Analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it.

Linear Impulse and Momentum

Analysis of motion of a particle by relating the kinetic energy of the body with work done by the external forces acting on it.

Work and Energy

A study of collision of particles and their motion before and after collision.

Impact

Analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system.

Conservation of Energy

Welcome to the course and course outline. Review of kinematics and kinetics of particles concepts.

Introduction

Definition of work. Determining the work done by a force under various conditions.

Work

Determining instantaneous power, average power, and efficiency of a force by the principle of work and energy.

Power and Efficiency

Introduction to angular momentum, relation between angular momentum and moment of a force, principle of angular impulse and momentum, conservation of angular momentum.

Angular Impulse and Momentum

Analysis of motion of a particle with respect to the forces causing the motion by work-energy and impulse-momentum principles.

Tutorials for undergraduates in engineering and physical sciences.

Max Engineering Tutorials

Kinetics of Particles by Energy and Momentum Methods - Engineering Mechanics (Dynamics)

Kinematics of curvilinear motion of a point on a rigid body undergoing rotation about a fixed axis, and its applications in gears, pulleys, etc.

Rotation About a Fixed Axis (2)

Meaning of rigid bodies; different kinds of motion undergone by rigid bodies.

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.

 Relative Velocity Analysis

Kinematics of angular motion of a rigid body (or a line on a rigid body) undergoing rotation about a fixed axis.

Rotation About a Fixed Axis (1)

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.

Relative Acceleration Analysis

Analysis of motion of a rigid body undergoing general plane motion by locating an instantaneous centre of zero velocity.

Instantaneous Centre of Rotation

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.

Absolute Motion Analysis

Kinematics of motion of a rigid body undergoing general plane motion using parameters measured relative to a reference frame in rotation.

Motion Relative to a Rotating Frame

In this course, you will learn the fundamentals of two-dimensional kinematics of rigid bodies, which is the branch of mechanics that deals with the geometry of the motion of rigid bodies without considering the forces that cause it. You will learn how to use different coordinate systems and reference frames to express the position, velocity, and acceleration of various points on a rigid body in plane motion.

Empower yourself with the knowledge and skills needed to excel in diverse fields such as mechanical engineering, robotics, aerospace engineering, and beyond. Imagine designing a robotic arm that moves with precision, or optimizing the performance of a rotating machinery. These are some of the countless applications of rigid-body kinematics you will learn in this course.

By the end of this course, you will be able to:
- Understand the rotation of rigid bodies about fixed axes and its applications
- Analyze absolute motion to understand how rigid bodies move through space
- Explore relative velocity analysis to solve complex motion problems
- Master the concept of instantaneous centres of rotation for precise motion analysis
- Understand relative acceleration analysis to predict the behavior of moving bodies
- Analyze motion relative to a rotating frame to unravel the dynamics of rotating systems

Whether you're a seasoned professional looking to expand your knowledge or a curious beginner eager to explore the motion of rigid bodies, this course is for you.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

2D Kinematics of Rigid Bodies - Engineering Mechanics (Dynamics)

Meaning of mechanics, dynamics, kinematics, kinetics and other terms; general problem solution method; units of measurement.

Analysis of rectilinear motion with variable acceleration.

General Rectilinear Motion

Analysis of the curvilinear motion of particles using components normal and tangential to the trajectory of motion.

 Curvilinear Motion (2)

Analysis of relative independent motion of particles, and absolute and relative dependent motion of connected (or constrained) particles.

Special Rectilinear Motion (2)

Analysis of the curvilinear motion of particles using radial and transverse components.

Curvilinear Motion (3)

Analysis of the curvilinear motion of particles using rectangular (Cartesian) coordinates.

Curvilinear Motion (1)

Analysis of rectilinear motion with constant acceleration - uniform motion and uniformly-accelerated motion.

Special Rectilinear Motion (1)

Analysis of erratic rectilinear motion problems using graphs relating the motion parameters.

Graphical Analysis

Do you want to learn how to describe and analyze the motion of particles in one and two dimensions?
Do you want to apply your knowledge of kinematics to solve real-world problems in engineering, physics, and sports?
Do you want to master the use of different coordinate systems and reference frames to simplify your calculations and enhance your understanding?
If you answered yes to any of these questions, then this course is for you!

Engineering Mechanics: Kinematics of Particles comprehensively addresses the fundamental concepts and principles of particle kinematics. You will learn how to:
- Define and measure the position, velocity, and acceleration of a particle moving along a straight or curved path.
- Use various methods to determine the motion of a particle, such as equations of motion, graphical solutions, and numerical solutions.
- Apply the concepts of relative and dependent motion to analyze the motion of several particles or connected bodies.
- Choose the most suitable coordinate system for a given problem, such as rectangular, polar, normal-tangential, or radial-transverse coordinates.
- Understand the effects of different reference frames on the observed motion of a particle, such as inertial, non-inertial, or rotating frames.

By the end of this course, you will have a solid foundation in particle kinematics that will enable you to tackle more advanced topics in dynamics, mechanics, and other fields of engineering and science. You will also have the skills and confidence to apply your knowledge to real-world situations, such as the trajectory of a snowboarder, the orbital speed of a satellite, or the accelerations during acrobatic flying.

This course is designed for students, engineers, and enthusiasts who have a basic background in calculus, physics, and vector algebra. 

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Kinematics of Particles - Engineering Mechanics (Dynamics)

Force-acceleration analysis of rectilinear motion of a particle.

Rectilinear Motion (1)

Meaning of mechanics, dynamics and kinetics, overview of Newton's second law and impulse-and-momentum methods; units of measurement of mass and force.

Force-acceleration analysis of curvilinear motion of particles using radial and transverse components.

Force-acceleration analysis of curvilinear motion of particles using normal and tangential components.

Curvilinear Motion (2)

Force-acceleration analysis of curvilinear motion of particles in rectangular coordinates.

Force-acceleration analysis of absolute and relative motion of particles connected by rigid links or light, inextensible strings passed over pulleys.

Rectilinear Motion (3)

Force-acceleration analysis of absolute and relative rectilinear motion of two or more particles in direct contact.

Rectilinear Motion (2)

This course will equip you with the skills and knowledge to tackle various engineering and scientific problems involving kinetics of particles, which is the branch of mechanics that deals with the relation between the forces acting on a particle and its resulting motion. From the basics of mechanics, dynamics, and kinetics to getting comfortable with Newton's second law and momentum methods, you will clearly understand how forces cause motion.

Boost your problem-solving skills and open up new career opportunities in fields like aerospace engineering, mechanical engineering, civil engineering, biomedical engineering, physics, chemistry, and more. Imagine being able to predict how a ball flies through the air, or understanding why a car behaves the way it does in a crash. This course helps you do these and many more!

By the end of this course, you will be able to:
- Explain the fundamentals of mechanics, dynamics, and kinetics
- Use Newton's second law to analyze how forces make bodies speed up or slow down
- Learn about energy, how forces do work, and how these relate to motion of bodies
- Figure out how collisions work and what motion happens before and after collisions

This course is designed for students, engineers, scientists, and anyone who is interested in learning the basics of kinetics of particles. The course assumes that you have a basic background in calculus, physics, vector algebra, and statics.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Kinetics of Particles by Newton's Second Law - Engineering Mechanics (Dynamics)

Meaning, operations and properties of eigenvalues and eigenvectors of matrices.

Eigenvalues and Eigenvectors

Diagonalization of matrices; evaluating polynomials and transcendentals of matrices.

Diagonalization of Matrices

Quadratic and canonical forms; transformations using symmetric matrices and orthogonal diagonalizing matrices.

Quadratic and Canonical Forms

Welcome and course outline. Review of elementary matrix concepts.

Diagonalization of symmetric matrices - orthogonal diagonalizing matrix, the Gram-Schmidt orthogonalization procedure, and related concepts.

Symmetric Matrices

This course provides a clear and structured exploration of eigenvalues, eigenvectors, and diagonalization, focusing on both theory and real-world applications. 

You’ll learn how to compute eigenvalues and eigenvectors, understand their geometric significance, and apply diagonalization to simplify complex matrix operations. 

Topics include linear transformations, dynamical systems, and applications in physics, engineering, and machine learning. 

The course is designed for students, engineers, and data scientists seeking a strong foundation in matrix methods. By the end, you'll confidently apply these concepts in problem-solving and computational modeling.

Eigenvalues, Eigenvectors and Diagonalization of Matrices

Meaning, operations and properties of matrix inverses.

Matrix Inverses

Meaning of matrices, types of matrices, and other descriptive terminologies. 

Addition of matrices, multiplication of matrices by scalars, multiplication of matrices by matrices, etc.

Algebra of Matrices

Transposition of matrices and properties of matrix transposes.

Transposition of Matrices

Meaning, operations and properties of determinants.

Determinants

Elementary row and column operations on matrices; row echelon and reduced row echelon  forms; rank and nullity of matrices.

Elementary Transformations

Manipulating matrices with Microsoft Excel (Google Sheets) software.

Computer-Aided Handling

Application of matrices, determinants and inverses in solving systems of linear equations, consistency of systems of linear equations and applicable theorems.

Systems of Linear Equations

Do you want to learn how to work with matrices and their properties, operations, and applications? Do you want to understand the concepts of determinants, eigenvalues, eigenvectors, diagonalization, quadratic and canonical forms? Do you want to master the skills of solving systems of linear equations, finding inverses, and computing matrix functions using different methods and tools?
If you answered yes to any of these questions, then this course is for you!

This course covers the fundamentals of matrix theory and its applications in mathematics and science. You will learn how to:
- Define and classify matrices and their special types, such as symmetric, orthogonal, diagonal, and identity matrices
- Perform matrix addition, subtraction, multiplication, and scalar multiplication using the algebraic properties of matrices
- Find the transpose, conjugate, and adjoint of a matrix and use them to simplify matrix operations and expressions
- Perform elementary row and column transformations on matrices and use them to find the row echelon form, reduced row echelon form, rank, and nullity of a matrix
- Find the minors, cofactors, and determinants of matrices and use them to calculate the area, volume, and orientation of geometrical figures
- Find the inverse of a matrix using the adjoint method or the row operations method and use it to solve systems of linear equations
- Find the eigenvalues and eigenvectors of a matrix using the characteristic polynomial and the Cayley-Hamilton theorem and use them to analyze the behavior and stability of dynamical systems
- Diagonalize a matrix using the eigenvalues and eigenvectors and use it to compute matrix functions, such as polynomials, exponentials, sines, and cosines of matrices
- Find the quadratic and canonical forms of an equation using the coefficient matrix and the transformation matrix and use them to classify and graph conics and quadrics
- Use computer software, such as MS-Excel, MATLAB, and Python, to perform matrix operations and computations efficiently and accurately

This course is suitable for anyone who wants to learn or review the basics of matrix theory and its applications. It is especially useful for students and professionals in algebra, calculus, differential equations, linear programming, optimization, cryptography, computer graphics, data science, machine learning, and other related fields.

By the end of this course, you will have a firm grasp of the theory and applications of matrices and determinants. You will also be able to apply the knowledge and skills you gain to solve real-world problems and challenges that involve matrices.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Matrices, Determinants, and Systems of Linear Equations

Definition of a space, linear vector space, with examples.

Definition and examples of linear vector subspaces.

Vector Subspaces

Basis and dimension of linear vector spaces.

Basis and Dimension

Linear combinations of two or more vectors and linear spans of vector spaces.

Linear Combinations and Spans

Linear dependence and independence of vectors in a vector space.

Linear Dependence and Independence

Meaning, bases and dimensions of vector spaces derived from matrices - row, column and null spaces.

Matrix Spaces

Sums and intersections of subspaces of a vector space - their basis, dimension and other properties.

Sums and Intersections

Meaning of coordinates of a vector in a vector space with respect to a given basis, and how to find the coordinates.

Coordinates

Do you want to learn how to work with abstract spaces and transformations that preserve their structure? Do you want to understand the concepts of vector subspaces, linear combinations, linear dependence, basis, dimension, coordinates, and properties of vector spaces? Do you want to master the skills of defining and manipulating linear maps, their kernels, images, matrix representations, and transition matrices?
If you answered yes to any of these questions, then this course is for you!

Linear Algebra: Linear Vector Spaces and Linear Maps is a comprehensive and engaging course that covers the fundamentals of vector spaces and linear maps and their applications in mathematics and science. You will learn how to:
- Define and classify vector spaces and their subspaces over a given scalar field
- Perform operations on vectors using linear combinations and scalar multiplication
- Determine whether a set of vectors is linearly dependent or independent and find a basis and dimension for a vector space or subspace
- Find the coordinates of a vector with respect to a given basis and change the basis using transition matrices
- Define and classify linear maps between vector spaces and find their domains, codomains, ranges, and null spaces
- Find the kernel and image of a linear map and use them to determine whether a linear map is one-to-one or onto
- Represent a linear map using a matrix and perform matrix operations such as addition, multiplication, and inversion
- Use different methods and tools to solve systems of linear equations, such as Gaussian elimination, row reduction, and inverse matrices

This course is suitable for anyone who wants to learn or review the basics of vector spaces and linear maps and their applications. It is especially useful for students and professionals in algebra, geometry, analysis, differential equations, optimization, cryptography, computer graphics, data science, and other related fields.

By the end of this course, you will have a solid foundation of the theory and practice of vector spaces and linear maps and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vector spaces and linear maps.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Linear Vector Spaces - Linear Algebra

Meaning of the range of a linear map, with worked examples.

Range

Meaning of the kernel of a linear map, with worked examples.

Kernel

Definition, examples and general properties of linear maps.

Linear Maps

Matrix representation of a linear map, with worked examples.

Matrix Representation

Meaning and properties of the transition matrix between two bases of a vector space.

Transition Matrix

Welcome and course outline. Review of elementary matrix and linear vector space concepts.

Definition of a map (also mapping or transformation) between two sets, notations and some general properties of maps.

Maps

Further operations on linear maps involving their definition and properties.

Operations on Linear Maps

Analysis of the vector space of all linear maps between two given vector spaces. Addition, scalar multiplication, composition and inverse of linear maps.

Algebra of Linear Maps

A comprehensive study of linear transformations (or maps) - definition, kernel, range, matrix representation and related matters.

Linear Maps (Transformations) - Linear Algebra

Real-valued functions - meaning, domain, range and graphs.

Real-Valued Functions

A look at different kinds of real-valued functions - composites, piecewise functions, polynomials, rational functions, algebraic functions, transcendental functions, odd and even functions.

Kinds of Real-Valued Functions

What are real numbers, and how do they differ from natural numbers, integers, rational numbers, irrational numbers? Meaning of infinity; defining finite and infinite intervals.

Meaning, examples and properties of transcendental functions.

Transcendental Functions

This course introduces the basic concept of a function of a single real variable. It explores how such functions are represented algebraically and graphically, emphasizing interpretation and behavior on the real number line.

You’ll learn to identify domain, range, and key features of graphs such as intercepts, symmetry, and asymptotic behavior. The goal is to build a solid understanding of how functions behave visually and analytically.

This course sets the foundation for everything else in calculus. It is designed to be intuitive, but also precise in its treatment of core ideas.

Single-Variable Functions and Their Graphs

Equality and roots of complex numbers in polar form.

Roots

Natural numbers, integers, rational numbers, real numbers, and an introduction to complex numbers and their descriptions.

Exponential (Euler's) representation of complex numbers; powers of complex numbers in exponential form.

Exponential Form

Operations on complex numbers; conjugates of complex numbers and their properties; equality of complex numbers.

Algebra of Complex Numbers

Polar representation of complex numbers; multiplication and division of complex numbers in polar form; powers of complex numbers in polar form (De-Moivre's theorem).

Polar Form

Manipulating sines and cosines with complex numbers.

Trigonometric Functions

Manipulating hyperbolic functions with complex numbers.

Hyperbolic Functions

Manipulating logarithms with complex numbers.

Logarithmic Functions

Geometric representation of complex numbers on the Argand plane; modulus of a complex number; general and principal arguments of a complex number.

Complex Numbers on the Argand Plane

Equations in two-dimensional coordinate geometry using complex numbers.

Graphing on the Complex Plane

Do you want to learn how to work with numbers that go beyond the real line? Do you want to understand the concepts of imaginary unit, conjugate, modulus, argument, and polar and exponential forms of complex numbers? Do you want to master the skills of performing algebraic and geometric operations on complex numbers using different methods and tools?
If you answered yes to any of these questions, then this course is for you!

In this course, you will learn how to:
- Define and classify complex numbers and their real and imaginary parts
- Perform addition, subtraction, multiplication, and division of complex numbers using the standard form a + bi
- Find the conjugate, modulus, and argument of a complex number and use them to compare and simplify complex numbers
- Represent complex numbers on the Argand plane and visualize their geometric properties and transformations
- Convert complex numbers from rectangular to polar and exponential forms and vice versa
- Use De-Moivre's theorem and Euler's formula to find the powers and roots of complex numbers in polar and exponential forms
- Use complex numbers to define and manipulate trigonometric and hyperbolic functions and their inverses
- Use complex numbers to define and manipulate logarithmic functions and their properties
- Use complex numbers to graph and solve equations of circles, lines, and other curves on the complex plane

This course is suitable for anyone who wants to learn or review the basics of complex numbers and their applications. It is especially useful for students and professionals in engineering, physics, computer science, cryptography, and other related fields.

By the end of this course, you will have a solid understanding of complex numbers and their operations. You will also be able to apply the knowledge and skills you gain to real-world problems and challenges that involve complex numbers.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Complex Numbers

Mean centre (geometric centre) of a number of points; weighted mean centres.

Centroids

Definitions of scalars, vectors and tensors; representation of a vector by a directed line segment; kinds of vectors - free, localized, equal, null, unit, like and unlike vectors.

Position Vectors

Ratio division of a line internally and externally; collinearity of points.

Division of a Line

Meaning of vector components; resolution of vectors into components in two and three dimensions; unit vectors, direction cosines and angle between two vectors in the three-dimensional Cartesian coordinate system.

Vector Components

Projection of a vector on another vector; projection of a vector on a plane.

Vector Projections

Vector addition - triangle and parallelogram laws; multiplication of a vector by a scalar; relations on mid-points of sides of a triangle; vector algebra on quadrilaterals and other polygons; parallel vectors; laws of vector algebra.

Vector Algebra

Do you want to learn how to work with quantities that have both magnitude and direction? Do you want to understand the concepts of scalars, vectors, tensors, components, projections, products, and equations of vectors? Do you want to master the skills of performing algebraic, geometric, differential, and integral operations on vectors using different methods and tools?
If you answered yes to any of these questions, then this course is for you!

This course covers the fundamentals of vectors and their applications in mathematics and mechanics. You will learn how to:
- Define and classify scalars, vectors, and tensors and their properties
- Represent vectors by directed line segments, unit vectors, direction cosines, and coordinates
- Perform vector addition, subtraction, and multiplication by a scalar using the triangle and parallelogram laws
- Apply vector algebra to various geometrical problems involving mid-points, parallelism, and collinearity
- Find the position vector of a point and use it to locate the point in space
- Resolve vectors into components in two and three dimensions and use them to simplify vector operations
- Divide a line in a given ratio internally or externally using vectors
- Project a vector on another vector or a plane and use it to find the angle or distance between them
- Find the centroid of a set of points or a polygon using vectors
- Find the scalar and vector products of two vectors and use them to calculate the area, volume, and orthogonality of geometrical figures
- Find the scalar and vector triple products of three vectors and use them to determine the coplanarity and linear dependence of vectors
- Solve vector equations with unknown vectors or scalars using various techniques
- Find the vector equation of a line or a plane and use it to describe the direction, intersection, angle, and distance of lines and planes
- Find the parametric and non-parametric equations of circles, parabolas, ellipses, and hyperbolas using vectors
- Differentiate and integrate vector-valued functions and use the rules of vector differentiation and integration
- Apply vector differentiation and integration to find the derivatives, arc length, and curvature of parametric curves
- Find the tangential, normal, and binormal vectors and the osculating, normal, and rectifying planes of a parametric curve using the Frenet-Serret formulas
- Apply vectors to various problems in mechanics, such as forces, equilibrium, work, energy, momentum, displacement, velocity, acceleration, and motion in different coordinate systems and frames of reference

This course is suitable for anyone who wants to learn or review the basics of vectors and their applications. It is especially useful for students and professionals in engineering, physics, geometry, calculus, and other related fields.

By the end of this course, you will have a firm understanding of vectors and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vectors.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

Vector Algebra and Geometry - Introduction to Vectors

Continuity (at an interior point, at an endpoint, on an interval) of real-valued functions - graphical illustration, formal and informal definitions.

Understanding the max-min theorem and the intermediate-value theorem.

Theorems on Continuous Functions

Examples of continuous functions, worked problems on continuity.

Continuous Functions

Various types of discontinuities - meaning and examples.

Types of Discontinuity

This course defines what it means for a function to be continuous at a point and on an interval. It connects the idea of a limit to the real-world expectation that a continuous function should have no breaks or jumps.

We go over types of discontinuities and how to classify them. You'll learn how to test for continuity using limit laws and understand the significance of continuity in applied contexts.

Continuity is a gateway concept that prepares you for more advanced ideas like differentiability and integrability.

Continuity of Functions — Single-Variable Calculus

Formal and informal definitions and proofs of limits at infinity and infinite limits.

Proving Limits Involving Infinity

Meaning of the limits of a real-valued functions - graphical illustrations and formal  (epsilon-delta) definitions.

Different methods of evaluating limits of real-valued functions - direct substitution, theorems, graphing, factorization, conjugates.

Evaluating Finite Limits (1)

Different methods of evaluating limits of real-valued functions at infinity and infinite limits.

Evaluating Limits at Infinity

How to prove that a given finite limit as x approaches a finite value is correct, using the formal or epsilon-delta definition.

Proving Finite Limits

Other methods of evaluating finite limits - L’Hôpital’s rule, use of known special limits, squeeze theorem, limits of piecewise-defined functions, etc.

Evaluating Finite Limits (2)

Intuitive methods of evaluating finite limits of real-valued functions.

Evaluating Finite Limits (3)

Limits form the conceptual entry point into calculus. This course focuses on the idea of approaching a value — what it means for a function to tend toward a limit, and how to analyze this behavior rigorously.

We examine left-hand and right-hand limits, infinite limits, and limits at infinity. You'll also learn to handle indeterminate forms and use algebraic techniques to simplify complex limit expressions.

By the end of the course, you’ll have a clear grasp of how limits underpin both continuity and derivatives, and why they matter.

Limits of Functions — Single-Variable Calculus

Meaning of differential equations, order, degree, solutions, etc., of differential equations.

Applications of first-order ordinary differential equations.

Applications of First-Order Ordinary Differential Equations

A comprehensive treatise of ordinary differential equations covering solutions of first-order and second-order ordinary differential equations, and applications of first-order ordinary differential equations.

Courses

Customize your learning experience

Kinetics of Particles by Energy and Momentum Methods - Engineering Mechanics (Dynamics)

2D Kinematics of Rigid Bodies - Engineering Mechanics (Dynamics)

Kinematics of Particles - Engineering Mechanics (Dynamics)

Kinetics of Particles by Newton's Second Law - Engineering Mechanics (Dynamics)

Eigenvalues, Eigenvectors and Diagonalization of Matrices

Matrices, Determinants, and Systems of Linear Equations

Linear Vector Spaces - Linear Algebra

Linear Maps (Transformations) - Linear Algebra

Single-Variable Functions and Their Graphs

Complex Numbers

Vector Algebra and Geometry - Introduction to Vectors

Continuity of Functions — Single-Variable Calculus

Limits of Functions — Single-Variable Calculus

Ordinary Differential Equations - Advanced Calculus

Differentiability and Derivatives of Functions — Single-Variable Calculus

COMPUTER-AIDED DESIGN: Introduction to SolidWorks

Numerical Methods - Advanced Calculus

Set Theory - Introductory Abstract Algebra

Calculus of Scalar and Vector Fields

Relations - Introductory Abstract Algebra

Analysis of Structures - Engineering Mechanics (Statics)

Partial Differentiation and Its Applications - Advanced Calculus

3D Coordinates and Quadric Surfaces - Analytic Geometry

Equilibrium of Rigid Bodies - Engineering Mechanics (Statics)

Statics of Particles - Engineering Mechanics (Statics)

Systems of Forces on Rigid Bodies - Engineering Mechanics (Statics)

Dry Friction - Engineering Mechanics (Statics)