NUC CCMAS

This course provides a complete guide to the statics of particles, a foundational topic in engineering mechanics. It covers the principles of force vectors, resultants, and components, first in two dimensions and then extending to three-dimensional space. The core of the course is the analysis of particles in equilibrium, establishing the conditions required for a particle to remain at rest under the influence of multiple concurrent forces.

Statics is the essential science behind structural and mechanical design. The principles covered are the basis for designing every stable structure, from bridges and skyscrapers to aircraft frames and engine components. A command of statics is non-negotiable for any engineer, as it provides the fundamental tools required to analyse forces and ensure the safety and integrity of physical systems.

By the end of this course, you will be able to resolve any force into its components and calculate the resultant of any system of concurrent forces in both 2D and 3D. You will also be able to draw a complete free-body diagram for any particle and apply the equations of equilibrium to solve for unknown forces, tensions, and reactions in a variety of engineering problems.

This course is for undergraduate students in any engineering discipline, including civil, mechanical, and aerospace. It is a core component of any engineering mechanics curriculum and assumes a prerequisite knowledge of introductory physics and vector mathematics. It is the essential foundation for subsequent courses in dynamics and the mechanics of materials.

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Engineering Mechanics

Statics of Particles - Engineering Mechanics (Undergraduate Advanced)

This course is a comprehensive guide to the effects of forces on rigid bodies, a critical topic in engineering mechanics. It moves beyond particles to analyse systems where the point of application of a force is crucial, introducing the concepts of moments and couples. The material covers the calculation of moments in two and three dimensions, the properties of couples, and the methods for reducing complex force systems into simpler, statically equivalent systems.

Understanding moments is fundamental to all structural and mechanical analysis. These principles are used to calculate the bending and twisting stresses in beams, shafts, and machine components, and to ensure the rotational stability of structures and vehicles. A command of this subject is non-negotiable for designing any object intended to withstand real-world loads without failing or rotating unintentionally.

By the end of this course, you will be able to calculate the moment of a force about any point or axis using both scalar and vector methods. You will also be able to determine the moment of a couple, and reduce any complex system of forces and couples acting on a rigid body to its simplest equivalent form, such as a single resultant force and couple moment at a specified point.

This course is for undergraduate students in any engineering discipline who have already completed a course on the statics of particles. It is the direct prerequisite for the study of the equilibrium of rigid bodies, and is a necessary foundation for advanced courses in dynamics, mechanics of materials, and structural analysis.

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

Equilibrium is the foundation of all structural and mechanical analysis. This course provides a rigorous study of the equilibrium of rigid bodies in two and three dimensions. It covers reactions, equilibrium equations, constraints, and statical determinacy, supported by extensive worked examples.

Engineers, architects, and applied scientists constantly rely on equilibrium principles to design safe, efficient, and reliable systems. From bridges and buildings to machines and vehicles, every stable structure depends on correct modelling of supports, forces, and constraints. Mastery of equilibrium ensures accuracy in analysis and prevents costly or dangerous failures.

By completing this course, you will be able to draw free-body diagrams, apply equilibrium equations in 2D and 3D, and classify and analyse different support and constraint conditions. You will understand when a system is properly constrained, over-constrained, or indeterminate, and you will have practical experience solving a wide range of equilibrium problems.

This course is intended for undergraduate students in mechanical, civil, and structural engineering, but it is also useful to anyone studying applied mechanics at an advanced level. It provides both a theoretical foundation and practical problem-solving skills valuable to practising engineers, technical instructors, or anyone needing precise understanding of equilibrium in rigid body mechanics.

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Equilibrium of Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Analysis of trusses, frames and machines.

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Analysis of Structures - Engineering Mechanics (Undergraduate Advanced)

Analysis of equilibrium of rigid bodies subjected to dry (Coulumb) friction, and its applications to screws, wedges, belts and bearings.

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Dry Friction - Engineering Mechanics (Undergraduate Advanced)

Analysis of centroids and moments of inertia.

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Centroids and Centres of Gravity - Engineering Mechanics (Undergraduate Advanced)

Analysis of the second moments of areas and its applications.

moments-of-inertia-engineering-mechanics-undergraduate

Moments of Inertia - Engineering Mechanics (Undergraduate Advanced)

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

Kinematics of Particles - Engineering Mechanics (Undergraduate Advanced)

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

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

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

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

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

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

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

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

Master the non-negotiable principles of Engineering Mechanics. This track delivers a rigorous, complete programme in statics and dynamics, built to the NUC GET 207 core curriculum. It moves methodically from force systems and equilibrium to the kinematics of rigid bodies and the kinetics of particles. This is the foundation of all structural and mechanical analysis.

This programme is for first and second-year undergraduate engineering students. It is an essential requirement for students in Mechanical, Civil, Structural, Aerospace, and Mechatronics engineering. A working knowledge of introductory physics and calculus is assumed.

On completion, you will be able to analyse and solve complex problems in statics and particle dynamics. You will draw free-body diagrams, apply equilibrium equations, analyse trusses and frames, and solve motion problems using Newton's laws, work-energy, and momentum methods. This programme prepares you for advanced courses, particularly Mechanics of Materials, and future professional engineering practice.

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

Olowojaye Rufus

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.

Applied Mechanics

GET 207: Applied Mechanics

This course provides a rigorous foundation in the concept of functions, the building block of calculus. We begin with the real number system - rationals, irrationals, intervals, and infinity - before defining real-valued functions, their domains, and ranges. You will systematically study all key function families: polynomial, rational, algebraic, piecewise-defined, and transcendental, including exponential, logarithmic, trigonometric, and hyperbolic types.

A command of functions is essential for all technical and quantitative disciplines. These principles are directly applied in physics to model motion, in economics for supply-demand curves, in engineering for signal processing, and in computer science to analyse algorithm complexity. This course delivers the core mathematical tools required for effective modelling and problem-solving in these fields and beyond.

By the end of this course, you will be able to: calculate the domain and range of any given function; classify functions and identify their fundamental properties; analyse functions for key characteristics like symmetry (odd and even); and accurately construct graphs for a wide range of standard and piecewise-defined functions directly from their equations.

This course is designed for first-year undergraduates in science, technology, engineering, mathematics (STEM), and economics. It is also critical for any student preparing for advanced calculus or for professionals who require a solid mathematical base for roles in finance, data science, or technical research.

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Single-Variable Calculus

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

This course provides a rigorous introduction to the concept of the limit, the theoretical bedrock upon which all of calculus is built. We will move from an intuitive understanding of what it means for a function to 'approach' a value to the algebraic techniques required for precise evaluation. The course covers the limit laws, methods for handling indeterminate forms, and the behavior of functions at infinity.

Understanding limits is non-negotiable for any serious study of calculus. The principles developed here are not merely abstract; they are the tools used to formally define the core concepts of calculus that are used to model the mechanics of change that govern engineering, physics, economics, and computer science.

By the end of this course, you will be able to: evaluate limits graphically, numerically, and algebraically; apply the Squeeze Theorem and L???H??pital???s Rule; analyse the end-behavior of functions; and identify vertical and horizontal asymptotes.

This course is designed for first-year undergraduates in STEM fields who are beginning their calculus sequence. It is an essential prerequisite for subsequent courses on continuity and differentiability and is also invaluable for any student or professional seeking to rebuild their mathematical foundation from first principles.

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

This course provides a focused and rigorous examination of continuity, a fundamental property of functions that underpins the whole of differential and integral calculus. We move from an intuitive understanding of "unbroken" graphs to the formal, limit-based definition of continuity. The course systematically explores the different types of discontinuities and the powerful theorems that apply only to continuous functions.

A command of continuity is essential for understanding why calculus works. This concept ensures that functions are predictable and well-behaved, a necessary condition for modeling real-world phenomena and for the validity of the major theorems of calculus. It is the bridge between the concept of a limit and the concept of a derivative, explaining why a function must be continuous to be differentiable.

By the end of this course, you will be able to use the three-part definition to test for continuity at a point, identify and classify removable, jump, and infinite discontinuities, and apply the Intermediate Value Theorem and the Extreme Value Theorem to analyse function behavior on a closed interval.

This course is designed for first-year undergraduates in science, technology, engineering, and mathematics who have completed a course on limits. It is a critical prerequisite for the study of differentiability and is essential for any student seeking a deep understanding of calculus theory.


continuity-of-functions-single-variable-calculus

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

This course provides a rigorous, theoretical introduction to differential calculus. We will move beyond computation to understand the fundamental nature of the derivative, beginning with its formal definition as the limit of a difference quotient. The curriculum is designed to build a deep conceptual understanding of what it means for a function to be differentiable and the profound consequences of this property.

The primary focus is on formal proofs and theoretical results. We will systematically derive the rules of differentiation, including the product, quotient, and chain rules, directly from first principles. This course emphasizes the "why" behind the mechanics of calculus, establishing the logical framework upon which all applications are built, including the cornerstone theorems of Rolle, the Mean Value Theorem, and Taylor's Theorem.

By the end of this course, you will be able to: explain the derivative from its limit definition; prove the relationship between differentiability and continuity; formally derive all major differentiation rules; and understand the theoretical significance of the Mean Value Theorem and Taylor's Theorem.

This course is designed for first-year undergraduates in mathematics, physics, and engineering who require a deep theoretical foundation for their studies. It is the ideal precursor to subsequent courses on differentiation techniques and applications, providing the essential logical underpinnings for those more practical subjects.


differentiability-and-derivatives-of-functions

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

This course provides a complete guide to the calculus of several variables. It builds from the foundational concepts of multivariable functions, limits, and continuity to the core techniques of differentiation, including partial derivatives, the chain rule, and implicit differentiation. The material culminates in advanced topics such as Taylor's theorem for several variables and the use of Jacobians.

Multivariable calculus is the language of modern science, engineering, and economics. Its principles are used to model complex surfaces, analyse thermodynamic systems, create 3D computer graphics, and solve critical optimisation problems in business and finance. This is the mathematical toolkit for working with systems that have multiple interacting variables.

By the end of this course, you will be able to calculate partial derivatives, apply the multivariable chain rule, and find directional derivatives using the gradient vector. You will also be able to solve both unconstrained and constrained optimisation problems by finding extreme values and using the method of Lagrange multipliers, and apply these derivatives to find tangent planes to surfaces.

This course is for students who have completed a full single-variable calculus sequence. It is the standard curriculum for a multivariable calculus (Calculus III) module and is a direct prerequisite for the study of vector calculus, differential equations, and advanced courses in physics, engineering, and economics.

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Multivariable Calculus

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

Master advanced matrix algebra and linear systems through rigorous technical training. This course covers matrix definitions; algebraic operations; transpositions; and elementary row transformations. You will investigate determinants; matrix inverses using the adjoint method; and the structural properties of similar matrices. Computational methods using MS-Excel or Google Sheets are included to handle large-scale data sets efficiently.

These mathematical structures are the engines behind modern engineering and data science. Structural engineers use matrices to calculate stress in bridges; computer scientists use them to render 3D graphics; and economists use linear systems to model market equilibrium. Mastering these tools allows you to solve multi-variable problems that are impossible to handle manually.

By the end, you will possess the skills to execute matrix additions; multiplications; and scalar operations with absolute precision. You will demonstrate competence in reducing matrices to row echelon form; calculating rank and nullity; and evaluating determinants of any order. Furthermore, you will command the ability to solve complex systems of linear equations using Cramer's rule or matrix inversion; identify special matrix types like orthogonal or symmetric; and automate these calculations using software.

This curriculum is built for undergraduate students in engineering; mathematics; and physics requiring a high-level command of linear algebra. Professionals in data science or finance will find the content vital for understanding the algorithms governing their software. Even those in general sciences will benefit from the structured logical thinking and numerical methods required to manage complex variables in any technical field.

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Linear Algebra

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

Vectors are the primary tool for describing quantities with both magnitude and direction. This course provides a complete foundation in their algebraic and geometric properties. We move systematically from the basic definition and classification of vectors to the core operations of vector algebra: addition and scalar multiplication. The curriculum then progresses to essential geometric applications, including position vectors, Cartesian components, direction cosines, the division of lines, vector projections, and centroids.

A command of vector algebra is not optional; it is essential for any technical or scientific discipline. This knowledge is the bedrock of classical mechanics, electromagnetism, and fluid dynamics. Engineers use these principles to analyse forces, computer scientists use them to build 3D graphics engines, and data scientists apply them in advanced linear algebra. This course provides the indispensable mathematical toolkit required for these fields.

Upon completion, you will be able to perform all fundamental vector operations with precision. You will resolve vectors into Cartesian components and use direction cosines. You will solve geometric problems involving position vectors, the internal and external division of lines, and collinearity. Furthermore, you will master the calculation of vector projections and the determination of centroids in geometric systems.

This course is designed for first-year undergraduate students in Engineering, Physics, Mathematics, and Computer Science. It serves as a critical foundation for anyone beginning studies that rely on applied mathematics. It is also a rigorous and efficient refresher for professionals or advanced students who need to solidify their understanding of foundational vector principles before tackling more complex material.

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Vectors

Vector Algebra and Geometry - Vectors (Undergraduate Foundation)

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!

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

Calculus

Calculus of Scalar and Vector Fields (Undergraduate Advanced)

Master the mathematical language of engineering. This programme delivers the complete analytical toolkit required for a successful engineering career, covering single-variable calculus, multivariable calculus, linear algebra, and vector analysis. It provides the essential foundation for all subsequent engineering courses.

This programme is for second-year undergraduate students across all engineering disciplines. It delivers the official NUC CCMAS curriculum for Engineering Mathematics, providing the core training required for advanced modules in mechanics, thermodynamics, and circuit theory.

Model and analyse complex physical systems using calculus, linear algebra, and vector analysis. You will be equipped to solve problems in dynamics, statics, and field theory, providing the quantitative proficiency required for advanced engineering study and professional practice.

Engineering Mathematics I

GET 209: Engineering Mathematics I

UI, Ibadan

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.

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Introductory Abstract Algebra

Set Theory - Introductory Abstract Algebra (Undergraduate Advanced)

This course provides a complete toolkit for the study of infinite sequences and series. It begins with a rigorous treatment of the convergence of sequences and the algebra of limits. The course then covers the foundational theory of infinite series and provides a comprehensive study of all standard tests for convergence, culminating in an introduction to power series.

The concepts of convergence and infinite series are essential in physics, engineering, and computer science. They are used to solve differential equations, analyse signals with Fourier series, calculate probabilities, and determine the accuracy of numerical approximations. This is the mathematical machinery behind precision in scientific modelling.

By the end of this course, you will be able to determine if an infinite sequence converges and find its limit. You will also be able to apply the complete suite of convergence tests???including the Integral, Comparison, Ratio, Root, and Alternating Series tests???to determine if an infinite series converges, and find the radius and interval of convergence for any power series.

This course is for students who have completed a foundational calculus course. It is the standard curriculum for a second-semester calculus (Calculus II) module and is a direct prerequisite for the study of differential equations, complex analysis, and advanced physics.

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Advanced Calculus

Convergence of Infinite Sequences and Series - Advanced Calculus (Undergraduate Advanced)

This learning track provides the complete theoretical machinery of single-variable calculus and analysis. We build the subject from first principles, establishing the rigorous logical framework required for advanced quantitative disciplines. This is the 'why' behind the mathematics that powers science and engineering.

This track is built for second-year engineering and physical science students, particularly those at the University Of Ibadan. It is also structured for any student requiring the same rigorous theoretical foundation for advanced quantitative study.

On completion, you will command the complete theoretical basis of single-variable calculus. You will construct formal proofs, rigorously analyse function behaviour, and determine the convergence of infinite series. This programme provides the non-negotiable prerequisite knowledge for advanced study in differential equations, complex analysis, and theoretical physics.

Real Analysis

MAT 223: Real Analysis

OAU, Ife

Analysis of equilibrium of rigid bodies by the method of virtual work.

method-of-virtual-work-engineering-mechanics

Method of Virtual Work - Engineering Mechanics (Undergraduate Advanced)

Master the science of structural stability. This programme provides a complete education in engineering statics, covering the analysis of forces, moments, and equilibrium in rigid bodies. It delivers the non-negotiable principles required to design safe and reliable structures.

This learning track is for first or second-year undergraduate students in Civil, Mechanical, Aerospace, and Structural Engineering. It is the foundational mechanics course upon which all subsequent design and analysis subjects are built.

Analyse the forces within any static structure, from simple trusses to complex machines. You will master free-body diagrams, equilibrium equations, and structural analysis methods. This programme equips you with the core analytical skills for a career in structural, mechanical, or civil design.

Statics

MEE 205: Engineering Mechanics - Statics

Do you want to learn how to apply the laws of physics to analyze the motion of rigid bodies in two dimensions?

Do you want to understand the concepts and methods of mass moment of inertia, general equations of motion, work, energy, impulse, and momentum?

Do you want to design and optimize mechanical systems and devices that involve the rotation and translation of rigid bodies?

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

In this course, you will learn the fundamentals of two-dimensional kinetics of rigid bodies, which is the branch of mechanics that deals with the relation between the forces acting on a rigid body and its resulting motion. The course will equip you with the skills and knowledge to solve various engineering and scientific problems involving the motion of rigid bodies in two dimensions. You will be able to apply the concepts and methods of two-dimensional kinetics of rigid bodies to fields such as mechanical engineering, aerospace engineering, civil engineering, robotics, biomechanics, and more. You will also be able to appreciate the power and elegance of the physical laws that govern the motion of rigid bodies.

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

- Define and explain the meaning of kinetics, rigid body, and plane motion

- Calculate the mass moment of inertia of a rigid body using integration or parallel axis theorem

- Derive and use the general equations of motion for a rigid body in plane motion

- Analyze the motion of a rigid body undergoing translation, rotation about a fixed axis, or general plane motion

- Apply the principle of work and energy to determine the motion of a rigid body or a system of rigid bodies

- Apply the principle of conservation of energy to determine the motion of a rigid body or a system of rigid bodies under conservative forces

- Apply the principle of impulse and momentum to determine the motion of a rigid body or a system of rigid bodies

- Apply the principle of conservation of momentum to determine the motion of a rigid body or a system of rigid bodies

Tailored for students, engineers, scientists, and anyone passionate about learning the basics of 2D kinetics of rigid bodies, this course assumes 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.

2-d-kinetics-of-rigid-bodies-by-newtons-second-law

2D Kinetics of Rigid Bodies by Newton's Second Law - Engineering Mechanics (Undergraduate Advanced)

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

2-d-kinetics-of-rigid-bodies-by-energy-and-momentum-methods

2D Kinetics of Rigid Bodies by Energy and Momentum Methods - Engineering Mechanics (Undergraduate Advanced)

This course teaches the fundamentals of dynamic systems modelling and simulation. You will learn how to:

- Define and classify static and dynamic systems by their mathematical models

- Use differential equations, transfer functions, and state-space models to describe the behavior of dynamic systems

- Analyze the stability, controllability, and observability of dynamic systems

- Model and simulate translational, rotational, electrical, electromechanical, hydraulic, and thermal systems

- Draw analogies between different types of systems and exploit their similarities

- Use popular software tools such as MATLAB/SIMULINK to implement and test your models

By the end of the course, you will have a solid foundation in dynamic systems modelling and simulation, and you will be able to apply it to your own projects and interests. You will also gain a valuable skill that is in high demand in many industries and disciplines, such as:

- Engineering: design, control, and optimization of dynamic systems such as robots, vehicles, machines, power systems, etc.

- Science: understanding and prediction of natural phenomena such as population dynamics, climate change, epidemics, etc.

- Economics: modelling and analysis of economic systems such as markets, supply chains, production, consumption, etc.

- Policy: evaluation and improvement of policy actions and interventions in complex social systems such as health, education, environment, etc.

Whether you are a student, a professional, or a hobbyist, this course will help you master the art and science of dynamic systems modelling and simulation, and open up new possibilities for your learning and career.

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.

introduction-to-dynamic-systems-and-vibration-engineering

Introduction to Dynamic Systems and Vibration - Engineering Mechanics (Undergraduate Advanced)

Master the principles governing the motion of engineering systems. This learning track provides a complete education in dynamics, systematically building from the kinematics of particles to the kinetics of rigid bodies and culminating in an introduction to dynamic systems and vibration. You will learn to analyse and predict how mechanical systems behave under the influence of forces.

This programme is for undergraduate students in mechanical, aerospace, civil, or related engineering disciplines. It is also essential for practising engineers and applied scientists who require a rigorous, first-principles command of dynamic analysis for their professional work. A prerequisite knowledge of statics, calculus, and vector algebra is assumed.

Upon completion, you will possess the analytical tools to solve complex dynamics problems for particles and rigid bodies using force, energy, and momentum methods. This provides the essential foundation for advanced study in mechanical design, control systems, and structural analysis, and prepares you for demanding technical roles in the engineering sector.

Dynamics

MEE 206: Engineering Mechanics - Dynamics

This course provides the formal, proof-based foundation for the concepts of convergence covered in calculus. It moves beyond computation to explore the deep theoretical questions of why sequences and series converge. The material covers the topological properties of sequences, key convergence theorems like Bolzano-Weierstrass, Cauchy sequences, and the advanced topic of uniform convergence for series of functions.

This subject is the gateway to higher mathematics. The rigorous proof-writing and analytical skills developed here are non-negotiable for any student pursuing a degree in pure or applied mathematics. These principles are the theoretical bedrock upon which advanced concepts in differential equations, functional analysis, and theoretical physics are built.

By the end of this course, you will be able to construct rigorous proofs for statements about the convergence of sequences. You will also be able to apply the Monotone Convergence and Bolzano-Weierstrass theorems, use the Cauchy Criterion to prove convergence, and analyse the uniform convergence of a series of functions using the Weierstrass M-Test.

This course is for mathematics majors and advanced students who have already completed a full Calculus II course. It is the standard curriculum for a first module in Real Analysis and is an essential prerequisite for graduate-level study in mathematics, physics, and theoretical computer science.

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Analysis of Infinite Sequences and Series - Real Analysis (Undergraduate Advanced)

This course covers numerical methods for solving problems that have no exact analytical solution. It is a practical study of iterative approximation techniques. The material is focused on two core areas: finding the roots of single-variable equations using the Bisection and Newton's methods, and approximating definite integrals using the Trapezoidal and Simpson's rules.

Numerical methods are the foundation of all modern computational problem-solving in science, engineering, and finance. These are the algorithms that power computer simulations, engineering design software, and financial modelling tools. The ability to find approximate solutions to complex equations is a fundamental skill for any technical or scientific professional.

By the end of this course, you will be able to apply the Bisection and Newton's methods to find the roots of single-variable equations. You will also be able to use the Trapezoidal and Simpson's rules to calculate the approximate value of definite integrals, providing a core toolkit for numerical approximation.

This course is for undergraduate foundation students in engineering, physics, and computer science. It is an essential topic for anyone who will use computational tools to solve mathematical problems. A solid understanding of single-variable calculus is a prerequisite.

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Numerical Methods

Introduction to Numerical Methods (Undergraduate Foundation)

This course provides a complete guide to solving ordinary differential equations (ODEs). It covers the classification of differential equations and details the solution methods for first-order equations, including separable, homogeneous, exact, and linear types. The course then moves to second-order linear equations with constant coefficients and covers the methods of undetermined coefficients and variation of parameters.

Differential equations are the mathematical language used to model dynamic systems in science and engineering. They are used to describe the motion of objects, the flow of electric circuits, population growth, radioactive decay, and chemical reaction rates. A command of this subject is a non-negotiable requirement for any serious study in physics, engineering, or applied mathematics.

By the end of this course, you will be able to classify any ordinary differential equation by its order, degree, and linearity. You will be able to solve a wide variety of first-order ODEs and constant-coefficient second-order ODEs. You will also be able to model and solve real-world problems, such as orthogonal trajectories, exponential growth and decay, and simple electric circuits.

This course is for undergraduate students in mathematics, physics, engineering, and chemistry. It is a standard module in any mathematical methods curriculum and assumes a full prerequisite knowledge of single and multivariable calculus. It is an essential foundation for the study of partial differential equations, control theory, and advanced physics.

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Mathematical Methods

Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

This learning track delivers the complete mathematical toolkit required for a university-level science, engineering, or computing degree. It systematically covers the entire MTH 201 curriculum, building from the foundational principles of single-variable calculus - functions, limits, continuity, and differentiability - to the advanced methods of multivariable calculus, infinite series, numerical methods, and ordinary differential equations. This is the definitive preparation for advanced quantitative study.

This programme is designed for second-year students offering MTH 201 at Obafemi Awolowo University, Ile-Ife, Nigeria. It is also helpful for any student in a STEM field - including physics, engineering, and computer science - who requires a rigorous and comprehensive command of calculus and its applications.

This track delivers a full skill set in mathematical analysis and applied problem-solving. Graduates will be able to solve a wide range of problems, from optimising multivariable functions to modelling dynamic systems with differential equations and testing the convergence of infinite series. This programme directly prepares students for success in advanced courses in vector calculus, partial differential equations, and real analysis, providing the necessary foundation for a career in engineering, data science, or theoretical physics.

Mathematical Methods I

MTH 201: Mathematical Methods I

Multiple integration; line, surface and volume integrals.

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Multiple Integration and Its Applications - Calculus (Undergraduate Advanced)

Mastering advanced calculus is essential for modelling complex systems in science and engineering. This track delivers the rigorous mathematical foundation demanded by the official NUC CCMAS curriculum for MTH 201. It systematically builds your expertise from fundamental single-variable theory to the sophisticated multivariable analysis used to solve critical problems in physics, economics, and technology.

This programme is for undergraduates in engineering, mathematics, physics, and computer science requiring a deep theoretical and practical command of calculus. It also serves economics students needing advanced quantitative tools or professionals in finance and data science seeking a solid mathematical base for technical research.

You will gain the analytical skills to construct formal proofs for differentiation rules and apply cornerstone theorems like Mean Value and Taylor's. You will master multivariable techniques, enabling you to solve constrained optimization problems with Lagrange multipliers and compute multiple integrals across line, surface, and volume domains. This track is the requisite preparation for advanced studies in differential equations, vector analysis, and complex engineering modelling.

Definitions of differential equations and related terminologies, identification of different differential equations and their solutions.

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Introduction to Differential Equations - Mathematical Methods (Undergraduate Foundation)

This course breaks down the key types of first-order ordinary differential equations (ODEs) ??? separable, homogeneous, exact, linear, and more ??? plus how to handle tricky non-homogeneous and inexact ones by transformations.

You???ll also learn how to reduce certain higher-order equations into first-order ones you already know how to solve.

The course is straight to the point, method-focused, and designed to build your confidence with step-by-step explanations and examples.

If you're a science, engineering, or math student or professional who wants clarity without fluff, this is for you.

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Solutions of First-Order and Reducible Higher-Order Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

Solutions and applications of linear ordinary differential equations.

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Linear Ordinary Differential Equations and Their Applications - Mathematical Methods (Undergraduate Advanced)

Solutions and applications of systems of ordinary differential equations.

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Systems of Linear Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

Mastering differential equations is essential for modelling dynamic systems in science and engineering. This learning track delivers the complete MTH 202 curriculum based on NUC CCMAS standards, equipping you with the mathematical command to describe motion, analyse electrical circuits, and predict rates of change across physical phenomena.

This programme is targeted at undergraduates in mathematics, physics, engineering, and chemistry who possess a strong background in single and multivariable calculus. It also serves professionals requiring a rigorous, method-focused refresher on fundamental mathematical modelling tools.

You will achieve competence in classifying equations and deploying solution methods for first-order, reducible higher-order, and general linear ordinary differential equations. You will learn to solve systems of linear ODEs and apply these techniques directly to real-world physical and technical problems. Completion establishes the necessary foundation for advanced studies in partial differential equations, control theory, and advanced physics.

Elementary Differential Equations

MTH 202: Elementary Differential Equations

Standard numbers cannot solve every square root. This course teaches you to use complex numbers for such problems. You will learn number systems, algebra, and how to use the Argand plane. Lessons cover polar forms, De Moivre's theorem, and finding roots. You will also study sine, cosine, and log functions through many worked examples.

These methods are vital for electrical engineering, physics, and signal processing. You need these skills to calculate electricity flow and wave behaviour. Engineers use these tools to build machines and structures. Mastering this allows you to solve the difficult maths used in modern technology and research. It provides the logic needed for all advanced technical work.

You will learn to add, multiply, and divide complex numbers. You will switch between rectangular, polar, and exponential forms using Taylor series. You will gain the skill to find Nth roots of unity and solve hyperbolic equations. You will also learn to draw complex equations on a graph accurately. By the end, you will handle advanced mathematical expressions without errors.

This course is for university students in engineering or maths who must pass advanced modules. It also serves technical workers who need to refresh their skills. The step-by-step examples make the topics easy to follow for anyone starting out. This knowledge is a requirement for anyone pursuing a career in high-level science or technology.

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Complex Numbers - Mathematical Methods (Undergraduate Advanced)

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.

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Linear Vector Spaces - Linear Algebra (Undergraduate Advanced)

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

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

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.

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

Comprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors.

Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Mathematical Methods II

MTH 202: Mathematical Methods II

This course focuses on mappings???one of the core tools in modern mathematics and abstract algebra.

We cover functions, injectivity, surjectivity, bijections, and composition. You'll see how mappings connect sets, preserve structure, and lay the groundwork for understanding homomorphisms in algebraic systems.

Straightforward, precise, and built for learners taking their first steps into abstract algebra.

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Mappings - Introductory Abstract Algebra (Undergraduate Advanced)

This course builds up a key part of the foundation for abstract algebra???relations.

We explore equivalence relations, partitions, orderings, and how they help us organize and understand mathematical structures. These ideas connect directly to how we define and work with algebraic systems like groups and rings.

Clear, focused, and made for first-time learners stepping into abstract algebra.

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Relations - Introductory Abstract Algebra (Undergraduate Advanced)

This course introduces binary operations???the basic building blocks of algebraic structures.

We explore how operations combine elements of a set, and what it means for them to be associative, commutative, or have an identity or inverse. These ideas form the core of how structures like groups and rings are defined.

Clear, hands-on, and designed for anyone beginning their journey into abstract algebra.

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Binary Operations - Introductory Abstract Algebra (Undergraduate Advanced)

This course introduces groups???one of the fundamental structures in abstract algebra.

We cover the group axioms, explore classic examples like integers under addition and symmetry groups, and show how groups model structure and transformations in math.

Clear, focused, and designed for learners new to abstract algebra.

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Groups - Introductory Abstract Algebra (Undergraduate Advanced)

This course dives into subgroups???key pieces within groups that reveal deeper structure.

You???ll learn how to identify subgroups, understand their properties, and see why they matter in the bigger picture of group theory. We???ll also explore examples and criteria that help recognize subgroups quickly.

Clear, practical, and perfect for first-time learners ready to explore group structures more deeply.

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Subgroups - Introductory Abstract Algebra (Undergraduate Advanced)

This course introduces rings and fields???two central structures in abstract algebra.

You???ll learn how rings extend the idea of groups with two operations, and how fields bring in the familiar arithmetic of fractions and equations. We explore key examples like integers, polynomials, and modular systems.

Simple, structured, and made for first-time learners building up their algebra toolkit.

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Rings and Fields - Introductory Abstract Algebra (Undergraduate Advanced)

This course explores homomorphisms???the maps that connect algebraic structures while preserving their operations.

You???ll learn what makes a function a homomorphism, see examples between groups and rings, and understand how these mappings reveal similarities and relationships between structures.

Clear, focused, and designed for first-time learners ready to deepen their understanding of algebraic connections.

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Homomorphisms - Introductory Abstract Algebra (Undergraduate Advanced)

This course brings in elementary number theory as a foundation for abstract algebra.

We cover divisibility, prime numbers, greatest common divisors, modular arithmetic, and congruences???all with a focus on the ideas that connect naturally to groups, rings, and fields.

Clean, intuitive, and designed for learners building a solid entry point into algebra through number theory.

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Elementary Number Theory - Introductory Abstract Algebra (Undergraduate Advanced)

Abstract algebra is the structural foundation of modern advanced mathematics. This track delivers the complete NUC CCMAS MTH 203 curriculum, rigorously transitioning you from computational arithmetic to abstract mathematical reasoning. It provides the necessary prerequisite framework for understanding complex mathematical systems and their applications.

This programme is targeted at undergraduate students in mathematics, computer science, and physics requiring a firm grounding in fundamental algebraic structures. It also serves professionals in fields like cryptography or theoretical computer science who need a rigorous theoretical refresher.

You will master the precise definitions, properties, and relations of core algebraic structures, including groups, subgroups, rings, and fields. You will gain competence in constructing formal proofs using set theory and logic, and understand how homomorphisms preserve mathematical structure. Completion establishes the critical theoretical base demanded for advanced studies in algebra, coding theory, and algorithm design.

Sets, Logic and Algebra I

MTH 203: Sets, Logic and Algebra I

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