This chapter establishes the course framework. It defines physics as a science of precise measurement and outlines the fundamental approach required for all subsequent topics. Master this section to understand the structure of the course and what is required to succeed.

Key objectives: define the scope and methodology of physics; understand the course structure and assessment; and confirm your command of the required mathematical prerequisites.

Introduction

Precise measurement is the foundation of physics. This chapter introduces the core concepts of physical quantities and the standards that define them. We will establish the International System of Units (SI), the formal framework required for all subsequent quantitative work.

Key objectives: distinguish between fundamental and derived quantities; identify the seven SI base units; and explain the role of standards in defining physical units.

Measurements

This chapter examines the three fundamental quantities of mechanics: mass, length, and time. We will establish their formal definitions and the SI standards used to quantify them. A precise understanding of these core concepts is the absolute prerequisite for the study of motion.

Key objectives: define mass, length, and time and state their SI units; distinguish clearly between the concepts of mass and weight; and identify the standard instruments used to measure these quantities.

Length, Mass and Time

A physical equation must be dimensionally consistent to be valid. This chapter details the method of dimensional analysis, a critical tool for verifying equations and preventing errors in technical work. Mastery of this technique is a non-negotiable skill for problem-solving.

Key objectives: determine the dimensions of physical quantities; apply the principle of homogeneity to test the validity of equations; and use dimensional analysis to deduce relationships between variables.

Dimensional Analysis

Physical quantities have either magnitude (scalars) or magnitude and direction (vectors). This chapter defines this critical distinction and establishes the complete mathematical framework for vector algebra. Command of vectors is non-negotiable for describing forces, velocity, fields, or any change in physical systems.

You will: distinguish scalars from vectors; resolve vectors into components; add vectors analytically; calculate scalar and vector products; and differentiate vector functions.

Scalars and Vectors

This chapter consolidates the course's core analytical tools. It summarises the complete toolkit ??? dimensional analysis, vector algebra, and vector calculus ??? confirming your command of the non-negotiable foundation for all subsequent study in the physical sciences.

You will: consolidate your understanding of the course's analytical methods; recognise their direct application in mechanics; and verify your readiness for the next physics course.

Conclusion

Physics is not a collection of facts; it is a quantitative language. This course establishes that language. We cover the formal system of measurement and units, the rigorous method of dimensional analysis, the complete framework of vector algebra, and the use of calculus to describe how vector quantities change. This is the essential grammar of science.

The tools in this course have immediate, practical applications. Correct dimensional analysis is a critical technique for verifying equations and preventing catastrophic errors in any technical calculation. Vectors are the required language for describing forces, displacements, velocities, and fields in any engineering or scientific discipline. Mastering this material is the first step to becoming a competent technical professional.

Upon completion, you will command the mathematical toolkit for physics. You will perform dimensional analysis to validate equations. You will resolve vectors into components, calculate vector sums and products, and differentiate vector functions to analyse rates of change, such as deriving velocity from a position vector.

This course is the mandatory starting point for first-year university students of engineering, physics, computer science, and related disciplines. A firm command of secondary school algebra, geometry, and trigonometry is a prerequisite. It is also suitable for professionals who require a rigorous and efficient refresher on the foundational mathematical tools of science.

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

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Physics

Introduction to engineering mechanics, fundamental concepts, systems of units and general analysis procedure.

Force vectors and how to obtain the resultant of two or more forces - using parallelogram and triangle rules.

Resultant of Forces in a Plane

Resolution of a force into its rectangular and non-rectangular components.

Components of a Force in a Plane

Calculating the resultant of several concurrent forces using their rectangular components.

Resultant by Components in a Plane

Determining the components of forces in three dimensions.

Components of a Force in Space

Equilibrium of particles under the action of three-dimensional forces.

Equilibrium in Space

Equilibrium of particles under the action of planar forces.

Equilibrium in a Plane

Vector addition of force vectors in three dimensions.

Resultant of Forces in Space

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

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

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

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

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

This chapter defines the principle of mathematical induction and its role in formal logic. You will understand the domino effect analogy and why this method is necessary for proving statements across infinite sets of integers. It provides the essential foundation for all subsequent proof techniques in this course.

You will master defining the principle of induction, verifying the base case for n equals one, formulating the inductive hypothesis for n equals k, and executing the inductive step to prove the statement for n equals k plus one.

This chapter covers proofs for the sums of series with terms written as fractions. It is a vital section because it forces you to use advanced algebraic manipulation and common denominators to link the inductive hypothesis to the final goal.

By the end, you will master handling terms with product denominators, using common factors to simplify fractional expressions, and proving telescoping series identities through the inductive step.

Fractional Series

This chapter teaches how to use induction to prove that algebraic expressions are exactly divisible by specific integers. It is a critical skill for number theory and cryptography, moving beyond simple addition to master the manipulation of factors and remainders in a logical sequence.

You will master expressing divisibility as a linear equation, manipulating exponents to isolate common factors, and applying the inductive hypothesis to prove that expressions like n cubed plus 2n are multiples of three.

Divisibility

This chapter focuses on using induction to prove formulas for the sum of arithmetic and geometric sequences. It is the most common application of the method and essential for verifying that a general summation formula holds true for any number of terms.

By the end, you will master proving linear and quadratic series identities, applying the inductive hypothesis to algebraic summations, and simplifying complex fractional series expressions to reach the required right-hand side.

Series

This chapter covers using induction to prove mathematical inequalities where one expression is always greater than another. It is a vital section because it requires logical estimation and transitivity rather than simple equality. This skill is essential for analyzing algorithm efficiency and bounding errors in numerical analysis.

You will master handling base cases where n is greater than one, applying the inductive hypothesis to inequalities, and using algebraic estimation to prove that exponential growth eventually exceeds polynomial growth.

Inequalities

This chapter applies induction to sequences where each term depends on those before it. It is critical for computer science and engineering because it provides the mathematical proof for how recursive algorithms and loops function. You will learn to verify that a general formula correctly predicts the value of any term in a repeating sequence.

You will master defining terms using recurrence relations, proving explicit formulas for recursive sequences, and applying the inductive step to link successive terms.

Recursive Sequences

This chapter covers miscellaneous induction proofs that do not fit into standard categories. It tests your ability to apply logical steps to unfamiliar mathematical structures, ensuring you can use the base case and inductive step on any technical problem.

By the end, you will master proving formulas for the nth power of a matrix, calculating total subsets for a set with n elements, and applying inductive logic to non-standard algebraic identities.

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

Build the mathematical foundation required to excel in social science degrees and data-driven careers. This track follows the official NUC syllabus for DSS 103 to teach sets, number operations, counting methods, logical proofs, binomial expansions, complex numbers, and trigonometry. Each topic connects directly to the quantitative skills you need for statistics, research methods, and economic analysis.

This programme is for first-year university students studying economics, sociology, political science, psychology, geography, or other social science disciplines. It is also for secondary school leavers preparing for university entry and professionals who must strengthen their maths for postgraduate study or analytical roles in government, NGOs, or private sector research.

After completing this track, you will solve equations, handle algebraic proofs, manipulate trigonometric formulas, and apply counting principles to real-world data problems. These skills prepare you for advanced coursework in econometrics, statistical analysis, social research, and policy evaluation. You will have the confidence to tackle quantitative modules and compete for roles in banking, public service, consulting, and development work.

Mathematics for Social Scientists I

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Mathematics

This chapter introduces the fundamental language and notation of set theory. Mastering these primary definitions is mandatory for structuring logical arguments and categorising data in all advanced mathematical and computational disciplines.

You will master four objectives: defining sets and elements with precision; using roster and set-builder notation; identifying finite and infinite collections; and applying basic symbols for membership and subsets.

This chapter defines the hierarchical inclusion of sets and the precise conditions for set equality. Mastery of subset logic is critical for constructing rigorous proofs and managing data inheritance in computational architecture.

You will master four objectives: distinguishing between proper and improper subsets; proving set equality through mutual inclusion; calculating the total number of subsets for finite collections; and defining the universal set and empty set within inclusion frameworks.

Subsets

This chapter covers the algebraic manipulation of sets to form new collections through rigorous logical rules. Mastering these operations is foundational for database querying, probability theory, and complex data stratification in engineering and analytical systems.

You will master four objectives: performing unions, intersections, and set differences; calculating absolute and relative complements; applying De Morgan's laws to simplify set expressions; and identifying disjoint sets.

Operations on Sets

This chapter defines the rigorous classification of numerical collections and their hierarchical inclusion. Mastery of these standard sets is mandatory for defining domains in calculus, establishing computational constraints, and ensuring logical consistency in mathematical proofs.

You will master four objectives: categorising natural, integer, rational, and irrational numbers; identifying the real and complex number systems; applying interval notation for continuous subsets; and mapping the nested relationship between numerical sets.

Sets of Numbers

This chapter covers the fundamental laws governing set operations and the formal proof of set identities. Mastering this symbolic logic is essential for simplifying complex boolean expressions and ensuring the validity of analytical arguments in computer science and mathematical engineering.

You will master four objectives: applying idempotent, associative, and commutative laws; implementing distributive and absorption laws; proving identities using De Morgan's laws; and simplifying expressions using identity and complement laws.

Algebra of Sets

This chapter introduces the visual representation of set relationships and the spatial logic of inclusions. Mastery of Venn diagrams is essential for mapping data overlaps, solving combinatorial problems, and verifying set identities through geometric interpretation.

You will master four objectives: constructing diagrams for two and three sets; shaded representation of unions and intersections; interpreting regions of relative and absolute complements; and solving practical survey problems using the principle of inclusion-exclusion.

Venn Diagrams

This chapter defines the construction of ordered pairs and the product of distinct sets. Understanding these mappings is mandatory for defining relations, functions, and the multidimensional coordinate systems used in database schema design and linear algebra.

By the end of this chapter, you will master: constructing ordered pairs and n-tuples; calculating the cardinality of product sets; applying the non-commutative property; and executing distributive operations over unions and intersections.

Cartesian Products

This chapter explains how elements from different sets interact through specific rules. These principles are the building blocks for computer programming and advanced calculus. You will learn to link data points accurately and transform inputs into valid outputs.

You will master identifying relations and functions; performing algebraic and composite operations; classifying injective, surjective, and bijective mappings; and calculating inverse functions.

Relations, Mappings and Functions

Mathematics begins with sets. This course covers everything from basic definitions and membership notations to complex set algebra and De Morgan's laws. You will master cardinality, power sets, and the classification of number systems including rational, irrational, and complex numbers. The curriculum moves from simple operations like union and intersection into element-wise proofs, Cartesian products, and the mechanics of relations and functions.

Set theory is the language of modern data and logic. These concepts are essential for computer programming, database management, and statistical analysis. Understanding functions and mappings allows you to model real-world dependencies in engineering, economics, and the sciences. Mastering these foundations provides the exact logical framework needed to solve complex problems in technology and research.

Upon completion, you will be able to simplify set expressions and solve grouping problems using Venn diagrams and the inclusion-exclusion principle. You will know how to perform element-wise proofs and calculate set cardinalities. You will also gain the ability to evaluate composite functions and prove whether a mapping is one-to-one, onto, or bijective.

This course is designed for undergraduate students and secondary school leavers entering STEM disciplines. It provides a necessary logical foundation for anyone moving into calculus, data science, or advanced mathematics. The clear, direct instruction ensures that any student can develop the systematic thinking required for professional technical roles.

set-theory-mathematics-undergraduate-foundation

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

Applications of first-order ordinary differential equations.

Applications of First-Order Ordinary Differential Equations

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

Solutions of Second-Order Ordinary Differential Equations (1)

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

Solutions of Second-Order Ordinary Differential Equations (2)

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

Solutions of First-Order Ordinary Differential Equations

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

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

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

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

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

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

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

Elementary Differential Equations

ordinary-differential-equations-mathematical-methods

Mathematical Methods

This chapter provides a foundational classification of chemical transformations. It introduces the main types of chemical reactions, providing a framework for predicting the products of simple reactions.

Key learning objectives include: identifying and providing examples of the common reaction types, such as synthesis, decomposition, and displacement.

Chemical Reactions

This chapter provides the roadmap for the course. It outlines the foundational concepts of chemistry to be covered, from the scientific method and measurement to the classification of matter and reactions.

Key learning objectives include understanding the overall course structure and appreciating how these distinct topics interconnect to form the basis of chemical science.

This chapter covers the fundamental classification of matter as required by the syllabus. It provides the formal definitions for atoms, molecules, elements, compounds, and mixtures, and explores the changes matter undergoes.

Key learning objectives include: defining and differentiating between the classifications of matter; and distinguishing between physical and chemical changes.

Matter

This chapter consolidates your mastery of the non-negotiable concepts required for advanced study in the chemical sciences, acting as a final knowledge checkpoint before you proceed.

Key objectives are to review all core concepts and outline the immediate next steps required in your university-level chemistry curriculum.

Chemistry is the science of matter. This course provides a rigorous introduction to its fundamental principles, moving from the definition of matter and its states to the atomic and molecular structures that govern its behaviour. We will classify matter into elements, compounds, and mixtures, and establish the critical distinction between physical and chemical changes.

A command of chemistry is essential for any quantitative science. The principles covered here are foundational to medicine, engineering, environmental science, and materials development. Understanding how matter is structured and how it transforms is the basis for creating new materials, developing pharmaceuticals, and managing industrial chemical processes safely and efficiently.

Upon completion, you will possess a clear conceptual framework for chemistry. You will be able to classify different types of matter, distinguish between physical and chemical changes, and define elements, compounds, and mixtures. You will also be able to identify the fundamental roles of atoms, molecules, and ions in chemical reactions.

This course is designed for first-year university students beginning their studies in any scientific or engineering discipline. It serves as a mandatory prerequisite for further study in chemistry, chemical engineering, biology, and medicine. It is also suitable for anyone requiring a concise and formal review of foundational chemical concepts.

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

introduction-to-chemistry-undergraduate-foundation

Chemistry

This chapter establishes the rigorous classification and fundamental operations of the real number system. You will master the structural hierarchy of numbers and basic algebraic manipulations, providing the essential precision required for solving complex equation systems and inequalities in subsequent chapters.

You will master: classifying real numbers into rational and irrational subsets; applying order of operations to complex expressions; identifying properties of real number subsets; and executing fundamental algebraic simplifications.

This chapter establishes the rigorous mechanical framework for resolving equations of varying degrees and structures. Mastering these transformation techniques is essential for isolating variables in engineering models and scientific formulas with absolute logical consistency.

You will master the systematic isolation of unknowns in linear and quadratic forms; the resolution of rational and radical equations; and the reduction of cubic, biquadratic, and symmetric expressions into solvable factors.

Equations in One Unknown

This chapter governs the manipulation and factorisation of higher-degree algebraic expressions. You will master the structural logic of polynomial functions, establishing the essential skills required for advanced partial fraction decomposition and the analysis of non-linear systems in engineering and physics.

You will master: executing polynomial long division and synthetic division; applying the Remainder and Factor Theorems; factorising cubic and higher-order expressions; and identifying roots of polynomial equations.

Polynomials

This chapter governs the resolution of mixed systems where linear and non-linear dependencies intersect. You will master the algebraic techniques required to solve for variables across multiple constraints, providing the essential logic for intersecting geometric paths and complex equilibrium states in engineering and economics.

You will master: executing substitution and elimination for dual linear systems; identifying points of intersection between straight lines and curves; resolving homogeneous quadratic systems through variable substitution; and simplifying complex rational and product constraints to determine precise coordinate solution sets.

Simultaneous Equations

This chapter governs the mechanics of exponential notation and the foundational laws for manipulating powers. You will master these operations to establish the technical proficiency required for solving complex exponential equations and performing the logarithmic transformations essential to scientific and financial data analysis.

You will master: applying the product, quotient, and power laws; evaluating zero, negative, and fractional indices; and simplifying complex exponential expressions through systematic reduction.

Indices

This chapter covers the inverse operation of fraction addition by breaking down complex rational expressions into simpler parts. Mastery of this decomposition is a prerequisite for advanced calculus and engineering system analysis.

You will master identifying proper and improper functions; decomposing expressions with distinct or repeated linear factors; resolving irreducible quadratic denominators; and applying polynomial long division to handle high-degree numerators.

Partial Fractions

This chapter governs the algebra of non-equality and region-based constraints. You will master the rigorous handling of directionality in mathematical relationships, establishing the essential logic required for economic optimisation, engineering tolerance analysis, and defining valid data ranges in computational algorithms.

You will master: executing sign-reversal rules during manipulation; solving linear, quadratic, and rational inequalities; using interval notation; and shading valid regions.

This chapter establishes the inverse relationship between powers and exponents to handle nonlinear data. Mastery of logarithmic transformations is essential for solving complex exponential equations and modelling growth patterns in engineering and financial sectors.

You will master: converting between index and logarithmic forms; applying the product, quotient, and power laws; executing the change of base formula; and solving algebraic equations involving unknown exponents or bases.

Logarithms

This chapter covers surds, which are roots that do not have whole number answers. You must learn to use them to keep your calculations exact, as using decimals in engineering and science leads to errors.

You will master simplifying and performing arithmetic on surds; rationalising denominators using conjugates; finding square roots of compound surds; and solving algebraic equations involving radical terms.

Surds

This chapter governs the synthesis of indices and logarithms to solve equations where variables appear as exponents. You will master the algebraic techniques required to isolate and resolve unknown indices, providing essential analytical tools for modelling exponential growth, decay constants, and complex scaling in engineering and financial data.

You will master: equating bases for direct solution; applying logarithmic transformations; reducing equations to quadratic forms; and solving non-linear simultaneous systems involving mixed bases.

Equations with Unknown Index

Mathematics requires absolute precision. This course provides a rigorous grounding in real number operations, from integers and rational numbers to complex systems and algebraic laws. You will learn to handle polynomials, solve equations ranging from linear to biquadratic, and navigate simultaneous systems. The syllabus covers inequalities, sign tables, partial fractions, indices, logarithms, and the systematic simplification of surds.

These tools are essential for success in engineering, accounting, and the sciences. Clear mathematical thinking allows you to model financial risks, calculate structural loads, and write efficient computer code. Proficiency in these operations ensures accuracy in any career that relies on quantitative data and logical deduction.

You will gain the ability to classify number systems, apply algebraic theorems, and solve complex equations in one or more unknowns. You will acquire the skills to manipulate inequalities, resolve algebraic fractions, and simplify expressions using the laws of indices and logarithms. The course provides the technical competence required to handle surds and find roots of compound expressions effectively.

This training is built for undergraduate foundation students and secondary school leavers entering university. It provides a necessary bridge for anyone needing to strengthen their mathematical base before advanced study. Even those in non-technical roles will find value in the disciplined analytical approach required to master these foundational concepts.

operations-with-real-numbers-mathematics-undergraduate

This chapter moves from the general definition of a function to a systematic classification of key function families. We will identify and analyse the core algebraic types - including polynomial, rational, and piecewise functions - that form the basis of mathematical modelling across scientific disciplines.

By the end of this chapter, you will be able to: classify functions as polynomial, rational, or algebraic; determine the natural domain for each of these types; interpret and analyse piecewise-defined functions; and test any function for symmetry.

Kinds of Real-Valued Functions

This chapter establishes the foundational concepts of the real number system. A command of these definitions is a prerequisite for defining and analysing the functions that form the core of this course.

By the end of this chapter, you will be able to: differentiate between key number systems from natural to real; define and represent intervals on the real line; and correctly apply the mathematical concept of infinity.

This chapter introduces the function - the central object of study in calculus. We will formally define what constitutes a real-valued function and establish the critical concepts of its valid inputs (domain) and possible outputs (range).

By the end of this chapter, you will be able to: formally define a function; precisely calculate the domain for various real-valued functions; and understand the meaning and importance of a function's range.

Real-Valued Functions

This chapter covers transcendental functions, the non-algebraic tools used to model natural phenomena like population growth, radioactive decay, and wave mechanics. We will systematically analyse the properties and graphs of exponential, logarithmic, trigonometric, and hyperbolic functions.

By the end of this chapter, you will be able to: differentiate between algebraic and transcendental functions; analyse the domains and graphs of exponential, logarithmic, and trigonometric types; and define their corresponding inverse functions.

Transcendental Functions

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

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

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

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

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

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

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

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

Mathematical Methods I

functions-and-their-graphs-single-variable-calculus

Single-Variable Calculus

Analysis of frames under various loading conditions.

Frames

Analysis of machines under various loading conditions.

Machines

Meaning, classification, load transmission and modelling of planar trusses.

Planar Trusses (1)

Analysis of planar trusses by the method of sections.

Planar Trusses (3)

Analysis of planar trusses by the method of joints.

Planar Trusses (2)

Modelling and analysis of space trusses - by methods of joints and sections.

Space Trusses

Welcome to the course, review of fundamental concepts - equilibrium of rigid bodies, internal forces, external forces, differences between trusses, frames and machines.

Analysis of trusses, frames and machines.

analysis-of-structures-engineering-mechanics

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

Analysis of rectilinear motion with variable acceleration.

General Rectilinear Motion

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

Special Rectilinear Motion (2)

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

Curvilinear Motion (3)

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

Curvilinear Motion (1)

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

Curvilinear Motion (2)

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

Special Rectilinear Motion (1)

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

Graphical Analysis

Do you want to learn how to describe and analyze the motion of particles in one and two dimensions?

Do you want to apply your knowledge of kinematics to solve real-world problems in engineering, physics, and sports?

Do you want to master the use of different coordinate systems and reference frames to simplify your calculations and enhance your understanding?

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

Engineering Mechanics: Kinematics of Particles comprehensively addresses the fundamental concepts and principles of particle kinematics. You will learn how to:

- Define and measure the position, velocity, and acceleration of a particle moving along a straight or curved path.

- Use various methods to determine the motion of a particle, such as equations of motion, graphical solutions, and numerical solutions.

- Apply the concepts of relative and dependent motion to analyze the motion of several particles or connected bodies.

- Choose the most suitable coordinate system for a given problem, such as rectangular, polar, normal-tangential, or radial-transverse coordinates.

- Understand the effects of different reference frames on the observed motion of a particle, such as inertial, non-inertial, or rotating frames.

By the end of this course, you will have a solid foundation in particle kinematics that will enable you to tackle more advanced topics in dynamics, mechanics, and other fields of engineering and science. You will also have the skills and confidence to apply your knowledge to real-world situations, such as the trajectory of a snowboarder, the orbital speed of a satellite, or the accelerations during acrobatic flying.

This course is designed for students, engineers, and enthusiasts who have a basic background in calculus, physics, and vector algebra. 

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

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

kinematics-of-particles-engineering-mechanics

Conditional permutation deals with arrangements limited by specific rules. You will learn to count outcomes when items must stay together or stay apart. This logic is essential for advanced scheduling and security where specific conditions apply.

You will master the tie-together method for items that stay together; apply the gap method for items that must stay apart; solve problems with fixed positions; and calculate arrangements with restricted letter and digit placements.

Conditional Permutation

Permutation with identical objects covers arrangements where some items are not distinguishable. Swapping identical items creates no new pattern, so you must divide to find unique results. This is essential for calculating arrangements in words, passwords, and digital data accurately.

You will master the formula for n items with repetitions; calculate arrangements for words with repeated letters; solve grid-based path problems; and use factorial division to remove duplicate counts.

Permutation with Identical Objects

This chapter introduces the logic of counting required for all arrangement and selection problems. You will master the foundational rules used to calculate total outcomes without manual listing, forming the essential groundwork for the entire course.

You will understand and apply the product rule for sequential events; the sum rule for separate choices; the difference rule for total minus unwanted cases; and the division rule to remove duplicate counts.

Permutation focuses on the arrangement of objects where the specific order is essential. You will learn to calculate total outcomes when selecting and ordering items from a set, a skill required for creating secure PINs and scheduling tasks. This chapter provides the mathematical formulas needed to handle arrangements of all available items or just a specific portion of them.

You will master the use of factorials to count arrangements of all n objects; apply the nPr formula to arrange r items from a larger set; and solve practical problems involving distinct objects in fixed positions.

Permutation

Cyclic permutation covers arrangements in a circle where the starting position is not fixed. You will learn to remove repeated patterns to ensure accurate counting. This section explains the difference between arrangements viewed from one side and those that can be turned over.

You will master the formula for circular arrangements where clockwise and anticlockwise orders differ; calculate unique patterns for items that can be flipped like beads; and solve problems involving symmetry.

Cyclic Permutation

This chapter applies combinatorial logic to solve geometry problems involving points, lines, and shapes. You will learn to calculate the number of possible geometric figures that can be formed from a given set of points, which is essential for spatial reasoning and advanced coordinate geometry.

By the end of this chapter, you will master calculating the number of straight lines from points; determining the number of triangles and quadrilaterals; and finding the total diagonals in a polygon.

Geometric Applications

Derangements cover scenarios where no item in a set returns to its original position. This chapter explains how to count failed matches, such as putting letters into wrong envelopes or seating people in different chairs. Mastering this prevents overcounting and solves problems where specific items must not occupy their natural spots.

You will learn the derangement formula, calculate subfactorials for small sets, solve problems with restricted positions, and apply these rules to real-world logic puzzles.

Derangements

Combination focuses on selection where order does not matter. It is essential for picking committees or groups where picking A then B is the same as B then A. You will learn to identify selection tasks to avoid overcounting and ensure accurate results.

You will master the nCr formula; solve committee problems with group restrictions; calculate lines and triangles in geometry; and handle selections from multiple sets.

Combination

Stop counting one by one. This course provides the mathematical tools to calculate arrangements and selections with speed. You will master the fundamental counting rules including product, addition, subtraction, and division. The curriculum covers linear and cyclic permutations, identical objects, and restricted placements where items must be together or apart. We conclude with combinations, derangements, and the calculation of shapes within geometric frameworks.

Counting is the engine of probability and modern computing. These skills are vital for cryptography, software development, and statistical analysis. You will apply these methods to calculate network paths, secure passwords, and optimise logistics. In any technical career, the ability to quantify possibilities is the difference between guessing and knowing.

You will solve complex arrangement problems using standard formulas and logical shortcuts. You will handle specific constraints like fixed positions or items that cannot be next to each other. You will learn to distinguish between permutations and combinations in practical scenarios. You will also calculate the number of lines, triangles, and diagonals in geometric figures using combinatorial principles.

This foundation is for undergraduate students and secondary school leavers aiming for high scores in competitive exams. It is also essential for professionals in engineering, finance, and data science who require a refresher on discrete mathematics. Anyone seeking to improve their logical deduction and analytical speed will find value here.

permutation-and-combination-mathematics-undergraduate

This chapter covers determinants, the specific values used to identify singular matrices and solve linear systems. Mastering these is vital for calculating inverses and analysing matrix properties.

You will master evaluating determinants of any order; applying minors and cofactors; using algebraic properties to simplify calculations; and solving linear systems using Cramer's rule.

Determinants

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

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

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

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

Courses

Introduction to Physics (Undergraduate Foundation)

Statics of Particles - Engineering Mechanics (Undergraduate Advanced)

Mathematical Induction - Mathematics (Undergraduate Foundation)

Set Theory - Mathematics (Undergraduate Foundation)

Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

Introduction to Chemistry (Undergraduate Foundation)

Operations with Real Numbers - Mathematics (Undergraduate Foundation)

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

Analysis of Structures - Engineering Mechanics (Undergraduate Advanced)

Kinematics of Particles - Engineering Mechanics (Undergraduate Advanced)

Permutation and Combination - Mathematics (Undergraduate Foundation)

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