title>

            <video:description><![CDATA[
Curly arrows map electron flow in organic reactions. Can you draw them correctly without breaking mechanism logic? This walkthrough fixes common notation errors using standard rules.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/5Kp8aCl41B/Previews/1083/F8kRhfC_lp3z.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/WAj_1mnRKH</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/WAj_1mnRKH.jpg</video:thumbnail_loc>

            <video:title>Reverse product rule</video:title>

            <video:description><![CDATA[
Integration reverses differentiation rules. How does the product rule transform into a formula for integrating products? This lesson derives the integration by parts identity.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/WAj_1mnRKH.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R1NwYfRE13</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/R1NwYfRE13.jpg</video:thumbnail_loc>

            <video:title>Some special cases</video:title>

            <video:description><![CDATA[
Standard integration by parts fails on complex integrands. How do you handle lone functions, looping pairs, or iterative powers? This lesson details tactical adjustments for these special cases.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/R1NwYfRE13.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/MweIaNpZ_CQS</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1595/MweIaNpZ_CQS.jpg</video:thumbnail_loc>

            <video:title>Measuring instruments</video:title>

            <video:description><![CDATA[
Instruments define reality through range, least count and sensitivity. What hides behind a positive zero error or a non-linear scale? We expose these properties so you judge any tool by its true limits.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1595/MweIaNpZ_CQS.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/vjguvPhBTL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/vjguvPhBTL.jpg</video:thumbnail_loc>

            <video:title>Algebraic-trig match</video:title>

            <video:description><![CDATA[
Algebraic-trigonometric products require precise term assignment. How do you apply LIATE to eliminate the algebraic factor correctly? This walkthrough demonstrates the complete solution path. Solved: Obtain \int x \cos x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/vjguvPhBTL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SKu0HrVPbgLE</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/SKu0HrVPbgLE.jpg</video:thumbnail_loc>

            <video:title>Composite wire current density</video:title>

            <video:description><![CDATA[
When a single current passes through two wires of different diameters welded together, the current density is not the same in both. How do you find the current density in each section from the wire diameters and the total current? This lesson walks you through the calculation. Solved: One end of an aluminium wire with diameter 3.0 \text{ } \mathrm{mm} is welded to one end of a copper wire with diameter 2.0 \text{ } \mathrm{mm}. The composite carries a steady current i of 2.5 \text{ } \mathrm{A}. For points that are not next to the junction, what is the current density in (a) the aluminium wire and (b) the copper wire? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/SKu0HrVPbgLE.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/cvoUBu06CLDD</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/cvoUBu06CLDD.jpg</video:thumbnail_loc>

            <video:title>Layered algebraic clearing</video:title>

            <video:description><![CDATA[
Higher-degree algebraic terms demand repeated application of parts. How do you use iterative reduction to clear the polynomial factor? This walkthrough executes the multi-step elimination process. Solved: Find \int x^2 e^x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/cvoUBu06CLDD.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/k_rHsttGBF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/k_rHsttGBF.jpg</video:thumbnail_loc>

            <video:title>Algebraic-exponential match</video:title>

            <video:description><![CDATA[
Algebraic-exponential products demand strict LIATE application. How do you assign terms to eliminate the linear factor? This walkthrough executes the correct integration sequence. Solved: Determine \int x e^x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/k_rHsttGBF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BcrR_OiV7WVk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/BcrR_OiV7WVk.jpg</video:thumbnail_loc>

            <video:title>Power-log variant</video:title>

            <video:description><![CDATA[
Power-log products require strict LIATE priority. How do you correctly assign the logarithmic factor for differentiation? This lesson resolves the selection process for this variant. Solved: Find \int x^{2} \ln x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/BcrR_OiV7WVk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/a6KVP_m9AT4A</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/a6KVP_m9AT4A.jpg</video:thumbnail_loc>

            <video:title>Lone inverse trig</video:title>

            <video:description><![CDATA[
Lone inverse trig functions resist direct integration. How does the product with one strategy yield the antiderivative? This walkthrough executes the required parts sequence. Solved: Determine \int \tan^{-1} x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/a6KVP_m9AT4A.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/7PkjARdnFfaL</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/7PkjARdnFfaL.jpg</video:thumbnail_loc>

            <video:title>Transcendental-radical pair</video:title>

            <video:description><![CDATA[
Transcendental-radical quotients require careful term assignment. How do you apply LIATE when a logarithm pairs with a root? This walkthrough resolves the priority for correct differentiation. Solved: Determine \int \frac{\ln x}{\sqrt{x}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/7PkjARdnFfaL.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/TTg_zjlgDSiF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/TTg_zjlgDSiF.jpg</video:thumbnail_loc>

            <video:title>Exponential-trigonometric loop</video:title>

            <video:description><![CDATA[
Exponential-trigonometric pairs regenerate under integration. How do you solve for the integral as an algebraic unknown? This walkthrough executes the looping strategy to isolate the result. Solved: Find \int e^x \cos x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/TTg_zjlgDSiF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/R1OxsMunDQTb</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/R1OxsMunDQTb.jpg</video:thumbnail_loc>

            <video:title>Substitution to parts</video:title>

            <video:description><![CDATA[
Composite transcendental arguments block direct integration. How does preliminary substitution expose a solvable product for parts? This walkthrough executes the combined technique sequence. Solved: Find \int e^{\sqrt{x}} \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/R1OxsMunDQTb.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ZgvNFLJFzz02</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/ZgvNFLJFzz02.jpg</video:thumbnail_loc>

            <video:title>Nonuniform current density</video:title>

            <video:description><![CDATA[
When current density varies with radial distance inside a wire, you cannot simply multiply by the total area. How do you integrate a radially dependent current density function to find the current through a specific annular region of the cross section? This lesson demonstrates the technique. Solved: The magnitude J of the current density in a certain laboratory wire with a circular cross section of radius R = 3.00 \text{ } \mathrm{mm} is given by J = J_0 \frac{r}{R}, with J in amperes per square metre and radial distance r in metres, where J_0 = 4.00 \times 10^4 \text{ } \mathrm{A/m^2}. What is the current through the outer section bounded by r = 0.800R and r = R? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/ZgvNFLJFzz02.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SuCxdmHhUgjx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/SuCxdmHhUgjx.jpg</video:thumbnail_loc>

            <video:title>Current in a gas discharge tube</video:title>

            <video:description><![CDATA[
In a gas discharge tube, both electrons and positive ions move in opposite directions, each contributing to the total current. How do you calculate the net current when two types of charge carrier move in opposite directions through the same cross section? This lesson clarifies how to combine their contributions correctly. Solved: A current is established in a gas discharge tube when a sufficiently high potential difference is applied across the two electrodes in the tube. The gas ionises; electrons move toward the positive terminal and singly charged positive ions toward the negative terminal. (a) What is the current in a hydrogen discharge tube in which 4.8 \times 10^{18} electrons and 1.6 \times 10^{18} protons move past a cross-sectional area of the tube each second? (b) Is the direction of the current density \vec{J} toward or away from the negative terminal? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/SuCxdmHhUgjx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/9BKUhNBvh5pV</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Thumbnails/1387/9BKUhNBvh5pV.jpg</video:thumbnail_loc>

            <video:title>Radial current density</video:title>

            <video:description><![CDATA[
A cylindrical wire carries current with a current density that depends on the radial distance from its central axis. How much current flows through a thin annular ring at a given radius? This lesson shows you how to apply the current density concept to a differential area element. Solved: The magnitude J(r) of the current density in a certain cylindrical wire is given as a function of radial distance from the centre of the wire's cross section as J(r) = Br, where r is in metres, J is in amperes per square metre, and B = 3.50 \times 10^5 \text{ } \mathrm{A/m^3}. This function applies out to the wire's radius of 2.50 \text{ } \mathrm{mm}. How much current is contained within the width of a thin ring concentric with the wire if the ring has a radial width of 12.0 \text{ } \mathrm{\mu m} and is at a radial distance of 1.80 \text{ } \mathrm{mm}? 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/cjzf7dpDEh/Previews/1387/9BKUhNBvh5pV.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/UHMUcd1KgjZF</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1130/UHMUcd1KgjZF.jpg</video:thumbnail_loc>

            <video:title>Secant or cosecant loop</video:title>

            <video:description><![CDATA[
Secant and cosecant odd-power integrals resist standard methods. How do trigonometric identities force the original species to reappear? This walkthrough solves the integral algebraically via looping. Solved: Determine \int \sec^3 x \, dx. 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1130/UHMUcd1KgjZF.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ODGXWyuyRUke</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Thumbnails/1118/ODGXWyuyRUke.jpg</video:thumbnail_loc>

            <video:title>Use of calculator for MCQs</video:title>

            <video:description><![CDATA[
Calculators solve any non-implicit differentiation MCQ. How do you extract the correct option without deriving manually? This walkthrough demonstrates the numerical substitution method. Solved: 1. Find \frac{dy}{dx} if y = x^{\tan x}A. \frac{dy}{dx} = -x^{\tan x}\left(\frac{\tan x}{x} - \sec^2 x \ln|x|\right)B. \frac{dy}{dx} = -x^{\tan x}\left(\frac{\tan x}{x} + \sec^2 x \ln|x|\right)C. \frac{dy}{dx} = x^{\tan x}\left(\frac{\tan x}{x} - \sec^2 x \ln|x|\right)D. \frac{dy}{dx} = x^{\tan x}\left(\frac{\tan x}{x} + \sec^2 x \ln|x|\right)[UNILAG (MTH 102), 2026] 2. Differentiate y = \log(x^3 - x) + 7^{\frac{2}{3}x}A. \frac{3x^2-1}{x(x^2-1)} - 7^{\frac{2}{3}x}\left(\frac{2}{3}\log 7\right)B. -\frac{3x^2-1}{x(x^2-1)} - 7^{\frac{2}{3}x}\left(\frac{2}{3}\log 7\right)C. -\frac{3x^2-1}{x(x^2-1)} + 7^{-\frac{2}{3}x}\left(\frac{2}{3}\log 7\right)D. \frac{3x^2-1}{x(x^2-1)} + 7^{\frac{2}{3}x}\left(\frac{2}{3}\log 7\right)[UNILAG (MTH 102), 2026] 3. If y = \frac{e^{\sin 2x}}{\cos 2x}, find \frac{dy}{dx}A. \frac{dy}{dx} = 2e^{\sin 2x}\left[1 - \sec 2x \tan 2x\right]B. \frac{dy}{dx} = 2e^{\sin 2x}\left[1 - \sec 2x \cos 2x\right]C. \frac{dy}{dx} = 2e^{\sin 2x}\left[1 + \sec 2x \tan 2x\right]D. \frac{dy}{dx} = 2e^{\sin 2x}\left[1 + \sec 2x \cos 2x\right][UNILAG (MTH 102), 2026] 4. If y = e^{2x}\log(x+6), find \frac{dy}{dx}A. \frac{dy}{dx} = e^{2x}\left[\frac{1}{x+6} + 2\log(x+6)\right]B. \frac{dy}{dx} = e^{2x}\left[\frac{1}{x+6} - 2\log(x+6)\right]C. \frac{dy}{dx} = e^{-2x}\left[\frac{1}{x+6} + 2\log(x+6)\right]D. \frac{dy}{dx} = e^{-2x}\left[-\frac{1}{x+6} - 2\log(x+6)\right][UNILAG (MTH 102), 2026] 5. Obtain \frac{d}{dx}\left\{\ln\left(\frac{x^2}{x^2+1}\right)\right\}A. \frac{2}{x(x^2+1)}B. -\frac{2}{x(x^2+1)}C. -\frac{5}{x(x^2+1)}D. \frac{5}{x(x^2+1)}[UNILAG (MTH 102), 2026] 6. Find \frac{dy}{dx}, if y = \log_e \cos xA. \cot xB. -\cot xC. -\tan xD. \tan x[UNILAG (MTH 102), 2026] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/4z6NFyO8NP/Previews/1118/ODGXWyuyRUke.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/0uZF5_ti1lVB</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Thumbnails/1133/0uZF5_ti1lVB.jpg</video:thumbnail_loc>

            <video:title>Use of calculator for MCQs</video:title>

            <video:description><![CDATA[
Calculators solve integration MCQs without manual working. How do you verify the correct option when the integral is unknown? This walkthrough demonstrates the numerical evaluation method. Solved: 1. Simplify \int e^x \sin x \, dxA. \frac{e^x}{4}(\cos x - \sin^2 x) + CB. \frac{e^x}{3}(\cos^2 x + \sin x) + CC. \frac{e^x}{2}(\sin x - \cos x) + CD. e^x(\cos x - \sin x) + C[UNILAG (MTH 102), 2026] 2. Simplify \int \frac{4x-5}{x^2-x-2} \, dxA. \ln|x-1| + \ln|x+2| + CB. 3\ln|x+1| + \ln|x-2| + CC. \ln|x-1| - 2\ln|x-2| + CD. 4\ln\left|\frac{x-2}{x-1}\right| + C[UNILAG (MTH 102), 2026] 3. Evaluate \int \frac{dx}{x^2+4x+7}A. \frac{1}{\sqrt{2}}\tan^{-1}\left(\frac{x+3}{\sqrt{2}}\right)+CB. \frac{1}{\sqrt{3}}\tan^{-1}\left(\frac{x+2}{\sqrt{3}}\right)+CC. \frac{1}{\sqrt{6}}\tan^{-1}\left(\frac{x+7}{\sqrt{6}}\right)+CD. \frac{1}{\sqrt{5}}\tan^{-1}\left(\frac{x+6}{\sqrt{5}}\right)+C[UNILAG (MTH 102), 2026] 4. Evaluate \int \frac{e^{2x}+e^{-2x}}{e^{2x}-e^{-2x}} \, dxA. \frac{1}{4}\ln|e^{2x}-e^{-2x}|+CB. \frac{1}{2}\ln|e^{2x}+e^{-2x}|+CC. \frac{1}{2}\ln|e^{2x}-e^{-2x}|+CD. \frac{1}{4}\ln|e^{2x}+e^{-2x}|+C[UNILAG (MTH 102), 2026] 5. Evaluate \int \cos^3 x \, dxA. \sin x - \frac{1}{3}\sin^3 x + CB. \cos x + \frac{1}{3}\cos^3 x + CC. \sec x - \frac{1}{3}\sec^3 x + CD. \tan x - \frac{1}{3}\tan^3 x + C[UNILAG (MTH 102), 2026] 6. Evaluate \int \frac{\cos(\ln x)}{x} \, dxA. \sec(\ln x) + CB. \tan(\ln x) + CC. \cot(\ln x) + CD. \sin(\ln x) + C[UNILAG (MTH 102), 2026] 7. Simplify \int \ln x \, dxA. x\ln x + x^2 + CB. x - x^2\ln x + CC. x\ln x - x + CD. x^2 - \ln x^2 + C[UNILAG (MTH 102), 2026] 8. Simplify \int 3x^2 e^{x^3} \, dxA. e^{x^2}+CB. e^{x^3}+CC. e^{x^4}+CD. e^{x^5}+C[UNILAG (MTH 102), 2026] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/VbWezt5iT8/Previews/1133/0uZF5_ti1lVB.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/48lz0x4urIlR</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1478/48lz0x4urIlR.jpg</video:thumbnail_loc>

            <video:title>Definitions</video:title>

            <video:description><![CDATA[
Economics and economy are often confused but mean different things. What is the true meaning of each, and how do they actually relate? This lesson clarifies both concepts and their connection.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1478/48lz0x4urIlR.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jg3MWG2qE7dK</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1478/jg3MWG2qE7dK.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
You are about to begin your study of Economics, a subject that explains how people make decisions every day. What exactly is Economics and why does it matter to you personally? This lesson outlines the entire course and shows you exactly where to start.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1478/jg3MWG2qE7dK.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/etAJQ3Tbydmj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1479/etAJQ3Tbydmj.jpg</video:thumbnail_loc>

            <video:title>Resource allocation</video:title>

            <video:description><![CDATA[
Scarcity forces every economy to decide how best to use what little it has. What role does scarcity play in driving the allocation of resources, and how does it make the study of Economics essential? We resolve this exact relationship. Solved: The main concern of economists is toA. control the growth of populationB. redistribute income between the rich and the poorC. satisfy all human wantsD. allocate scarce resources to satisfy human wants.[JAMB (UTME), 2018, Q17] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1479/etAJQ3Tbydmj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/C_k2DD8ZXv1O</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1479/C_k2DD8ZXv1O.jpg</video:thumbnail_loc>

            <video:title>Insatiable nature</video:title>

            <video:description><![CDATA[
Wants never stop multiplying, no matter how much is already satisfied. Why exactly are human wants described as insatiable, and what does this imply about the resources meant to satisfy them? We work through this exact case. Solved: Human wants are insatiable because wants areA. limited while means are scarceB. unlimited and means are also unlimitedC. limited and means are also limitedD. unlimited while means are scarce.[JAMB (UTME), 2018, Q24] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1479/C_k2DD8ZXv1O.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/J4_l3Y5bS9o_</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1479/J4_l3Y5bS9o_.jpg</video:thumbnail_loc>

            <video:title>Why Economics is necessary</video:title>

            <video:description><![CDATA[
The existence of scarce resources is what makes Economics a necessary field of study. What specific condition renders the discipline indispensable, and how does it connect to the fundamental economic problem? This lesson resolves the trap. Solved: The study of Economics becomes necessary because of theA. large population size of the worldB. scarcity of resourcesC. opportunity cost of goods and servicesD. need to satisfy every desire of man.[JAMB (UTME), 2018, Q19] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1479/J4_l3Y5bS9o_.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/jmN_NHS8SyEv</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1478/jmN_NHS8SyEv.jpg</video:thumbnail_loc>

            <video:title>Economics as a science</video:title>

            <video:description><![CDATA[
Economics follows the scientific method to derive laws from human behaviour. But why is it a social science rather than a natural one? This lesson explains the distinction and validates the classification.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1478/jmN_NHS8SyEv.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/zIvfjr03q7av</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1479/zIvfjr03q7av.jpg</video:thumbnail_loc>

            <video:title>The fundamental problem</video:title>

            <video:description><![CDATA[
The tension between boundless desires and finite means creates the fundamental economic problem. How exactly do unlimited wants and limited resources interact to force every society into making difficult trade-offs? This lesson connects the two concepts and shows why the relationship is unavoidable.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1479/zIvfjr03q7av.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/e5SFd4P9X6xj</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1478/e5SFd4P9X6xj.jpg</video:thumbnail_loc>

            <video:title>Branches</video:title>

            <video:description><![CDATA[
Economics splits into branches by scale and purpose. How do micro, macro, pure, and applied economics differ without overlapping? This lesson maps the two independent axes clearly.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1478/e5SFd4P9X6xj.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/YpKQkDmGppfx</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1479/YpKQkDmGppfx.jpg</video:thumbnail_loc>

            <video:title>Scarcity</video:title>

            <video:description><![CDATA[
Resources are never enough to cover everything people desire. How does Economics define scarcity, and why is it considered the central problem of the discipline? This lesson clarifies the concept and its implications.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1479/YpKQkDmGppfx.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/wgkaCb_qLMty</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Thumbnails/1479/wgkaCb_qLMty.jpg</video:thumbnail_loc>

            <video:title>Human wants</video:title>

            <video:description><![CDATA[
Human wants drive every economic decision you will ever make. What exactly defines a want, and why do economists treat it as the starting point of all economic analysis? This lesson defines wants and unpacks their key characteristics.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/wXekRubc6Q/Previews/1479/wgkaCb_qLMty.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qrAsCGPZo1k5</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/qrAsCGPZo1k5.jpg</video:thumbnail_loc>

            <video:title>Derived quantities</video:title>

            <video:description><![CDATA[
Most quantities you encounter in physics are not fundamental — they are constructed from the base quantities through mathematical relationships. How do we systematically build the unit of any derived quantity from the fundamental units? This lesson shows the method.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/qrAsCGPZo1k5.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/SOaJat2L39q9</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/SOaJat2L39q9.jpg</video:thumbnail_loc>

            <video:title>Derived quantity classification</video:title>

            <video:description><![CDATA[
A mixed list of physical quantities is presented and you must identify which are derived. Temperature looks scientific — does that make it derived? We apply the classification test to each item. Solved: Which of the following are derived quantities?I. Thrust II. Temperature III. Area IV. PressureA. I and IV onlyB. II, III and IV onlyC. I, III and IV onlyD. I, II, III and IV 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/SOaJat2L39q9.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/lmWfhm3QtWrC</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/lmWfhm3QtWrC.jpg</video:thumbnail_loc>

            <video:title>SI prefixes</video:title>

            <video:description><![CDATA[
Physical measurements span an enormous range — from nanometres to megametres. How does the SI system handle extremely large or extremely small values without writing endless zeros? This lesson introduces the standard prefixes.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/lmWfhm3QtWrC.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/S9PZLFiaj4b0</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/S9PZLFiaj4b0.jpg</video:thumbnail_loc>

            <video:title>Fundamental quantities</video:title>

            <video:description><![CDATA[
Every measurement in physics rests on a small set of quantities that cannot be broken down further. Which quantities are truly fundamental, and why can none of them be defined in terms of the others? This lesson establishes the foundation of the entire unit system.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/S9PZLFiaj4b0.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/rGtB_H0NosF1</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/rGtB_H0NosF1.jpg</video:thumbnail_loc>

            <video:title>Derived unit identification</video:title>

            <video:description><![CDATA[
You are given a list of units and asked to pick out the derived ones. Some items look fundamental but are not. How do you avoid the trap of special-named derived units? We work through a typical exam question. Solved: Which of the following are derived units?I. Metre II. Coulomb III. Kilogram IV. Ampere V. JouleA. I and III onlyB. II and V onlyC. II, IV and V onlyD. All of them 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/rGtB_H0NosF1.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/2vzly3fLvfqe</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/2vzly3fLvfqe.jpg</video:thumbnail_loc>

            <video:title>Non-fundamental SI unit</video:title>

            <video:description><![CDATA[
One of these units does not belong to the set of SI base units. The radian is dimensionless and is not a base unit — but can you eliminate all the others confidently? Solved: Which of the following is NOT a fundamental S.I Unit?A. MetreB. AmpereC. KelvinD. SecondE. Radian[JAMB (UTME), Q11] 
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          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/2vzly3fLvfqe.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/XVEhpCwcXTLr</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/XVEhpCwcXTLr.jpg</video:thumbnail_loc>

            <video:title>Fundamental quantity identification</video:title>

            <video:description><![CDATA[
Heat capacity, torque, density and reactance all sound like standard physics quantities — but one item on this list is truly fundamental. Can you separate the base quantity from the derived ones? Solved: Which of the following is a fundamental quantity?A. Heat capacityB. Electric currentC. TorqueD. ReactanceE. Density[JAMB (UTME), Q16] 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/XVEhpCwcXTLr.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/xqHsmeboGJpk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/xqHsmeboGJpk.jpg</video:thumbnail_loc>

            <video:title>Kilowatt-hour equivalence</video:title>

            <video:description><![CDATA[
The kilowatt-hour is a commercial unit of energy, not power. Which physical expression has the same unit? This lesson tests whether you can trace a compound unit back to its fundamental form. Solved: Which of the following quantities has the same unit as the kilowatt-hour?A. Force x accelerationB. Force x velocityC. Force x distanceD. Force x time 
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          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/xqHsmeboGJpk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/pD5cJ9USP8XY</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/pD5cJ9USP8XY.jpg</video:thumbnail_loc>

            <video:title>Fundamental unit identification</video:title>

            <video:description><![CDATA[
Not every unit with a short, simple name is a fundamental unit. Which item in this list is genuinely a base unit of the SI system? This lesson tests your recall against common distractors. Solved: Which of the following is a fundamental unit?A. NewtonB. WattC. JouleD. Second 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/pD5cJ9USP8XY.mp4</video:content_loc>

          <video:duration>61</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/qL5jjTI0pFWk</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/qL5jjTI0pFWk.jpg</video:thumbnail_loc>

            <video:title>Correct unit matching</video:title>

            <video:description><![CDATA[
You are given a list of quantities with proposed units and must decide which pairings are correct. Some units can be expressed in more than one equivalent form. How do you verify each one systematically? Solved: In which of the following quantities are the units correctly indicated?I. Weight \mathrm{[N]} II. Energy \mathrm{[N\,m]} III. Momentum \mathrm{[kgms^{-1}]} IV. Acceleration \mathrm{[Nkg^{-1}]}A. I and II onlyB. III and IV onlyC. I, II and III onlyD. I, II, III and IV 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/qL5jjTI0pFWk.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/Ik9mR3L65rzy</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1595/Ik9mR3L65rzy.jpg</video:thumbnail_loc>

            <video:title>Measurement</video:title>

            <video:description><![CDATA[
Every law in physics rests on the ability to assign a number and a unit to an observable quantity. What makes a measurement meaningful rather than just a guess? This lesson establishes why precision, accuracy, and a standard unit system are non-negotiable in physics.  
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          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1595/Ik9mR3L65rzy.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/BIWqnN1x_8_e</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/BIWqnN1x_8_e.jpg</video:thumbnail_loc>

            <video:title>Unit of power</video:title>

            <video:description><![CDATA[
The watt can be expressed in several equivalent forms. Which expression correctly gives the watt in terms of fundamental units? This lesson tests your ability to expand derived units to their base components. Solved: The watt is equivalent toA. \mathrm{Nms^{-1}}B. \mathrm{Js}C. \mathrm{kgm^2s^{-2}}D. \mathrm{Ns} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/BIWqnN1x_8_e.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/eqS6Y2TokwnM</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1596/eqS6Y2TokwnM.jpg</video:thumbnail_loc>

            <video:title>Unit of momentum</video:title>

            <video:description><![CDATA[
Momentum has no special named unit of its own. How do you express its unit in terms of fundamental units, and which common alternative form is equivalent? This lesson resolves the typical trap. Solved: The unit of momentum isA. \mathrm{Js^{-1}}B. \mathrm{Ns}C. \mathrm{Ns^{-1}}D. \mathrm{Nms} 
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1596/eqS6Y2TokwnM.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
        <url>
          <loc>https://unidrills.com/video/ukYpTWW2eX2c</loc>

          <video:video>
            <video:thumbnail_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Thumbnails/1595/ukYpTWW2eX2c.jpg</video:thumbnail_loc>

            <video:title>Welcome</video:title>

            <video:description><![CDATA[
Physics is built on the foundation of precise measurement and clear classification of quantities. How does this course take you from basic units to the mathematics of vectors? This lesson maps out the entire journey and explains why each stage matters.  
]]>></video:description>

          <video:content_loc>https://media.unidrills.com/Courses/yyZ8kRDCBT/Previews/1595/ukYpTWW2eX2c.mp4</video:content_loc>

          <video:duration>90</video:duration>

          </video:video>

          
        </url>
    

   </urlset>
 