Definition, evaluation and properties of the divergence of a vector field, and an introduction to the Laplacian of scalar and vector fields.

Divergence of a Vector Field

Definition, evaluation and properties of the gradient of a scalar function.

Gradient of a Scalar Field

Definition, evaluation and properties of the curl (spin or rotor) of a vector field.

Curl of a Vector Field

Definitions, examples and some visualizations of scalar and vector fields.

Scalar and Vector Fields

Scalar (dot) and vector (cross) products of vectors using sign functions.

Scalar and Vector Products

Definitions and illustrations of coordinates, coordinate lines and coordinate surfaces for the Cartesian coordinate system, general curvilinear coordinates, and general orthogonal curvilinear coordinates.

Orthogonal Curvilinear Coordinates (1)

Definitions and operations of gradient of a scalar field and divergence and curl of a vector field using sign functions and conventions such as the Einstein summation, Kronecker delta and Levi-Civita notations.

Use of Sign Functions

The gradient operator and contravariant bases vectors in general orthogonal curvilinear coordinates.

Orthogonal Curvilinear Coordinates (3)

Divergence and curl operators in general orthogonal curvilinear coordinates.

Orthogonal Curvilinear Coordinates (4)

The Laplacian operator in general orthogonal curvilinear coordinates.

Orthogonal Curvilinear Coordinates (5)

Some special curvilinear coordinates - cylindrical and spherical coordinate systems.

Orthogonal Curvilinear Coordinates (6)

Meaning of right-handed coordinate systems, vector products of covariant base vectors in right-handed systems, length and volume elements in general orthogonal curvilinear coordinate systems.

Orthogonal Curvilinear Coordinates (2)

Meaning of scalars, vectors and tensors; Einstein's summation convention, Kronecker delta and Levi-Civita notations; orthogonal and orthonormal vector bases.

Introduction

Do you want to learn how to manipulate and analyze scalar and vector fields using advanced calculus techniques? Do you want to understand the concepts and methods of scalar and vector products, gradient, divergence, curl, and Laplacian operators? Do you want to apply the principles of vector analysis to solve problems in physics, engineering, and other disciplines?

If you answered yes to any of these questions, then this course is for you!

In this course, you will learn the fundamentals of calculus of scalar and vector fields, which is the branch of mathematics that deals with functions and operators that map points in space to scalars or vectors. You will learn how to use different notations and conventions to express scalar and vector fields, such as Einstein's summation, Kronecker delta, and Levi-Civita symbols. You will learn how to perform scalar and vector products of vectors, which are useful for measuring angles, areas, and volumes. You will learn how to compute and interpret the gradient of a scalar field, which measures the rate and direction of change of a scalar function. You will learn how to compute and interpret the divergence and curl of a vector field, which measure the sources and vortices of a vector field. You will also learn how to use the Laplacian operator, which combines the divergence and the gradient, and is useful for studying heat conduction, electrostatics, and fluid dynamics.

This course will equip you with the skills and knowledge to solve various problems involving scalar and vector fields. You will be able to apply the concepts and methods of calculus of scalar and vector fields to fields such as physics, engineering, chemistry, biology, and more. You will also be able to appreciate the power of vector analysis theorems, such as Gauss', Green's, and Stokes' theorems, which relate the integrals of scalar and vector fields over different domains.

By the end of this course, you will be able to:

- Define and explain the meaning of scalars, vectors, and tensors

- Identify and use different notations and conventions for scalar and vector fields

- Perform scalar and vector products of vectors and calculate angles, areas, and volumes

- Compute and interpret the gradient of a scalar field and its properties

- Compute and interpret the divergence and curl of a vector field and their properties

- Compute and interpret the Laplacian of a scalar or a vector field and its applications

- Use different coordinate systems and bases to express scalar and vector fields and operators

- Compute and interpret the gradient, divergence, curl, and Laplacian in orthogonal curvilinear coordinates

- Recognize and use some special curvilinear coordinates, such as cylindrical and spherical coordinates

- Apply the vector analysis theorems, such as Gauss', Green's, and Stokes' theorems, to relate the integrals of scalar and vector fields over different domains

Created for students, engineers, scientists, and anyone passionate about learning the calculus of scalar and vector fields, this course assumes a basic background in calculus, linear algebra, and vector algebra. With engaging video lessons, interactive quizzes, practice problems, and supportive peer interactions, you'll embark on a journey of discovery and mastery like never before.

Seize the opportunity to advance your mathematical skills and unlock new problem-solving possibilities with an enrolment right away!

Our mission is to simplify complex concepts by teaching from first principles. We go beyond simple problem-solving to build a deep, foundational understanding of the "why" behind the "how."

Our content is meticulously designed for undergraduates navigating the rigorous curricula of top engineering and physical science programmes in Nigeria and globally.

As a core academic partner on UniDrills, we are committed to upholding the highest standards of clarity, precision, and professional excellence in education.

Max Engineering Tutorials

An academic and graduate engineer dedicated to explaining complex concepts in mathematics, computer science and engineering. I founded UniDrills to bring this vision to life, creating a world-class e-learning marketplace with a global outlook. I apply a first-principles approach to software architecture to build a professional and intuitive learning experience.

calculus-of-scalar-and-vector-fields-undergraduate

Calculus

Vector (cross) product of two vectors and its properties.

Vector Products

Vector triple product of three vectors and its properties.

Vector Triple Products

Scalar triple product of three vectors and its properties.

Scalar Triple Products

Scalar (dot) product of two vectors and its properties.

Scalar Products

This course delves into the essential topic of vector multiplication. We systematically explore the four main types of vector products, beginning with the scalar (dot) and vector (cross) products of two vectors. You will then advance to products involving three vectors: the scalar triple product and the vector triple product, uncovering their unique properties and applications.

Vector products are the key to unlocking the geometric power of vector analysis. They provide the tools to calculate angles, projections, areas, and volumes with elegant algebraic formulas. This course focuses on revealing these deep connections, showing how abstract multiplication rules translate into powerful methods for solving real-world problems in physics and engineering.

This is an intermediate course designed for students who have a solid grasp of foundational vector algebra and components. It is the perfect next step for students in A-Level or university STEM programmes looking to deepen their understanding of vector analysis. A strong foundation in the topics from our introductory course is highly recommended for success.

scalar-vector-and-triple-products-of-vectors-undergraduate

Vectors

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

Analytical solutions of homogeneous linear second-order ordinary differential equations with constant coefficients.

Solutions of Second-Order Ordinary Differential Equations (1)

Analytical solutions of non-homogeneous linear second-order ordinary differential equations by the methods of undetermined coefficients and variation of parameters.

Solutions of Second-Order Ordinary Differential Equations (2)

Analytical solutions of first-order ordinary differential equations, such as variable-separable equations, homogeneous equations, non-homogeneous equations convertible to homogeneous forms, exact differential equations, inexact differential equations, linear differential equations, Bernoulli equation, and Riccati equation.

Solutions 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.

ordinary-differential-equations-mathematical-methods

Mathematical Methods

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

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

Vector Projections

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

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

This course provides a comprehensive, first-principles guide to vector analysis. We begin with the essential definitions, distinguishing between scalars, vectors, and various vector types. You will then master the core rules of vector algebra—including the triangle and parallelogram laws of addition and scalar multiplication—before applying them to prove geometric properties of polygons. The curriculum progresses logically through key concepts such as position vectors, resolving vectors into Cartesian components, the division of lines, vector projections, and the calculation of centroids.

The true power of vectors lies in their ability to connect abstract algebra to tangible geometry. This course is built around that connection, with a heavy emphasis on practical application. Through dozens of meticulously worked examples, you will move beyond theory and develop a deep, intuitive understanding of how to represent and solve complex geometric problems, building the confidence and skill needed for more advanced study.

This programme is designed for students in late secondary school (such as A-Level or IB) and first-year university students in physics, engineering, mathematics, and computer science. It is the perfect starting point for anyone new to the subject and an invaluable refresher for those who need to solidify their foundational knowledge before tackling more advanced topics like linear algebra or vector calculus.

vector-algebra-and-foundational-geometry-vectors

This chapter covers everything you will be learning in High School physics

General Overview of Physics

This course introduces you to physics as if you are learning it for the first time. At the end of the course, you will be able to know what to expect as you continue to learn physics.

Our mission is simple- To help students gain admission into higher institutions and achieve all-round academic success through intensive teaching.  

PI Scholars Academy

I am a graduate of Mathematics with a strong passion for teaching and a commitment to helping learners build confidence and competence in both mathematics and physics. 
My teaching philosophy is rooted in the belief that any learner can grasp complex concepts when guided with clarity and patience: “If I can understand it, I can help you understand it as well—you just have to trust me.” I focus on starting with foundational principles and guiding learners step by step toward deeper understanding. My goal is to make learning both accessible and meaningful, fostering critical thinking and long-term retention.

Physics

What sets are, why they matter, and how to describe them. Covers everyday and mathematical examples, basic notation, set membership, subsets, and types of sets like finite, infinite, empty, universal, etc.

This chapter introduces key mathematical sets and notations that form the language of abstract algebra. You’ll explore sets like Z+, mZ, Z_m, Z*, R[x], and R(x), along with common subsets such as Q+, R*, Q*, and R+. These notations are essential for understanding mappings, relations, and algebraic structures.

Number Systems

This course lays the groundwork for understanding the structures that power modern mathematics.

We start with the basics of set theory—notation, logic, functions, and operations—and use it as a stepping stone into the world of abstract algebra. From there, we introduce groups, rings, and fields in a way that highlights both intuition and structure.

Clear, rigorous, and designed with first-time learners in mind.

set-theory-introductory-abstract-algebra-undergraduate

Introductory Abstract Algebra

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)

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

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

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.

2-d-kinematics-of-rigid-bodies-engineering-mechanics

Engineering Mechanics

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

Curvilinear Motion (2)

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

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.

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-newtons-second-law-engineering

Introduction to and motivation for a dedicated study of the kinetics of systems of particles.

Generalized Newton's second law application to kinetics of systems of particles.

Newton's Second Law

Analysis of motion in a system of particles involving steady mass flow into or out of it.

Steady Streams of Particles

Analysis of motion in a system of particles gaining or losing mass.

Systems Gaining or Losing Mass

Work-Energy principle and conservation of energy, impulse-momentum principle and conservation of momentum, for a system of particles.

Energy and Momentum Methods

Analysis of kinetics of generalized systems of particles by Newton's second law, work-energy principle and impulse-and-momentum methods.

kinetics-of-systems-of-particles-engineering-mechanics

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

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

Work

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

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.

kinetics-of-particles-by-energy-and-momentum-methods

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

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

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

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

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

linear-maps-transformations-linear-algebra

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.

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.

Courses

Customize your learning experience

Calculus of Scalar and Vector Fields (Undergraduate Advanced)

Scalar, Vector and Triple Products of Vectors (Undergraduate Foundation)

Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

Vector Algebra and Foundational Geometry - Vectors (Undergraduate Foundation)

Introduction to Physics (Senior Secondary)

Set Theory - Introductory Abstract Algebra (Undergraduate Advanced)

2D Kinematics of Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Kinematics of Particles - Engineering Mechanics (Undergraduate Advanced)

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

Kinetics of Systems of Particles - Engineering Mechanics (Undergraduate Advanced)

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

Matrices, Determinants, and Systems of Linear Equations - Linear Algebra (Undergraduate Advanced)

Linear Maps (Transformations) - Linear Algebra (Undergraduate Advanced)

Eigenvalues, Eigenvectors and Diagonalization of Matrices - Linear Algebra (Undergraduate Advanced)

Linear Vector Spaces - Linear Algebra (Undergraduate Advanced)

Complex Numbers - Mathematical Methods (Undergraduate Advanced)

Functions and Their Graphs - Single-Variable Calculus (Undergraduate Foundation)

Introduction to Numerical Methods (Undergraduate Foundation)

Relations - Introductory Abstract Algebra (Undergraduate Advanced)

Continuity of Functions - Single-Variable Calculus (Undergraduate Foundation)

Limits of Functions - Single-Variable Calculus (Undergraduate Foundation)

Differentiability and Derivatives of Functions - Single-Variable Calculus (Undergraduate Foundation)

Introduction to SolidWorks - Computer-Aided Design (Professional Practice)

Analysis of Structures - Engineering Mechanics (Undergraduate Advanced)

Partial Differentiation and Its Applications - Multivariable Calculus (Undergraduate Advanced)

3D Coordinates and Quadric Surfaces - Analytic Geometry (Undergraduate Advanced)

Equilibrium of Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Statics of Particles - Engineering Mechanics (Undergraduate Advanced)

Systems of Forces on Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Dry Friction - Engineering Mechanics (Undergraduate Advanced)