This chapter provides the necessary conceptual and computational tools to manage oxidation-reduction reactions, which underpin electrochemistry and many industrial processes. Mastering the systematic balancing of these electron-transfer reactions is essential because inspection methods are insufficient for complex redox systems.

You will master four key objectives: tracking changes in oxidation state; balancing redox equations using the half-reaction (electron transfer) method; applying the specific protocols for balancing in acidic medium; and applying the conversion protocol for balancing in alkaline medium.

Balancing Redox Reactions

This chapter introduces the fundamental rules of chemical reactions and the law of conservation of mass. It establishes the groundwork for predicting how substances interact and transform, which is necessary for all quantitative work in chemistry and engineering.

By the end of this chapter, you will master defining chemical stoichiometry, identifying reactants and products in an equation, understanding the role of state symbols, and appreciating why equations must be balanced for accurate yield predictions.

Introduction

This final chapter synthesises all balancing techniques and redox principles covered throughout the course. Mastery here validates your ability to resolve complex reaction stoichiometry, ensuring computational accuracy for theoretical yield predictions and industrial process modelling.

You will master four objectives: integrating conservation of mass across all equation types; resolving multi-step ionic and redox problems; verifying oxidation number assignments; and demonstrating proficiency through comprehensive practice problems.

Conclusion

This chapter provides the conceptual framework for understanding reactions in solution, focusing on ionic and redox chemistry, which is vital for later electrochemistry and analysis. We systematically move from simplifying standard equations to mastering the foundational definitions and rules required to quantify electron transfer reactions.

You will master four key objectives: converting molecular equations to net ionic forms; defining and distinguishing oxidation and reduction; identifying the roles of oxidizing and reducing agents; and accurately assigning oxidation numbers to atoms in any compound or ion.

Redox Reactions

This chapter applies balanced equations to calculate the exact amounts of substances used or made in a reaction. It is the practical core of the course, essential for predicting product yields and managing chemical resources in a laboratory or factory setting.

You will master converting between mass and moles using molar ratios, identifying the limiting reagent that stops a reaction, calculating theoretical yields, and determining the amount of excess reactants left over.

Stoichiometric Calculations

This chapter establishes the core skill of balancing chemical equations, which is mandatory for all quantitative chemical analysis; we apply the law of conservation of mass using three distinct, systematic methods to ensure numerical equality between reactants and products.

You will master three key balancing techniques: the inspection method for simple reactions, the algebraic method for complex systems, and the oxidation number change method specifically for redox reactions.

Balancing Chemical Equations

Master the quantitative prediction of chemical change with Stoichiometry of Reactions. This undergraduate foundation course focuses on transforming conceptual chemical reactions into balanced, calculable equations. We begin by applying the conservation of mass principle to balance equations through inspection, the algebraic method, and the oxidation number change method. Next, we simplify reactions in solution by deriving total and net ionic equations, rigorously defining redox reactions, and teaching the precise assignment of oxidation numbers. The final section culminates in balancing complex redox equations using the half-reaction (electron transfer) method in both acidic and basic media.

Accurate reaction stoichiometry is the cornerstone of chemical processing, environmental analysis, and energy generation. Learners will gain the necessary computational skills to predict theoretical yields, determine limiting reagents in industrial synthesis, and analyse electrochemical processes like batteries and corrosion. Correctly balancing and interpreting chemical equations ensures laboratory safety, validates experimental results, and underpins quantitative decision-making in chemical engineering, materials science, and biochemistry.

After completing this course, you will be proficient in balancing any chemical equation based on the conservation of mass; accurately converting molecular equations into total and net ionic forms; defining and identifying oxidation and reduction processes, including their agents; assigning oxidation numbers to elements in compounds; and confidently balancing complicated redox reactions in both acidic and basic solutions. The course concludes with comprehensive practice problems to cement computational accuracy in reaction stoichiometry.

This course is specifically designed for undergraduate students beginning foundational Chemistry or related programmes, including Chemical Engineering, Pharmacy, and pure Sciences, where proficiency in calculating reaction quantities is mandatory. It is also an ideal, focused resource for pre-university students seeking an advanced start, or for any professional needing a rapid, expert-led review of fundamental reaction stoichiometry principles for accreditation or further study.

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

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 

NUC CCMAS

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

stoichiometry-ii-chemical-equations-and-redox-reactions

Chemistry

This chapter provides the roadmap for the course. It outlines the progression from the fundamental nature of chemical bonds to the theories that predict the three-dimensional shapes of molecules.

Key learning objectives include: understanding the overall course structure and appreciating why the shape of a molecule is critical to its function.

This chapter focuses on mastering Valence Shell Electron Pair Repulsion (VSEPR) theory to accurately predict the three-dimensional geometry of molecules. Understanding molecular shape is non-negotiable; it governs all chemical properties, reactivity, and function, providing the framework for molecular design.

Upon completion, you will be able to: predict electron and molecular geometry for molecules with two to six electron domains, identify geometries in examples with multiple lone pairs, and master the step-by-step procedure for determining complex molecular shapes.

Shapes of Molecules

This chapter introduces Valence Bond Theory and the crucial concept of orbital hybridization. Hybridization is a necessary model for explaining molecular shapes and bond angles that cannot be accounted for by simple VSEPR theory alone, bridging the gap between bonding theory and observed molecular geometry.

Upon completion, you will be able to: define bonding as the overlap of atomic orbitals, explain the formation of sigma and pi bonds, and accurately determine the hybridization (from sp to sp3d2) for the central atom in any molecule.

Hybridization Theory

This chapter details intermolecular forces (IMFs) - the attractive forces between molecules. These non-covalent interactions dictate all physical properties, including melting points, boiling points, and solubility, which is critical for predicting substance behaviour.

Upon completion, you will be able to: define and identify London dispersion and dipole-dipole forces, explain the unique strength of hydrogen bonding, and use dipole moment and molecular symmetry to determine a molecule's overall polarity.

Intermolecular Forces

This chapter establishes the foundation by classifying and detailing the strong intramolecular forces that hold atoms together. Mastery of ionic and covalent bonding is the prerequisite for subsequent analysis of molecular structure. We also introduce the critical hydrogen bond.

Key objectives: Define ionic, covalent, and coordinate covalent bonds; contrast the physical properties of ionic and covalent substances; and understand hydrogen bonding.

Types of Bonds

This final chapter is dedicated to comprehensive application and synthesis of all course material. It reinforces the critical connections between Lewis structures, molecular geometry, and physical properties, ensuring foundational knowledge is secure for advanced topics.

Upon completion, you will be able to demonstrate mastery across: drawing Lewis structures, predicting VSEPR geometry, determining orbital hybridization and bond types, and identifying intermolecular forces in any given molecule.

This chapter establishes the Lewis structure framework, the fundamental method for mapping valence electron arrangement in molecules and ions. Mastering this structured approach is the prerequisite skill for predicting molecular geometry and understanding bond characteristics later in the course. We cover systematic rules for neutral species and polyatomic ions, including the essential concept of resonance.

By the end of this chapter, you will master: drawing valid Lewis structures for molecules and ions; identifying and drawing resonance structures; applying the three main octet rule exceptions; and calculating and using formal charges to select the most plausible structure.

Lewis Structures

The shape of a molecule dictates its function. This course provides a practical, foundational treatment of chemical bonding and molecular geometry - the principles governing how atoms connect to form substances. It covers ionic and covalent bonding, the drawing of Lewis structures, and methods for determining molecular shape using VSEPR theory and orbital hybridisation. Finally, we examine intermolecular forces that control a substance's physical properties.

A command of this material is essential for molecular design. Knowledge of bonding and geometry dictates the properties of everything from pharmaceuticals, where shape governs drug-receptor specificity, to new materials like polymers and catalysts. Mastery of this foundational knowledge is the starting point for developing or synthesising any new chemical compound. Our system uses comprehensive videos and allows you to ask questions directly, making it fully online and easy to master at your pace.

By the end of this course, you will be able to draw correct Lewis structures for any molecule, predict its three-dimensional geometry and polarity using VSEPR theory, determine the central atom's hybridisation and bond types, and identify the various intermolecular forces present in a substance.

This course is mandatory for all undergraduate students of chemistry, biochemistry, and materials science, and is a direct prerequisite for studying organic chemistry. It benefits anyone needing a rigorous, structured, student-centred refresher or initial exposure to this critical subject, assuming a complete understanding of atomic theory and electronic configuration.

chemical-bonding-and-shapes-of-molecules-chemistry

This chapter shows how equation coefficients relate to their roots. Learning these shortcuts helps you study and build equations quickly without solving them first.

You will master calculating the sum and product of roots; evaluating expressions like the sum of squares or cubes; constructing new equations from given roots; and identifying conditions for shared roots between equations.

Properties of Roots

This chapter provides the procedural core of the course by teaching the three primary methods for solving quadratic equations. Mastering these techniques is mandatory for any further study in calculus, physics, or engineering.

You will master solving equations by factorisation; using the method of completing the square; applying the universal quadratic formula; and reducing complex fractional equations into standard quadratic form.

Solving Quadratic Equations

This chapter consolidates all theoretical and practical aspects of quadratic equations covered in the course. It ensures you have a firm command of every analytical tool and solution method before advancing to higher mathematics.

You will master factorisation, completing the square, and the quadratic formula; interpreting the discriminant for the nature of roots; applying sum and product properties; and identifying turning points for optimisation.

This chapter focuses on the discriminant to predict the properties of roots without solving the equation. It is a critical analytical tool for determining the existence and type of solutions in engineering and physics models.

You will master calculating the discriminant; classifying roots as real, identical, or imaginary; identifying rational and irrational solutions; and applying tangency conditions to curves and lines.

Nature of Roots

This chapter establishes the foundation for quadratic analysis by defining the standard form and its real-world relevance. Mastering these basics is essential before attempting complex solving techniques or applications.

You will master identifying quadratic components; rearranging equations into standard form; understanding the concept of roots; and applying the non-zero coefficient constraint.

This chapter focuses on finding the highest or lowest points of quadratic graphs. It is vital for solving real-world optimisation problems in physics, engineering, and finance.

You will master identifying maximum and minimum turning points; locating the vertex of a parabola; using the completing the square method for optimisation; and proving numerical boundary limits for quadratic expressions.

Maximum and Minimum Values

This chapter covers solving quadratic inequalities and finding the ranges of rational functions. These skills are vital for defining valid domains and identifying excluded values in advanced physics and engineering models.

You will master solving quadratic inequalities using graph shapes and critical values; applying the discriminant to find unknown coefficient ranges; rearranging rational expressions into quadratic form; and identifying the exact sets of values a function can or cannot take.

Inequalities and Rational Expressions

Quadratic equations are the bedrock of advanced algebra and the starting point for mastering non-linear mathematical models. This course provides a rigorous analysis of these equations, covering standard forms, solving methods like factorisation and completing the square, and the critical use of the discriminant to determine root nature. You will study turning points for optimisation, solve complex quadratic inequalities, and master the relationship between roots and coefficients to build equations from scratch.

Mastering these models is essential for careers in engineering, physics, and finance where trajectories and profit levels must be calculated precisely. You will use these principles to describe projectile motion, design parabolic structures, and identify boundary limits in economic models. This is the mathematics of optimisation, providing the necessary tools to find the highest or lowest possible values in any system governed by second-degree polynomials.

By the end of this course, you will solve any quadratic equation using multiple methods; use the discriminant to identify real, identical, or imaginary roots; and determine the location and value of turning points. You will master solving quadratic inequalities; identifying valid ranges for rational expressions; and using symmetric identities to evaluate root properties without solving the original equation. These skills form the essential foundation for calculus and mechanics.

This course is built for first-year university students in mathematics, physics, engineering, and economics who need a solid algebraic foundation. It also serves secondary school leavers preparing for advanced entrance exams or technical professionals looking to refresh their analytical skills. Even those in data science or basic programming will benefit from the logical structuring and problem-solving techniques required to handle non-linear variables.

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Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science.

This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions.

Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

Elementary Mathematics I

Algebra and Trigonometry

Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings.

This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction.

You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

Basic Mathematics

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Mathematics

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.

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.

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.

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

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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

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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

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.

OAU, Ife

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

introduction-to-numerical-methods-undergraduate-foundation

Numerical 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

Courses

Stoichiometry of Reactions - Chemistry (Undergraduate Foundation)

Chemical Bonding and Shapes of Molecules - Chemistry (Undergraduate Foundation)

Theory of Quadratic Equations - Mathematics (Undergraduate Foundation)

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)

Dry Friction - Engineering Mechanics (Undergraduate Advanced)

Introduction to Numerical Methods (Undergraduate Foundation)

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