This chapter establishes the rigorous language of kinematics. It defines the core quantities of motion ??? displacement, velocity, and acceleration ??? with a critical focus on the distinction between their scalar and vector forms. This foundation is the prerequisite for all subsequent analysis.

Key objectives: distinguish between scalar and vector quantities; define average and instantaneous acceleration; and use differentiation to relate displacement, velocity, and acceleration.

Introduction

This chapter consolidates the core concepts of kinematics. It provides a structured summary of the mathematical tools and physical principles used to describe motion, reinforcing the foundation for the study of dynamics.

The conclusion summarises the key definitions and equations. It also provides a forward look to the next course, where Newton's laws will be used to explain the causes of motion.

Conclusion

This chapter extends kinematic analysis to two and three dimensions. It establishes the general vector framework and calculus-based methods required to describe motion in a plane and in space. This mathematical toolkit is the direct prerequisite for analysing specific cases like projectile motion.

Key objectives: describe position, velocity, and acceleration using standard vector notation; and apply differentiation and integration to these vectors to analyse motion with variable acceleration.

Motion in Two or Three Dimensions

This chapter provides a complete analysis of projectile motion, the primary application of two-dimensional kinematics. The core principle is the complete independence of horizontal motion (at constant velocity) and vertical motion (at constant acceleration).

Key objectives: apply the principle of independent components to projectile problems; derive and use the equations for range, maximum height, and time of flight; and solve projectile trajectory problems.

Projectile Motion

This chapter introduces the vector framework required to relate motion across different inertial frames of reference. Mastering these transformations is critical for solving complex real-world navigation and tracking problems where both the object and the observer are in motion.

You will master four key objectives: applying the subscript notation for relative velocity; calculating resultant velocities in one dimension; resolving perpendicular vector components in two dimensions; and determining optimal headings for aircraft and maritime transit.

Relative Motion

This chapter examines uniform circular motion, a special case of two-dimensional motion where an object's speed is constant but its velocity is not. We will introduce the concept of an acceleration that serves only to change the direction of the velocity vector.

Key objectives: define the descriptive quantities of circular motion (period, speed); explain the nature and direction of centripetal acceleration; and apply its formula to solve problems.

Uniform Circular Motion

This chapter applies kinematic principles to the simplest case: motion along a straight line. We will cover motion with variable acceleration using calculus, and then focus on the critical case of constant acceleration and its set of standard equations. Mastery of 1D motion is the required foundation for all further analysis.

Key objectives: use calculus to relate displacement, velocity, and acceleration; apply the kinematic equations to solve constant acceleration problems; and analyse vertical motion under gravity.

Motion in One Dimension

Motion is the most fundamental concept in physics. This course provides the mathematical framework to describe it with quantitative precision. We will systematically analyse motion in one, two, and three dimensions, progressing from motion along a straight line to the vector analysis of projectiles and general spatial motion. This requires a full command of both vector algebra and introductory calculus.

The principles of kinematics are the bedrock of physical analysis, engineering design, and biomechanics. This knowledge is required to analyse everything from vehicle performance and projectile trajectories to the movement of organisms and robotic motion. A command of this material is essential for any work involving the dynamics of moving systems, providing the tools to predict and control motion in the real world.

Upon completion, you will be able to analyse motion in multiple dimensions. You will solve one-dimensional problems using the standard kinematic equations for constant acceleration. You will analyse two-dimensional projectile motion by resolving vectors into independent components. Critically, you will use vector calculus to describe the general case of motion with variable acceleration.

This course is designed for first-year university students of the physical, biological, and medical sciences, as well as engineering and computer science. A firm command of vector algebra and introductory calculus (differentiation and integration) is a mandatory prerequisite. This material is the necessary foundation for the subsequent study of Newtonian dynamics and biomechanics.

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.

NUC CCMAS

This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering.

The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics.

This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

General Physics I

Mechanics

vectors-and-kinematics-of-motion-physics-undergraduate

Physics

This chapter explains how forces do work to change an object's kinetic energy. By using energy instead of just force and acceleration, you can find the speed of an object much faster. This method is the foundation for solving complex engineering and physics problems simply.

You will learn to calculate work for constant, variable, and vector forces; define kinetic energy; apply the work-energy theorem to find speeds; and measure machine performance using power and efficiency.

Work and Kinetic Energy

This chapter explains why energy and momentum methods solve motion problems faster than Newton's laws. It sets the foundation for using scalar and vector principles to handle complex engineering and physics systems.

You will master the course structure; understand the importance of scalar and vector methods; and identify how these principles simplify mechanics calculations.

This chapter teaches you how to simplify complex systems by treating them as a single point mass. This method is vital for analysing the motion of large objects, vehicles, and groups of particles without tracking every individual part.

You will learn to calculate the balance point for groups of particles; find the centre of mass for complex composite shapes; determine the velocity of a system's centre of mass; and apply internal motion principles to solve displacement problems.

Centre of Mass

This final chapter links energy and momentum methods to help you choose the best tool for any physics problem. It reinforces how these laws simplify complex motion and prepares you for more advanced engineering topics.

You will master the work-energy theorem; summarise the laws of conservation of energy and momentum; compare scalar and vector methods for solving problems; and identify how these principles apply to rotational motion.

This chapter introduces the conservation of mechanical energy as a primary tool for solving motion problems without tracking time-dependent forces. It defines how energy is stored in fields and springs, providing a reliable way to predict system behaviour in complex engineering and physics scenarios.

You will learn to calculate gravitational and elastic potential energy; distinguish between conservative and non-conservative forces; apply the law of conservation of energy to multi-stage systems; and use potential energy curves to identify stable or unstable equilibrium states.

Potential Energy and Conservation of Energy

This chapter introduces linear momentum as a vector tool for analysing collisions and systems with changing mass. It provides a way to predict motion after impacts even when the forces are too complex for Newton's laws alone. Mastering these principles is essential for engineering safety and space flight.

You will learn to calculate momentum and impulse; apply the impulse-momentum theorem to impact forces; use the law of conservation of momentum to solve collision problems; distinguish between elastic and inelastic impacts; and derive equations for systems with varying mass.

Linear Momentum and Collisions

Master the laws that govern how everything moves, from a simple football to a space rocket. This course teaches you to solve complex physics problems by tracking energy and momentum instead of just forces. You will learn to calculate work, power, and efficiency; use the work-energy theorem to predict speeds; apply conservation laws to collisions; and find the balance point of complex objects using centre of mass principles.

Understanding energy and momentum is the backbone of engineering and modern technology. These principles are used to design safe cars with crash zones, build efficient engines, and calculate rocket trajectories for space exploration. Mastering these concepts allows you to predict the outcome of physical events with high accuracy, making it an essential skill for anyone looking to build machines, design structures, or solve real-world technical problems.

By the end of this course, you will be able to calculate work done by constant and variable forces; apply the principles of kinetic and potential energy to find the velocity of moving objects; and use the law of conservation of energy to solve systems with springs and weights. You will also learn to analyse elastic and inelastic collisions using momentum; calculate impulse and impact forces; and determine the centre of mass for composite shapes and moving systems.

This course is specifically for first-year university students of physics and engineering who need a solid foundation in mechanics. It is also highly beneficial for secondary school leavers preparing for advanced placement exams or those entering technical fields who want to understand the physical laws behind machines and motion. Even those not pursuing a degree will gain a sharp, logical approach to solving problems by learning how energy and matter interact in the physical world.

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Friction resists motion between surfaces or through fluids. No real system is perfectly smooth; you must calculate this resistance to predict actual movement. This is essential for designing safe brakes, tyres, and efficient vehicles.

You will master the differences between sliding, rolling, and fluid friction; using coefficients to determine motion states; calculating air and water resistance; and resolving terminal velocity.

Friction

This chapter identifies the specific forces driving mechanical systems. You must master gravity, normal force, tension, and spring force to model physical interactions correctly. These forces are the required inputs for every dynamics equation you will solve.

You will master distinguishing mass from weight; calculating normal and spring forces; resolving tension in coupled systems; and constructing precise free-body diagrams to isolate bodies for force analysis.

Some Special Forces

This chapter defines force and moves from describing motion to explaining its causes. It provides the foundation for mechanics by treating forces as vector quantities. Master these basics to solve engineering problems.

You will master distinguishing contact from non-contact forces, representing forces as vectors, and using vector addition to find the resultant net force on an object.

Dynamics uses Newton's second law to relate force to acceleration. This is the foundation for predicting how vehicles and machinery move. You will learn to calculate the exact motion of particles when various forces act on them.

You will master drawing free-body diagrams for moving systems, resolving weight on ramps, calculating acceleration for connected blocks or pulleys, and determining stopping distances while accounting for kinetic friction.

Dynamics of Particles

Equilibrium happens when all forces on an object sum to zero, so it does not accelerate. This is the foundation for building safe structures and machines. You will learn how to calculate unknown forces for objects staying still or moving at a steady speed.

You will master drawing free-body diagrams, resolving forces into components, calculating rope tensions in different setups, and finding friction limits on flat floors and ramps.

Equilibrium of Particles

Uniform circular motion covers objects travelling in curved paths at constant speeds. This is vital for road engineering, satellite orbits, and machine design. You will calculate the net inward forces required to maintain these paths.

You will master defining centripetal acceleration; calculating safe speeds for flat and banked curves; resolving forces in conical pendulums; and finding critical speed and tension in vertical circles.

Newton's laws are the main rules for how objects move or stay still. This chapter explains why motion changes and how mass resists these changes. You need these laws to calculate force and acceleration in any machine or structure.

You will master using the first law to understand inertia; applying the second law to calculate net force; understanding how mass affects acceleration; and identifying action-reaction force pairs.

Newton's Laws of Motion

This chapter consolidates Newton's laws to fix your understanding of classical mechanics. It is the final check before you apply these forces to the next modules on work and energy.

You will master the summary of the three laws of motion, and the transition from force vectors to energy-based problem solving.

Dynamics explains why objects move, and Newton's laws provide the exact mathematical rules for this movement. This course transitions from basic motion to the rigorous use of force vectors, inertia, and action-reaction pairs. You will learn to handle gravity, tension, and springs while solving resistive problems involving static, kinetic, and fluid friction. We build from first principles to complex systems used in modern machinery.

Every machine and structure operates under these principles. Understanding these forces is required to predict when a system will fail, how to build safe cars, and how to design efficient engines. These analytical tools allow you to solve real problems in construction, manufacturing, and transport. This knowledge is the foundation for anyone building or maintaining physical systems.

After this course, you will construct precise free-body diagrams to isolate objects from their surroundings.  You will acquire the technical skill to calculate acceleration in systems with multiple forces, find centripetal force for circular motion, and use equilibrium laws to find unknown force values. You will master the mathematics of friction on ramps, calculate terminal velocity in fluids, and solve for tension in connected pulley systems.

This course is for first-year university engineering and physics students. It also helps technicians who need a refresher and secondary school leavers who want to prepare for undergraduate work. Anyone interested in how things work will find these structured methods useful for clear thinking and scientific problem-solving.

force-and-motion-newtons-laws-physics-undergraduate

Meaning and calculation of moment of a force about a point in three dimensions.

Moment About a Point in Three Dimensions

Meaning and calculation of the moment of a force about an arbitrary axis.

Moment About an Axis

Meaning and calculation of the moment of a force about a point in two dimensions.

Moment About a Point in Two Dimensions

Simplifying general systems of forces and couples on rigid bodies.

General Systems of Forces

Meaning and analysis of couples, moments of couples, and couple vectors.

Couples

Welcome to the course and review of fundamental concepts - meaning of rigid bodies, principle of transmissibility of forces, vector products, etc.

Meaning, scalar and vector forms of the moment of a force about a point and its relation to the moment about an axis; Varignon's theorem.

Moment of a Force

Analysis of simple force-couple systems - resolution of a single force into a force and a couple, and reduction of a force-couple system to a single equivalent force.

Force-Couple Systems

Simplifying systems of forces on rigid bodies involving distributed loads.

Distributed Loads

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.

University

Statics decides if a structure stands or fails. This track teaches force calculation, support reactions, and equilibrium analysis for stable engineering systems. You will move from particle resolution to full structural modelling. The curriculum delivers the exact mathematical foundation required for real design work.

This programme is for first and second-year engineering undergraduates. It suits mechanical, civil, aerospace, and structural students, plus polytechnic learners. You only need basic physics and vector algebra. The sequence provides the precise calculation methods your degree demands.

You will finish able to resolve two and three dimensional forces, compute moments and couples, and solve rigid body equilibrium problems. You will calculate truss loads, evaluate friction in screws and belts, locate centres of gravity, and verify systems using virtual work. These results secure high grades in advanced mechanics modules and prepare you for structural design, machine engineering, and civil site roles.

Engineering Mechanics I

Statics

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.

Applied Mechanics

systems-of-forces-rigid-bodies-engineering-mechanics

Engineering Mechanics

Analysis of equilibrium of rigid bodies in three dimensions.

3D Equilibrium Equations

General analysis of equilibrium of rigid bodies in two dimensions.

2D Equilibrium Equations (1)

Determining force and moment reactions at contacts, connections and supports for a rigid body under the action of co-planar forces - in order to produce its free-body diagram.

2D Reactions

Determining force and moment reactions at contacts, connections and supports for a rigid body under the action of three-dimensional forces - in order to produce its free-body diagram.

3D Reactions

Different conditions of constraints on rigid bodies in two dimensions and their statical determinacy.

2D Constraints and Statical Determinacy

Welcome to the course and review of fundamental concepts - internal and external forces, equilibrium conditions for rigid bodies, use of free-body diagrams, etc.

Different conditions of constraints on rigid bodies in three dimensions and their statical determinacy.

3D Constraints and Statical Determinacy

Analysis of special cases of equilibrium of rigid bodies in two dimensions - equilibrium under the action of only two or three forces.

2D Equilibrium Equations (2)

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.

equilibrium-of-rigid-bodies-engineering-mechanics

This final chapter is a mandatory comprehensive assessment designed to confirm full mastery of the course material. Successful completion ensures you can confidently apply both the theoretical principles of the kinetic theory and the practical calculations derived from all gas laws. This is the required preparation for 'Stoichiometry I'.

Key objectives include: application of the Ideal Gas Equation and combined gas laws; explaining gas behaviour using kinetic postulates; and validating understanding of the states of matter.

This chapter establishes the course roadmap and introduces the Kinetic Theory of Matter. The theory provides the essential microscopic framework - the motion of particles - required to understand and explain the macroscopic properties and behaviour of gases studied in the following chapters.

Upon completion, you will be able to: outline the core postulates of the Kinetic Theory of Matter and appreciate the direct link between particle motion and measurable physical properties like pressure and temperature.

This chapter systematically applies the Kinetic Theory of Matter to explain the states of matter. We establish how the balance between particle kinetic energy (temperature) and intermolecular forces dictates whether a substance exists as a solid, liquid, or gas, governing phase changes.

Upon completion, you will be able to: differentiate the three states of matter based on particle movement, explain the microscopic basis for phase transitions (boiling, melting), and use the kinetic theory to describe the influence of temperature on state.

Kinetic Theory

This chapter establishes the core empirical laws that describe gas behaviour, starting with the kinetic explanation for pressure. Command of these relationships is essential for accurately calculating unknown state variables and understanding the practical limits of gas systems in engineering and physical science applications.

Key objectives include: applying Boyle's, Charles's, Avogadro's, and Gay-Lussac's Laws; deriving and calculating gas density; and mastering the Ideal Gas Equation, PV = nRT, for complex state variable analysis.

Gas Laws

This course provides a rigorous treatment of the Kinetic Theory and the Gas Laws, explaining the physical principles that control the behaviour of solids, liquids, and gases. We move from the foundational kinetic postulates to the precise mathematical relationships required to model matter's response to energy, pressure, and temperature.

These principles dictate real-world engineering, not just textbook theory. You will apply this knowledge to model atmospheric dynamics, design efficient chemical reactors, and optimise engine performance. A command of these laws allows you to quantify substance behaviour under varying conditions, solving the calculation pain points often faced in process engineering and physical science.

By the end of this course, you will confidently apply Boyle's, Charles's, Avogadro's, and the Combined Gas Laws to determine unknown state variables. You will derive and utilize the Ideal Gas Equation, PV = nRT, and explain gas properties using kinetic theory postulates. Additionally, you will analyse the structure of solids and calculate gas density. 

This is a mandatory foundation for Chemistry and Chemical Engineering undergraduates and a prerequisite for thermodynamics. It is intended for learners with a grasp of chemical bonding who require a structured, student-centred alternative to disjointed free resources.

A passionate teacher of Chemistry who is not just interested in teaching but has a strong desire in seeing students enjoying the beauty of the subject 

This learning track delivers the complete NUC CCMAS curriculum for General Chemistry I. It is a comprehensive programme designed to build a robust, university-level foundation in modern chemistry. The track systematically covers all essential topics, from atomic theory, chemical bonding, and the states of matter, to the quantitative principles of stoichiometry, equilibrium, thermodynamics, and kinetics.

This programme is for first-year undergraduates in science, technology, engineering, and mathematics (STEM) faculties who are required to take CHM 101. It is also essential for any student or professional globally who needs a rigorous and complete foundation in first-year university chemistry for further study or career development.

This track delivers a full skill set in chemical theory and quantitative problem-solving. Graduates will be able to determine molecular structures, calculate reaction quantities, analyse the energetics and rates of reactions, and solve complex equilibrium problems. This programme provides the non-negotiable prerequisite knowledge for all subsequent chemistry courses and for any degree in the physical sciences, engineering, or medicine.

General Chemistry I

kinetic-theory-of-matter-and-gas-laws-chemistry

Chemistry

General analysis of problems involving dry friction - for particles.

Problems Involving Dry Friction (1)

Analysis of frictional forces on journal bearings.

Journal Bearings

Analysis of frictional forces (rolling resistance) on wheels.

Wheels

Analysis of dry friction on square-threaded screws.

Screws

Wedges

Fundamental principles of dry friction - meaning of friction, coefficients of friction, angles of friction, etc.

Laws of Dry Friction

Welcome to the course and definition of terms - friction, dry friction, fluid friction, lubrication, etc.

Analysis of frictional forces on flat belts.

Belts

Analysis of frictional forces on thrust bearings - collar bearings, pivot (end) bearings and disks.

Thrust Bearings

General analysis of problems involving dry friction - for rigid bodies.

Problems Involving Dry Friction (2)

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

dry-friction-engineering-mechanics-undergraduate

Introduction, existence of solutions, and bisection method of numerical solutions of equations in one variable.

Equations in One Variable (1)

Introduction to numerical integration of single-variable functions. Trapezoidal rule.

Integration (1)

Simpson's 1/3 rule of numerical integration of single-variable functions.

Integration (2)

Numerical solutions of equations in one variable - Newton-Raphson's iterative method.

Equations in One Variable (2)

This chapter sets the foundation for the entire course. It defines what numerical methods are, explains why they matter, and outlines when and why they are used instead of analytical techniques. We establish the scope, assumptions, and limitations that shape all subsequent methods. If you skip this, you will misapply the rest.

By the end of this chapter, you should be able to:

??? Distinguish between analytical and numerical solutions.

??? Identify problems best suited for numerical methods.

??? Recognise key sources of numerical error.

??? Understand the structure of a typical numerical method.

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.

introduction-to-numerical-methods-undergraduate-foundation

Numerical Methods

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

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

Theorems on Continuous Functions

Various types of discontinuities - meaning and examples.

Types of Discontinuity

Examples of continuous functions, worked problems on continuity.

Continuous Functions

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.


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

Real Analysis bridges the critical gap between computational calculus and rigorous advanced mathematics. This learning track delivers the complete NUC CCMAS MTH 207 curriculum, transitioning you from intuitive understanding to formal mathematical proof. It establishes the theoretical foundation required for serious modelling in science, engineering, and pure mathematics.

This programme is targeted at mathematics majors and advanced undergraduates in physics and engineering who have completed foundational calculus. It is designed for students requiring the rigorous analytical skills demanded by graduate-level studies and theoretical research.

You will master the construction of rigorous proofs for sequence and series convergence, applying cornerstone theorems like Bolzano-Weierstrass and Cauchy criteria. You will achieve a formal command of continuity and differentiability, deriving major calculus rules from first principles. Completion provides the non-negotiable prerequisite knowledge for advanced studies in functional analysis, differential equations, and theoretical physics.

Real Analysis I

continuity-of-functions-single-variable-calculus

Single-Variable Calculus

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.

OAU, Ife

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.

Engineering Mechanics II

Dynamics

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

Transformation of coordinates by rotation.

Coordinates Transformation

Equations of circles, ellipses, parabolas and hyperbolas.

Second-Degree Plane Curves

Three-dimensional rectangular coordinates system, graphs.

Three-Dimensional Rectangular Coordinates

Points, distances, lines, angles, gradients, etc., on the two-dimensional coordinates system.

Two-Dimensional Rectangular Coordinates

Direct classification of quadric surfaces.

Classifying Quadric Surfaces I

Classification of quadric surfaces by variable substitution.

Classifying Quadric Surfaces II

The polar, cylindrical and spherical coordinates systems.

Other Coordinates Systems

Graphs of second-degree equations in three variables - ellipsoids, cones, cylinders, hyperboloids, paraboloids, etc.

Quadric Surfaces

Learn to analyze the three-dimensional Euclidean space using coordinates and equations with pin-point precision.

Designed for students, researchers, and professionals in fields such as engineering, computer graphics, physics, astronomy, medicine, biology, architecture, and building technology, this course provides a thorough understanding of coordinate systems, equations, and quadric surfaces.

On completing this course, you will have mastered:

- One-dimensional coordinate system and locating points

- Two-dimensional coordinate system, lines, and curves

- Conic sections and their equations

- Three-dimensional coordinate system and quadric surfaces

- Computer-aided visualization using Geogebra

- Coordinate transformation and rotation

- Equations in polar, cylindrical, and spherical coordinates

Throughout the course, you'll engage with high-quality video lessons, completely-solved examples, free-hand sketching techniques, and computer-aided visualizations. Multiple-choice quizzes will keep you focused and help reinforce your learning.

Prerequisites:

This course is designed for first-year undergraduate students in engineering and sciences. Prior knowledge of basic trigonometric ratios, determinants, and elementary row operations on matrices is helpful but not required, as the course is designed to be accessible to learners with varying backgrounds.

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.

Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables.

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

Engineering Analysis I

3-d-coordinates-and-quadric-surfaces-analytic-geometry

Analytic Geometry

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

Proving Limits Involving Infinity

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

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

Evaluating Finite Limits (1)

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

Evaluating Limits at Infinity

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.

Courses

Kinematics: Motion in One and Two Dimensions - Physics (Undergraduate Foundation)

Work, Energy, and Momentum - Physics (Undergraduate Foundation)

Force and Motion: Newton's Laws - Physics (Undergraduate Foundation)

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

Equilibrium of Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Kinetic Theory of Matter and Gas Laws - Chemistry (Undergraduate Foundation)

Dry Friction - Engineering Mechanics (Undergraduate Advanced)

Introduction to Numerical Methods (Undergraduate Foundation)

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

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

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

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