NUC CCMAS

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.

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Mathematics

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.

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Master the algebraic rules governing ordered lists of numbers and their total sums. This course establishes a solid foundation in the mechanics of sequences and series. We investigate precise definitions for arithmetic and geometric progressions; use formal notation for general terms; and handle finite and infinite series using sigma notation. The curriculum focuses on the structural properties required for university-level mathematical analysis.

Knowing how to handle numerical patterns is vital for many modern careers. Financial analysts use geometric series to calculate compound interest, loan repayments, and annuities. Computer scientists use sequence structures to organise data sets and analyse computer loops. This knowledge is necessary for measuring growth, decay, and accumulation in business and science with absolute accuracy.

You will learn to identify and define sequences using general terms and recurrence formulas. You will calculate the nth term and the sum of terms for arithmetic, geometric, and harmonic progressions. You will master sigma notation; determine when infinite series converge; convert recurring decimals into fractions; and use formulas to sum natural numbers, squares, and cubes.

This course is for students entering university foundation programmes in mathematics, finance, or computer science. It serves as an intensive refresher for professionals returning to academia or shifting into roles that demand precise numerical work. Even those outside these fields will benefit from the sharp logical thinking and problem-solving speed developed through pattern analysis.

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This course provides a rigorous, in-depth analysis of quadratic equations. It covers all methods for solving quadratics, determining the nature of their roots using the discriminant, and constructing equations from given roots. A full command of this topic is a cornerstone of algebra.

Quadratic models are essential in the physical and financial sciences. They are used in physics to describe projectile motion, in engineering to design parabolic structures like antennas, and in finance for profit optimisation. This is the mathematics of trajectories and optimisation.

By the end of this course, you will be able to solve any quadratic equation by factorisation, completing the square, or the quadratic formula, use the discriminant to determine the nature of the roots, apply the sum and product of roots to solve problems, and construct a quadratic equation from a given set of roots.

This course is critical for first-year university students in mathematics, physics, engineering, and economics. It provides the necessary algebraic foundation for calculus, mechanics, and any field involving the optimisation of non-linear models.

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Mathematical induction proves a statement is true for every whole number using a starting point and a logical link. It works like a chain reaction where one step confirms the next. This course explains the core principle and applies it to many types of problems. You will study standard series, fractional series, divisibility, and inequalities. The content also covers recursive sequences, matrix powers, and set theory to give you a complete understanding of the method.

Programmers use this logic to check that software code works without mistakes. Engineers use it to prove that formulas for structural designs or machines are safe. This skill is vital for anyone in technology, finance, or data science because it makes logical thinking a clear, repeatable process. It removes guesswork and provides the certainty needed for professional work in any technical field.

You will learn the three-step induction method to solve different kinds of mathematical proofs. You will prove formulas for series, check if expressions are divisible, and handle difficult inequalities. You will also find general formulas for repeating sequences and solve problems involving matrices and sets. By the end, you will write clear, logical proofs that are required for university mathematics examinations.

This course is for university students starting science or engineering degrees and senior secondary school students preparing for higher education. It is also helpful for workers who want to improve their reasoning and problem-solving. Even those not studying mathematics will benefit from the clear way of thinking this course teaches. It provides the basic skills needed for any career that requires logic and proof.

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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.

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Stop manually multiplying brackets. This course teaches the systematic expansion of binomial expressions using Pascal's triangle and the formal Binomial Theorem. We cover the fundamental proof for positive integers before moving to individual term identification and the general expansion for negative or fractional powers. You will master the mechanics of series expansion from simple squares to complex infinite series.

The Binomial Theorem is a core tool in probability, statistics, and financial engineering. It allows for the approximation of complex functions and the calculation of compounding interest or risk factors. Engineers and data scientists use these principles to manage error margins and optimise algorithms. Understanding these patterns is essential for any career involving quantitative analysis or technical forecasting.

You will expand binomials to any power and identify specific terms within a series without full expansion. You will demonstrate the theorem's proof and apply Pascal's triangle for rapid computation. You will also calculate expansions for non-integer indices and determine the range of validity for these series. These skills enable the simplification of advanced algebraic expressions.

This curriculum is for undergraduate students and secondary school leavers entering science or technology tracks. It provides the necessary foundation for engineering, physics, and economics degrees. Professionals needing a mathematical refresher for data analysis will find the direct approach efficient. Any learner requiring precise algebraic tools for higher education will gain immediate value.

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

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

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

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

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Mathematical Methods

This course provides a complete guide to trigonometry, from the principles of circular measure to functions of any angle. It covers the unit circle definitions and culminates in a full treatment of the addition and factor formulae. This is the mathematical language of cycles, waves, and angles.

A command of trigonometry is essential for any field that models periodic or geometric systems. It is used extensively in physics to analyse waves and oscillations, in engineering for structural analysis and signal processing, and in computer graphics for rotations and 3D modelling.

By the end of this course, you will be able to convert between degrees and radians, define the six trigonometric functions for any angle using the unit circle, and apply the addition and factor formulae to manipulate and simplify trigonometric expressions and solve equations.

This course is a mandatory prerequisite for any student of mathematics, physics, or engineering. It provides the necessary foundation for the study of calculus, complex numbers, and vector analysis.

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

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

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

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

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Linear Algebra

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.

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.

Elementary Mathematics I

Algebra and Trigonometry

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.

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Physics

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.

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Dynamics is the study of why objects move, and Newton's laws of motion provide the definitive mathematical framework for this analysis. This course transitions from kinematics to the rigorous application of force vectors, covering inertia, the quantitative relationship of mass and acceleration, and the necessity of action-reaction pairs. You will master the mechanics of special forces including gravity, tension, and springs, while resolving complex resistive interactions across static, kinetic, and fluid friction regimes.

Every mechanical system - from civil engineering structures to aerospace propulsion - operates under these foundational principles. Understanding the interaction of forces is essential for predicting system failure, calculating vehicular safety margins, and designing efficient machinery. This knowledge provides the analytical tools required to solve real-world problems involving particle equilibrium and dynamic acceleration in both linear and circular paths.

By the end of this course, you will be able to construct precise free-body diagrams to isolate bodies from their surroundings. You will acquire the technical skill to apply the second law to multi-force systems, calculate centripetal force requirements for uniform circular motion, and utilise the laws of equilibrium to solve for unknown force magnitudes and directions. These skills establish the mathematical competence required for advanced modules in work, energy, and momentum.

This course is a mandatory foundation for first-year university students of physics and engineering. It is equally beneficial for technical professionals needing a refresher on classical mechanics and pre-university students seeking a rigorous introduction to undergraduate dynamics. Mastery of these laws ensures a logical, structured approach to any scientific inquiry involving motion.

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This course provides an alternative, and often more efficient, approach to solving mechanics problems using the principles of work, energy, and momentum. It develops the work-energy theorem and the foundational laws of conservation of energy and conservation of linear momentum. These scalar (energy) and vector (momentum) methods are critical for analysing complex systems.

The conservation laws are among the most fundamental and powerful principles in all of science. They are applied in every field, from analysing planetary motion and particle collisions to understanding chemical reactions and engineering efficient machines. This course provides the mechanical foundation for these universal laws.

By the end of this course, you will be able to calculate the work done by a constant or variable force, apply the work-energy theorem to relate work and kinetic energy, solve problems using the principle of conservation of mechanical energy involving kinetic and potential energy, and apply the law of conservation of linear momentum to analyse collisions.

This course is a core requirement for all first-year university students of physics and engineering. It builds directly upon Newtonian dynamics and is the essential prerequisite for studying thermodynamics, fluid mechanics, and modern physics.

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This course extends the principles of linear mechanics to rotational motion. It provides a complete analysis of the dynamics of rotating objects, covering the concepts of torque, angular momentum, and moment of inertia. Mastery of this material is essential for understanding any system that spins or orbits.

The principles of rotational dynamics are fundamental to engineering and physics. They are required to analyse the operation of engines, turbines, and gyroscopes, and to model the orbital mechanics of planets and satellites. This course provides the required analytical tools for these complex systems.

By the end of this course, you will be able to calculate torque for a given force, determine the moment of inertia for simple objects, apply the rotational equivalent of Newton's second law, and solve problems using the principle of conservation of angular momentum.

This course is designed for first-year university students of physics and engineering. It is a mandatory course that builds directly on Newtonian dynamics and is a prerequisite for studying planetary mechanics and rigid body dynamics.

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This course provides a complete treatment of Newton's law of universal gravitation. It covers the principles governing the attractive force between masses, the concepts of gravitational fields and potential energy, and culminates in the application of these laws to the orbital mechanics of planets and satellites.

The law of gravitation is a fundamental principle of the cosmos. It is essential for understanding the motion of celestial bodies, launching and maintaining artificial satellites for communications and Earth observation, and for calculating interplanetary trajectories. This is the physics that governs the structure of the solar system and the universe.

By the end of this course, you will be able to apply Newton's law of universal gravitation to calculate the force between two masses, determine the gravitational potential energy of a system, explain Kepler's laws of planetary motion, and solve problems involving the orbital velocity and period of satellites.

This course is a mandatory part of the curriculum for first-year university students of physics and engineering. It directly builds upon the principles of rotational motion and dynamics and is a critical prerequisite for the study of astrophysics and celestial mechanics.

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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

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.

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Chemistry

This course provides a complete guide to the modern theory of the atom. It traces the historical development of atomic models, from Dalton's foundational theory to the modern understanding of electronic structure. The material covers subatomic particles, the contributions of Thomson and Rutherford, the Bohr model, wave-particle duality, and culminates in a full treatment of electronic configuration and its direct relationship to the periodic trends of the elements.

A command of atomic theory is the absolute foundation of modern chemistry. The electronic structure of the atom dictates all chemical properties and bonding behaviour. This knowledge is essential for understanding the periodic table, predicting chemical reactions, and is the prerequisite for the study of spectroscopy, materials science, and quantum mechanics.

By the end of this course, you will be able to describe the historical evolution of atomic theory. You will also be able to explain the atom's structure, including the roles of protons, neutrons, and electrons. You will determine the electronic configuration of any element and use periodic trends to predict and justify atomic properties like size, ionisation potential, and electronegativity.

This course is for students who have completed an introductory chemistry course. It is a mandatory prerequisite for any student pursuing a degree in chemistry, chemical engineering, materials science, or physics.

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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.

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

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

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

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

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Grasp the fundamental language of chemistry through Stoichiometry of Composition. This concise undergraduate-foundation course systematically establishes core quantitative concepts essential for all subsequent chemistry studies. We will precisely define and calculate relative atomic mass, master the critical mole concept to transition between the microscopic and macroscopic worlds, determine molar masses, and then apply these principles to calculate percent composition and accurately derive both empirical and molecular formulae from experimental data. The content is structured for immediate application, moving from foundational definitions to complex problem-solving.

Quantitative chemistry is not abstract theory; it is the practical basis for chemical synthesis and analysis across science and industry. Learners will develop the ability to accurately predict reactant and product ratios in chemical reactions, interpret laboratory data for compound identification, and correctly formulate materials in fields such as chemical engineering, pharmaceuticals, and materials science. Mastery of these stoichiometric calculations is non-negotiable for success in laboratory work and industrial scale-up.

Upon completion, you will be able to calculate and interpret relative atomic and molecular masses; confidently apply the mole concept to interconvert mass, moles, and number of particles; calculate the molar mass of any compound; precisely determine the percent composition of a substance; and successfully solve multi-step problems to deduce a compound's empirical and molecular formulae. The course culminates in extensive practice to secure computational fluency.

This course is essential for undergraduate students beginning any science or engineering programme that requires a solid foundation in Chemistry, particularly those preparing for university-level coursework. It also serves as an intensive, structured refresher for advanced students, technical professionals needing to reinforce core computational skills, and anyone using UniDrills to self-study for competitive professional examinations.

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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.

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Precision in volumetric analysis is the difference between experimental success and catastrophic failure in the laboratory. This course provides a rigorous mathematical framework for quantifying dissolved substances, beginning with fundamental concentration units like molarity and mass concentration before progressing to the principles of dilution and standard solution preparation. You will master the stoichiometric requirements of complex chemical interactions, including precipitation, acid-base neutralisation, and redox reactions, through a series of intensive worked examples covering advanced techniques such as back-titration and standardisation.

Quantitative titration skills are the industrial standard for quality control and analytical research. Proficiency in solution stoichiometry allows for the exact determination of drug purity in pharmaceuticals, contaminant levels in environmental monitoring, and reactant concentrations in industrial chemical synthesis. Mastering these computational methods ensures the accuracy required for professional competency in any clinical or academic laboratory setting.

By the conclusion of this course, you will be able to calculate precise concentrations from raw experimental data across multiple reaction types. You will acquire the technical ability to prepare primary standard solutions, apply dilution laws to reach target molarities, resolve limiting reagent problems in aqueous phases, and execute complex multi-step stoichiometric calculations for redox and back-titration scenarios. These skills are essential for converting laboratory observations into reportable analytical results.

This course is a mandatory requirement for undergraduate students in Chemistry, Pharmacy, Biochemistry, and Chemical Engineering. It also serves as a critical computational review for laboratory technicians and research assistants preparing for technical certification or professional exams. Even for those in peripheral scientific fields, the rigorous logic and mathematical precision developed here provide a necessary foundation for any discipline requiring core analytical data processing.

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This course provides a complete guide to chemical equilibria, the state where the rates of forward and reverse reactions are equal. It covers the law of mass action, the definition and calculation of the equilibrium constant, and the factors that can cause a shift in the equilibrium position. The course then applies these principles to the study of aqueous equilibria, including the properties of acids, bases, and salts, and the calculation of pH.

The principles of equilibrium govern the outcomes of all reversible reactions, from industrial synthesis to biological processes. A command of this topic is essential for chemists and chemical engineers to maximise the yield of a desired product, for environmental scientists to understand natural water systems, and for biochemists to analyse metabolic pathways.

By the end of this course, you will be able to write the expression for the equilibrium constant for any reversible reaction, use Le Chatelier's principle to predict how a system at equilibrium will respond to changes in concentration, pressure, or temperature, and perform calculations involving the pH of acidic and basic solutions.

This course is for students who have a solid foundation in stoichiometry. It is a mandatory course for all students of chemistry and chemical engineering and is a direct prerequisite for the study of analytical chemistry, biochemistry, and environmental science.

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Energy drives every chemical change in our universe. This course explains how heat, work, and internal energy dictate the behaviour of matter from simple phase changes to complex chemical reactions. You will master the laws of thermodynamics, enthalpy calculations, entropy changes, and the ultimate predictor of spontaneity, Gibbs free energy.

These principles are the backbone of modern industry. Chemical engineers use them to design efficient industrial reactors and cooling systems. Materials scientists apply them to develop better batteries and energy sources, while biochemists use these same laws to understand the energy flow within living cells. Mastering these concepts is essential for anyone aiming to solve energy-related problems in the real world.

By the end of this course, you will be able to distinguish between open, closed, and isolated systems and calculate heat changes using specific heat capacities. You will apply Hess’s law and bond energies to find reaction enthalpies and use the second law of thermodynamics to predict disorder through entropy. Finally, you will calculate Gibbs free energy to determine exactly if and when a reaction will occur naturally under various temperatures.

This course is built for undergraduate students in chemistry, chemical engineering, and materials science who need a solid foundation in physical chemistry. It also benefits secondary school leavers preparing for university-level science and professionals looking to refresh their technical knowledge of energy systems. Even those outside these fields will gain a logical framework for understanding how energy and disorder shape the physical world.

chemical-thermodynamics-chemistry-undergraduate-foundation

This course provides a complete guide to chemical kinetics, the study of the rates and mechanisms of chemical reactions. It covers the formal definition of reaction rate, the concept of reaction order, and the determination of rate laws from experimental data. The material also introduces the collision theory, the role of activation energy, and the Arrhenius equation.

Chemical kinetics is essential for controlling chemical reactions in industrial manufacturing, pharmaceutical development, and environmental science. The principles are used to optimise production yields by speeding up desired reactions, to develop catalysts that lower energy consumption, and to understand the complex reaction pathways in atmospheric and biological systems.

By the end of this course, you will be able to define the rate of a reaction and determine the rate law and rate constant from experimental data. You will also be able to use the concept of activation energy to explain the effect of temperature on reaction rate and understand the basic principles of reaction mechanisms.

This course is for students who have a solid foundation in stoichiometry and chemical equilibria. It is a mandatory course for all students of chemistry and chemical engineering and is a direct prerequisite for the study of physical chemistry, industrial chemistry, and biochemistry.

chemical-kinetics-chemistry-undergraduate-foundation

This course provides a complete guide to electrochemistry, the study of the relationship between chemical reactions and electrical energy. It covers the principles of oxidation-reduction (redox) reactions and their application in electrochemical cells. The material details the structure and function of both galvanic (voltaic) cells, which produce electricity, and electrolytic cells, which use electricity to drive non-spontaneous reactions.

Electrochemistry is the science behind all modern portable energy storage and industrial metal production. The principles covered are the basis for batteries, fuel cells, and rechargeable power sources. This knowledge is also critical for understanding corrosion, electroplating, and the industrial-scale electrolysis used to produce fundamental materials like aluminium and chlorine.

By the end of this course, you will be able to identify the components of any electrochemical cell and predict the direction of electron flow. You will also be able to calculate standard cell potentials using a table of standard reduction potentials, apply Faraday's laws to electrolytic calculations, and use the Nernst equation to determine cell potential under non-standard conditions.

This course is for students who have a solid foundation in stoichiometry and redox reactions. It is a mandatory course for all students of chemistry and chemical engineering and is a direct prerequisite for the study of analytical chemistry, materials science, and electrical engineering.

electrochemistry-undergraduate-foundation

This course provides a complete introduction to radioactivity and nuclear chemistry. It covers the principles of radioactive disintegration, the different types of decay, and the concept of half-life. The material also introduces the powerful processes of nuclear fission and fusion, and explores the practical uses of radioisotopes.

An understanding of radioactivity is essential in the modern world. These principles are the foundation of nuclear power generation, medical imaging techniques like PET scans, and carbon dating in archaeology and geology. This knowledge is critical for applications in medicine, energy production, and environmental science.

By the end of this course, you will be able to describe the process of radioactive disintegration and identify the different types of nuclear radiation. You will also be able to explain the concepts of nuclear fission and fusion and describe the key applications of radioisotopes in medicine and industry.

This course is for students who have a solid foundation in atomic theory. It is a mandatory course for any student of nuclear engineering or health physics and provides essential knowledge for students of chemistry, physics, and medicine.

radioactivity-chemistry-undergraduate-foundation

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.

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 

General Chemistry I

OAU, Ife

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.

statics-of-particles-engineering-mechanics-undergraduate

Engineering Mechanics

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.

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

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

Analysis of trusses, frames and machines.

analysis-of-structures-engineering-mechanics

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

Analysis of centroids and moments of inertia.

centroids-and-centres-of-gravity-engineering-mechanics

Analysis of the second moments of areas and its applications.

moments-of-inertia-engineering-mechanics-undergraduate

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

method-of-virtual-work-engineering-mechanics

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

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

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

Statics

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

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

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

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

vector-algebra-and-foundational-geometry-vectors

Vectors

This course moves beyond basic vector algebra to cover the three critical methods of vector multiplication and their geometric applications. We systematically analyse the scalar (dot) product and vector (cross) product, followed by both scalar and vector triple products. The curriculum concludes by consolidating these skills to solve abstract vector equations and formulate the vector equations of straight lines in three dimensions.

These operations are not abstract; they are the language of physical science and engineering. The scalar product is the standard tool for calculating work done by a force and projecting vectors. The vector product is indispensable for defining torque, angular momentum, and magnetic forces. Mastery of these products allows for precise analysis of forces, rotations, and spatial relationships in real-world systems.

Upon completion, you will calculate scalar, vector, and triple products for any given vectors. You will apply these products to solve geometric problems, including testing for perpendicularity and parallelism and finding the area of a parallelogram. Critically, you will master the techniques required to solve complex vector equations and derive the vector equation of a line using various input conditions.

This course is designed for first-year undergraduate students in Engineering, Physics, and Applied Mathematics. It requires prior knowledge of basic vector addition and scalar multiplication. This programme provides the necessary rigorous foundation in vector products, making it a critical prerequisite for subsequent study in classical mechanics, electromagnetism, and linear algebra.

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

This course applies the principles of calculus to vector-valued functions. We move beyond static vectors to analyse how they change with respect to a parameter, such as time. The curriculum provides a rigorous treatment of vector differentiation, including specific rules for scalar and vector triple products. It then introduces vector integration, covering both anti-derivatives and the foundational concept of the line integral.

Vector calculus is the essential language of dynamics and physics. Its primary application is kinematics - the mathematical description of motion. Engineers use these methods to model trajectories, velocities, and accelerations in mechanical, aerospace, and robotic systems. Physicists apply them to describe particle paths and force fields. These tools are non-negotiable for any study involving motion in two or three dimensions.

Upon completion, you will be able to differentiate any vector-valued function and correctly apply the product rules. You will master the integration of vectors to solve initial-value problems, allowing you to determine position from acceleration or velocity. You will also gain the ability to set up and compute basic line integrals, a direct prerequisite for more advanced topics in vector analysis.

This course is a mandatory component for undergraduate students in Engineering, Physics, and Applied Mathematics. It directly follows foundational courses in single-variable calculus and vector algebra (including products). It is also an essential module for computer science students focusing on 3D graphics or physics simulations, and a critical refresher for anyone preparing for advanced courses in fluid dynamics or electromagnetism.

differentiation-and-integration-of-vector-valued-functions

This course provides the complete foundation in Two-Dimensional Coordinate Geometry, establishing the link between algebraic equations and geometric shapes. We systematically cover the algebraic definitions and analysis of straight lines and all four conic sections - the circle, ellipse, parabola, and hyperbola. The curriculum concludes by applying differential calculus to derive tangents and normals to these curves.

Command of this geometry is essential for technical modelling in all physical sciences. These equations are used to define component paths in mechanical design and model trajectories in physics. For example, ellipses model orbits, and parabolas model projectile motion and reflector shapes. This course provides the indispensable toolkit for translating visual problems into computable algebraic forms.

Upon completion, you will master calculating gradients and distances for straight lines and formulating their equations in various forms. You will derive and manipulate the algebraic equations for all conic sections. Furthermore, you will apply differentiation to find the equations of tangents and normals to any curve at a specified point.

This course is mandatory for first-year undergraduate students in Engineering, Physics, and Applied Mathematics. It requires prior knowledge of basic algebra and differential calculus. This programme provides the necessary rigorous foundation in 2D spatial analysis, which is a critical prerequisite for advanced subjects like mechanics and multi-variable calculus.

vector-equations-of-lines-planes-and-conics-vectors

Geometry

This course provides a rigorous introduction to classical mechanics using the language of vectors. We cover the two main branches of the subject: dynamics, where you will analyze forces, equilibrium, work, energy, and moments; and kinematics, where you will describe the motion of particles using position, velocity, and acceleration. You will learn to analyze a wide range of scenarios, including projectile and circular motion.

Mechanics is the science of how things move and interact, forming the foundation of all physical sciences and engineering. This course is designed to build your problem-solving intuition by applying vector principles to tangible, real-world scenarios. You will learn to model physical systems mathematically, providing a powerful framework for understanding the world around you.

This programme is designed for students who have completed our introductory course on vector calculus. It is the ideal next step for first-year university students in physics, engineering, and other physical sciences. This course provides the essential foundation required before tackling more comprehensive topics in the main Engineering Mechanics learning track.

introduction-to-vector-mechanics-vectors-undergraduate

This comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry.

Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time.

While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.

Elementary Mathematics III

Vectors, Geometry and Dynamics

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.

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

Single-Variable Calculus

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

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

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

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

limits-of-functions-single-variable-calculus

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

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

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

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


continuity-of-functions-single-variable-calculus

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

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

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

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


differentiability-and-derivatives-of-functions

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

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

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

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

convergence-of-infinite-sequences-and-series-advanced

Advanced Calculus

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

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

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

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

analysis-of-infinite-sequences-and-series-real-analysis

Real Analysis

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

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

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

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

partial-differentiation-and-its-applications-multivariable

Multivariable Calculus

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

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

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

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

introduction-to-numerical-methods-undergraduate-foundation

Numerical Methods

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.

ordinary-differential-equations-mathematical-methods

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

Multiple integration; line, surface and volume integrals.

multiple-integration-and-its-applications-calculus

Calculus

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.

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.

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

Analytic Geometry

Do you want to learn how to manipulate and analyze scalar and vector fields using advanced calculus techniques? Do you want to understand the concepts and methods of scalar and vector products, gradient, divergence, curl, and Laplacian operators? Do you want to apply the principles of vector analysis to solve problems in physics, engineering, and other disciplines?

If you answered yes to any of these questions, then this course is for you!

In this course, you will learn the fundamentals of calculus of scalar and vector fields, which is the branch of mathematics that deals with functions and operators that map points in space to scalars or vectors. You will learn how to use different notations and conventions to express scalar and vector fields, such as Einstein's summation, Kronecker delta, and Levi-Civita symbols. You will learn how to perform scalar and vector products of vectors, which are useful for measuring angles, areas, and volumes. You will learn how to compute and interpret the gradient of a scalar field, which measures the rate and direction of change of a scalar function. You will learn how to compute and interpret the divergence and curl of a vector field, which measure the sources and vortices of a vector field. You will also learn how to use the Laplacian operator, which combines the divergence and the gradient, and is useful for studying heat conduction, electrostatics, and fluid dynamics.

This course will equip you with the skills and knowledge to solve various problems involving scalar and vector fields. You will be able to apply the concepts and methods of calculus of scalar and vector fields to fields such as physics, engineering, chemistry, biology, and more. You will also be able to appreciate the power of vector analysis theorems, such as Gauss', Green's, and Stokes' theorems, which relate the integrals of scalar and vector fields over different domains.

By the end of this course, you will be able to:

- Define and explain the meaning of scalars, vectors, and tensors

- Identify and use different notations and conventions for scalar and vector fields

- Perform scalar and vector products of vectors and calculate angles, areas, and volumes

- Compute and interpret the gradient of a scalar field and its properties

- Compute and interpret the divergence and curl of a vector field and their properties

- Compute and interpret the Laplacian of a scalar or a vector field and its applications

- Use different coordinate systems and bases to express scalar and vector fields and operators

- Compute and interpret the gradient, divergence, curl, and Laplacian in orthogonal curvilinear coordinates

- Recognize and use some special curvilinear coordinates, such as cylindrical and spherical coordinates

- Apply the vector analysis theorems, such as Gauss', Green's, and Stokes' theorems, to relate the integrals of scalar and vector fields over different domains

Created for students, engineers, scientists, and anyone passionate about learning the calculus of scalar and vector fields, this course assumes a basic background in calculus, linear algebra, and vector algebra. With engaging video lessons, interactive quizzes, practice problems, and supportive peer interactions, you'll embark on a journey of discovery and mastery like never before.

Seize the opportunity to advance your mathematical skills and unlock new problem-solving possibilities with an enrolment right away!

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

This course provides a clear and structured exploration of eigenvalues, eigenvectors, and diagonalization, focusing on both theory and real-world applications. 

You???ll learn how to compute eigenvalues and eigenvectors, understand their geometric significance, and apply diagonalization to simplify complex matrix operations. 

Topics include linear transformations, dynamical systems, and applications in physics, engineering, and machine learning. 

The course is designed for students, engineers, and data scientists seeking a strong foundation in matrix methods. By the end, you'll confidently apply these concepts in problem-solving and computational modeling.

eigenvalues-eigenvectors-and-diagonalization-of-matrices

Complex numbers, variables, functions and series in the complex plane.

complex-variables-mathematical-methods-undergraduate

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

Beginner

Modern web development is not about memorizing code; it is about understanding the system you build for and mastering the tools of the trade. This course focuses on the non-negotiable foundations: how the web functions, how professionals think, and how to operate the tools that matter in real-world environments.

The skills taught here are not theoretical; they are used daily in every technical role. A command of the terminal, a properly configured editor, and version control are what separate efficient professionals from struggling amateurs. This is a practical knowledge required to contribute to projects and pass technical interviews.

You will be able to explain the lifecycle of a web request from a URL to a rendered page. You will configure a professional development environment in VS Code, manage your file system from the command line, and use Git and GitHub to track and share your work.

This course is built for aspiring developers and computer science students seeking to build a professional foundation. It is also essential for product managers, designers, and technical writers who need to understand development workflows to collaborate effectively with technical teams. No prior coding experience is required.

introduction-to-modern-web-development-concepts-and-tools

Web Development

HTML is not about memorizing tags; it is the professional practice of structuring information. This course teaches HTML5 by guiding you through the construction of a complete, portfolio-ready webpage. We move from a blank file, through a professional asset-preparation phase, to building a multi-section, feature-rich website based on a modern UI design.

A well-structured portfolio is a non-negotiable tool for any aspiring developer. The quality of your HTML directly impacts your site's performance, search ranking, and accessibility. This course teaches you to write the clean, semantic, and professional markup that separates a hobbyist's page from an impressive portfolio piece that gets you noticed.

You will master the full lifecycle of a modern HTML project. You will prepare all necessary assets using AI and design tools. You will structure a complete page with semantic landmarks, build complex components like project cards and interactive tables, and create a functional contact form. By the end, you will have a complete, well-structured project.

This course is designed for the absolute beginner with no prior coding experience. It is the essential starting point for aspiring developers and is invaluable for designers, content creators, and marketers who need to build or understand the fundamental structure of a professional website.

html-foundations-from-zero-to-your-first-web-page

Plain HTML is functional, but unstyled pages do not engage users. This course provides comprehensive training in modern CSS, guiding you from fundamental syntax and the box model to advanced, responsive layouts. You will transform a raw document into a professionally styled, multi-component webpage from scratch, learning the complete workflow for styling a real-world project.

Mastery of CSS is a non-negotiable skill for any web professional. The techniques covered are directly applicable to building professional portfolios, business websites, or the front end of any web application. This course equips you with the practical skills to translate design concepts into responsive, production-ready code for any device, ensuring your projects look polished and professional.

You will learn to write clean CSS and master selectors, specificity, and the box model. The course covers building a complete mobile-first layout with Flexbox and creating a consistent design system with CSS variables. You will finish by styling individual components like cards and forms, and controlling element context with the `position` property and `z-index`.

This programme is built for anyone with a basic knowledge of HTML, including aspiring front-end developers and university students. Experienced programmers will find it a direct path to modernising their layout skills, while UI/UX designers will gain a practical understanding of the medium for which they design.

css-foundations-style-your-first-web-page

A website without JavaScript is a static document. This course provides the foundational skills to make your webpages interactive. We cover the core language syntax, how to manipulate page elements in response to user events, and how to work with data structures and asynchronous code. You will apply these concepts directly to the portfolio project built in our CSS course, transforming it into a dynamic application.

JavaScript is the engine of the modern web, and proficiency in it is a core requirement for any web development role. This course is project-driven, focusing on adding real functionality to a live website. The skills you learn are directly applicable to building dynamic user interfaces, whether for personal projects, client work, or as part of a professional development team.

You will master core JavaScript syntax, including variables, functions, and conditional logic. Key skills include debugging in the browser, manipulating the DOM to change content, and handling user events. You will also learn to manage data with arrays and objects, fetch data from an API, store information with `localStorage`, and deploy your final, interactive project.

This programme is for anyone with a solid grasp of HTML and CSS. It is the essential next step for aspiring front-end developers, designers wanting to build interactive prototypes, and backend developers needing to understand client-side code.

javascript-foundations-your-first-interactive-web-page

This is the direct path to building professional-grade web development skills. This learning track is a comprehensive programme covering the entire modern front-end stack, engineered to take you from zero knowledge to possessing a practical, portfolio-worthy skillset. It moves logically from foundational web concepts and professional tools, through structuring content with HTML5, styling with modern CSS, and finally, building dynamic user experiences with JavaScript.

This programme is built for individuals starting a career in technology with no prior coding experience. It is the essential curriculum for aspiring front-end developers, full-stack engineers, and computer science students. It also serves professionals in adjacent roles - such as UI/UX designers and product managers - who require a practical understanding of web technologies to excel in their careers.

By the end of this learning track, you will have the ability to build, style, and launch a fully interactive, responsive website from a blank file. You will master the professional developer's toolkit - Git, the command line, and an AI-assisted editor - and write clean, semantic code. This track provides the foundational project and technical skills to confidently begin your career path toward junior developer roles and to build robust personal or business projects.

Modern Web Development Foundations

beginner-modern-web-development-foundations

From Zero to Your First Interactive Website

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

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

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

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

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

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

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

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

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

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

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

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

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

kinematics-of-particles-engineering-mechanics

This course will equip you with the skills and knowledge to tackle various engineering and scientific problems involving kinetics of particles, which is the branch of mechanics that deals with the relation between the forces acting on a particle and its resulting motion. From the basics of mechanics, dynamics, and kinetics to getting comfortable with Newton's second law and momentum methods, you will clearly understand how forces cause motion.

Boost your problem-solving skills and open up new career opportunities in fields like aerospace engineering, mechanical engineering, civil engineering, biomedical engineering, physics, chemistry, and more. Imagine being able to predict how a ball flies through the air, or understanding why a car behaves the way it does in a crash. This course helps you do these and many more!

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

- Explain the fundamentals of mechanics, dynamics, and kinetics

- Use Newton's second law to analyze how forces make bodies speed up or slow down

- Learn about energy, how forces do work, and how these relate to motion of bodies

- Figure out how collisions work and what motion happens before and after collisions

This course is designed for students, engineers, scientists, and anyone who is interested in learning the basics of kinetics of particles. The course assumes that you have a basic background in calculus, physics, vector algebra, and statics.

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

kinetics-of-particles-by-newtons-second-law-engineering

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

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

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

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

In this course, you will learn the fundamentals of two-dimensional kinematics of rigid bodies, which is the branch of mechanics that deals with the geometry of the motion of rigid bodies without considering the forces that cause it. You will learn how to use different coordinate systems and reference frames to express the position, velocity, and acceleration of various points on a rigid body in plane motion.

Empower yourself with the knowledge and skills needed to excel in diverse fields such as mechanical engineering, robotics, aerospace engineering, and beyond. Imagine designing a robotic arm that moves with precision, or optimizing the performance of a rotating machinery. These are some of the countless applications of rigid-body kinematics you will learn in this course.

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

- Understand the rotation of rigid bodies about fixed axes and its applications

- Analyze absolute motion to understand how rigid bodies move through space

- Explore relative velocity analysis to solve complex motion problems

- Master the concept of instantaneous centres of rotation for precise motion analysis

- Understand relative acceleration analysis to predict the behavior of moving bodies

- Analyze motion relative to a rotating frame to unravel the dynamics of rotating systems

Whether you're a seasoned professional looking to expand your knowledge or a curious beginner eager to explore the motion of rigid bodies, this course is for you.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tailored for students, engineers, scientists, and anyone passionate about learning the basics of 2D kinetics of rigid bodies, this course assumes a basic background in calculus, physics, vector algebra, and statics. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Dynamics

Do you want to learn how to work with abstract spaces and transformations that preserve their structure? Do you want to understand the concepts of vector subspaces, linear combinations, linear dependence, basis, dimension, coordinates, and properties of vector spaces? Do you want to master the skills of defining and manipulating linear maps, their kernels, images, matrix representations, and transition matrices?

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

Linear Algebra: Linear Vector Spaces and Linear Maps is a comprehensive and engaging course that covers the fundamentals of vector spaces and linear maps and their applications in mathematics and science. You will learn how to:

- Define and classify vector spaces and their subspaces over a given scalar field

- Perform operations on vectors using linear combinations and scalar multiplication

- Determine whether a set of vectors is linearly dependent or independent and find a basis and dimension for a vector space or subspace

- Find the coordinates of a vector with respect to a given basis and change the basis using transition matrices

- Define and classify linear maps between vector spaces and find their domains, codomains, ranges, and null spaces

- Find the kernel and image of a linear map and use them to determine whether a linear map is one-to-one or onto

- Represent a linear map using a matrix and perform matrix operations such as addition, multiplication, and inversion

- Use different methods and tools to solve systems of linear equations, such as Gaussian elimination, row reduction, and inverse matrices

This course is suitable for anyone who wants to learn or review the basics of vector spaces and linear maps and their applications. It is especially useful for students and professionals in algebra, geometry, analysis, differential equations, optimization, cryptography, computer graphics, data science, and other related fields.

By the end of this course, you will have a solid foundation of the theory and practice of vector spaces and linear maps and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vector spaces and linear maps.

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

linear-vector-spaces-linear-algebra-undergraduate

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

linear-maps-transformations-linear-algebra

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

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

Mathematical Methods II

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.

Learning Tracks

MTH 101: Elementary Mathematics I - Algebra and Trigonometry

PHY 101: General Physics I - Mechanics

CHM 101: General Chemistry I

MEE 205: Engineering Mechanics - Statics

MTH 103: Elementary Mathematics III - Vectors, Geometry and Dynamics

MTH 201: Mathematical Methods I

MTH 201: Mathematical Methods I

CHE 305: Engineering Analysis I

Modern Web Development Foundations - From Zero to Your First Interactive Website

MEE 206: Engineering Mechanics - Dynamics

MTH 202: Mathematical Methods II

GET 207: Applied Mechanics