Intermediate

This course moves beyond static documents. It teaches you to build dynamic, interactive web applications using the professional React ecosystem. You will master the fundamentals of React's component-based architecture, ensure your code is robust and error-free with TypeScript, and build production-ready applications using the Next.js framework. This is the modern standard for front-end development.

The skills taught here are a direct response to industry demand. Companies build scalable, maintainable applications with this exact stack: React for the user interface, TypeScript for safety, and Next.js for performance and structure. This is not academic theory; this is the practical skillset required to build complex, real-world products and to contribute effectively to a professional development team.

Upon completion, you will build full applications using React's component model and manage state with Hooks. You will write type-safe code using TypeScript to define props and state. You will structure a multi-page application using the Next.js App Router, fetch data from external sources, and understand modern rendering patterns like Server Components.

This course is designed for developers with a solid understanding of HTML, CSS, and vanilla JavaScript. It is the essential next step for aspiring front-end and full-stack engineers. It is also highly valuable for backend developers seeking to understand the modern front-end, and for UI/UX designers who want to build high-fidelity, functional prototypes.

react-foundations-building-modern-web-apps-with-typescript

Web Development

A front-end is only half the application. This course teaches you how to build the other half: the powerful, server-side API. We will use the modern, professional stack of Node.js, Express, and Prisma, with TypeScript enforcing type safety from the database to the API response. This is how robust, production-grade back-ends are built.

The skills taught here are a direct response to industry demand. Companies require fast, scalable, and maintainable back-end services. This stack allows you to build exactly that, providing a type-safe connection between your application and its data. This is the practical skillset required to build real-world products and secure a modern back-end or full-stack development role.

You will build a complete REST API from scratch using Node.js and Express. You will learn to model your database schema with Prisma, perform all core CRUD operations in a type-safe manner, and structure your application for professional-grade maintainability.

This course is designed for developers with a solid understanding of JavaScript or TypeScript who want to master back-end development. It is the essential next step for front-end developers moving to full-stack, as well as for back-end developers from other languages looking to learn the modern Node.js ecosystem.

node-js-foundations-building-type-safe-apis-with-express

A front-end and a back-end are useless in isolation. The real work of a developer is to make them communicate. This course teaches the final, critical step: integrating a front-end client with a back-end API to create a single, cohesive application, and then deploying that application to the web for the world to use. This is where you stop building parts and start building products.

An un-deployed application has zero value. The skills taught here bridge the gap between local development and a live, production-ready product that can handle real users. This is the complete, end-to-end workflow that employers expect and what is required to launch your own projects. It is the transition from writing code to shipping applications.

You will integrate a modern front-end with a back-end API. You will manage data flow, handle authentication, and prepare a full-stack application for a production environment. Finally, you will learn the principles of deployment and push your finished application to a live server.

This course is for the developer who has foundational knowledge of both front-end and back-end frameworks but has not yet combined them. It is the essential final step for those aiming for full-stack roles and for specialized developers who need to understand the complete application lifecycle to be effective.

full-stack-foundations-integrating-and-deploying-web

This learning track bridges the gap between knowing JavaScript and becoming a full-stack developer. You will stop writing isolated scripts and start building complete, modern web applications. We will construct a professional front-end with React and Next.js, build a type-safe back-end API with Node.js and Express, and then integrate and deploy the two halves into a single, cohesive product.

This programme is for the developer who has mastered the fundamentals of HTML, CSS, and JavaScript and is ready to build real-world applications. It is the essential next step for front-end developers aiming for full-stack roles, and for back-end developers seeking to master the modern JavaScript ecosystem.

At the end of this learning track, you will be able to build, integrate, and deploy a complete, type-safe, full-stack web application using the modern professional stack. This track provides the end-to-end skills required to secure a role as a modern full-stack web developer.

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

I'm a software engineer that specializes in frontend web development. My tech stack is HTML, CSS, Javascript, Typescript, React, Nextjs. 
I have over 4 years experience development web applications in different domains and industry. I'm so excited to share my knowledge and experience to new developers in the simplest and most engaging way possible. Cheers

Modern Full-Stack Development Foundations

intermediate-modern-full-stack-development-foundations

From Vanilla JS to Web Applications

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

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.

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.

Modern Web Development Foundations

beginner-modern-web-development-foundations

From Zero to Your First Interactive Website

OAU, Ife

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

Multiple integration; line, surface and volume integrals.

multiple-integration-and-its-applications-calculus

Calculus

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

Do you want to learn how to work with matrices and their properties, operations, and applications? Do you want to understand the concepts of determinants, eigenvalues, eigenvectors, diagonalization, quadratic and canonical forms? Do you want to master the skills of solving systems of linear equations, finding inverses, and computing matrix functions using different methods and tools?

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

This course covers the fundamentals of matrix theory and its applications in mathematics and science. You will learn how to:

- Define and classify matrices and their special types, such as symmetric, orthogonal, diagonal, and identity matrices

- Perform matrix addition, subtraction, multiplication, and scalar multiplication using the algebraic properties of matrices

- Find the transpose, conjugate, and adjoint of a matrix and use them to simplify matrix operations and expressions

- Perform elementary row and column transformations on matrices and use them to find the row echelon form, reduced row echelon form, rank, and nullity of a matrix

- Find the minors, cofactors, and determinants of matrices and use them to calculate the area, volume, and orientation of geometrical figures

- Find the inverse of a matrix using the adjoint method or the row operations method and use it to solve systems of linear equations

- Find the eigenvalues and eigenvectors of a matrix using the characteristic polynomial and the Cayley-Hamilton theorem and use them to analyze the behavior and stability of dynamical systems

- Diagonalize a matrix using the eigenvalues and eigenvectors and use it to compute matrix functions, such as polynomials, exponentials, sines, and cosines of matrices

- Find the quadratic and canonical forms of an equation using the coefficient matrix and the transformation matrix and use them to classify and graph conics and quadrics

- Use computer software, such as MS-Excel, MATLAB, and Python, to perform matrix operations and computations efficiently and accurately

This course is suitable for anyone who wants to learn or review the basics of matrix theory and its applications. It is especially useful for students and professionals in algebra, calculus, differential equations, linear programming, optimization, cryptography, computer graphics, data science, machine learning, and other related fields.

By the end of this course, you will have a firm grasp of the theory and applications of matrices and determinants. You will also be able to apply the knowledge and skills you gain to solve real-world problems and challenges that involve matrices.

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.

matrices-determinants-and-systems-of-linear-equations

Linear Algebra

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

Mathematical Methods

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

An introduction to numerical analysis - mathematical modelling, error analysis, numerical algorithms and pseudocodes.

introduction-to-numerical-analysis-numerical-methods

Numerical Methods

MATLAB fundamentals and its applications to numerical analysis.

introduction-to-programming-with-matlab-engineering

Engineering

Numerical solutions of equations in one variable.

solutions-of-equations-in-one-variable-numerical-analysis

Numerical Analysis

Lagrange polynomial interpolations and approximations.

interpolation-and-polynomial-approximation-numerical

Numerical differentiation (finite difference calculus) and its applications.

finite-differences-numerical-analysis-undergraduate

Solutions and applications of difference equations.

difference-equations-numerical-analysis-undergraduate

Numerical integration techniques and their applications.

integration-numerical-analysis-undergraduate-advanced

Numerical solutions of initial value problems for ordinary differential equations.

ordinary-differential-equations-numerical-analysis

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

Integral transforms (Laplace, Fourier, Mellin, Hankel and other transforms ), their inverses and applications to the solutions of ordinary differential equations.

integral-transforms-and-their-applications-mathematical

Series solutions of ordinary differential equations.

series-solutions-of-ordinary-differential-equations

Boundary value problems and Sturm–Liouville theory.

boundary-value-problems-ordinary-differential-equations

Ordinary Differential Equations

Advanced engineering mathematics covering numerical and analytical methods of engineering analysis.

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 II

NUC CCMAS

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.

introduction-to-chemistry-undergraduate-foundation

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.

atomic-structure-and-periodicity-of-elements-chemistry

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

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

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

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

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

This 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.

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

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.

stoichiometry-i-mole-and-chemical-formulae-chemistry

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.

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

Quantify the unknown with Stoichiometry of Solutions. This undergraduate foundation course provides rigorous training in volumetric analysis, the essential technique for determining the concentration of dissolved substances. We start with a detailed overview of titration principles, covering the apparatus, procedure, and the precise requirements for preparing primary and secondary standard solutions. The core of the course focuses on mastering titration calculations, specifically solving complex problems across acid-base, precipitation, redox, and advanced back titration scenarios using worked examples to build immediate computational accuracy.

Titration skills are indispensable across all analytical chemistry laboratories and industrial quality control. Learners will acquire the practical ability to determine solution concentrations accurately, which is vital for testing drug purity in pharmaceuticals, analysing contaminants in environmental monitoring, controlling product consistency in food and beverage production, and ensuring reaction completeness in industrial chemical synthesis. This quantitative skill translates directly into professional competency in clinical, industrial, and academic research settings.

By the course conclusion, you will be able to explain the principles of volumetric analysis; select and prepare accurate standard solutions; calculate concentrations using data from acid-base, precipitation, and redox titrations; and successfully apply stoichiometric principles to solve complex back titration problems. The emphasis is on converting experimental data into precise, reportable concentrations.

This course is a requirement for all undergraduate students in Chemistry, Chemical Engineering, Pharmacy, Biochemistry, and any field demanding core laboratory analytical skills. It provides the essential practical and theoretical foundation necessary for advanced laboratory modules. Additionally, it serves as an excellent, focused computational review for technicians, research assistants, and professionals preparing for laboratory certification or technical exams.

stoichiometry-iii-volumetric-analysis-chemistry

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.

chemical-equilibria-and-acid-base-chemistry-undergraduate

This course provides a complete guide to chemical thermodynamics, the study of the energy changes and spontaneity of chemical reactions. It covers the fundamental concepts of enthalpy (heat of reaction), entropy (disorder), and Gibbs free energy. The material details the principles of calorimetry, Hess's law for calculating enthalpy changes, and the use of standard heats of formation.

Chemical thermodynamics is essential for predicting the feasibility and energy efficiency of any chemical process. These principles are critical in chemical engineering for designing industrial reactors, in materials science for developing new energy sources and batteries, and in biochemistry for understanding the energy flow that drives metabolic pathways.

By the end of this course, you will be able to differentiate between exothermic and endothermic reactions and calculate enthalpy changes using Hess's law and standard heats of formation. You will also be able to use the concepts of entropy and Gibbs free energy to predict whether a chemical reaction will be spontaneous under a given set of conditions.

This course is for students who have a solid foundation in 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, materials science, and advanced thermodynamics.

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

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

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

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

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

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

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

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

Applied Mechanics

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’Hôpital’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 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

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

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

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

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

Engineering Mathematics I

UI, Ibadan

This course lays the groundwork for understanding the structures that power modern mathematics.

We start with the basics of set theory—notation, logic, functions, and operations—and use it as a stepping stone into the world of abstract algebra. From there, we introduce groups, rings, and fields in a way that highlights both intuition and structure.

Clear, rigorous, and designed with first-time learners in mind.

set-theory-introductory-abstract-algebra-undergraduate

Introductory Abstract Algebra

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

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

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

Real Analysis

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

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

This course establishes the foundational language of mathematics. It covers the core principles of set theory and applies them directly to the structure of the real number system. Mastery of this material is non-negotiable for further study in any quantitative field.

The principles of set theory are the structural basis for formal logic, database theory, and computer programming. Understanding number systems as structured sets is the prerequisite for all higher mathematics, including algebra and calculus. This course provides the essential logical framework for these disciplines.

By the end of this course, you will be able to use formal notation to define sets and their relationships, perform standard set operations such as union and intersection, use Venn diagrams to analyse set identities, and classify numbers within the real number system.

This course is designed for first-year university students of mathematics, computer science, and engineering. It is also required foundational material for any professional in data analysis, software development, or other technical fields requiring rigorous logical thought.

set-theory-and-number-systems-mathematics-undergraduate

Mathematics

This course provides a complete treatise of mathematical progressions. It formally defines sequences and series, with a specific focus on Arithmetic Progressions (APs) and Geometric Progressions (GPs). This material is the foundation for analysing patterns of growth, decay, and summation.

These principles are foundational to finance, computer science, and physics. The course provides the tools to calculate compound interest, analyse algorithm complexity, and model physical phenomena. Mastery is required for calculus and financial mathematics.

By the end of this course, you will be able to differentiate between sequences and series, apply all standard formulas for the nth term and sum of Arithmetic and Geometric Progressions, calculate the sum to infinity for a convergent GP, and solve problems involving arithmetic and geometric means.

This course is designed for first-year university students in mathematics, economics, finance, and engineering. It is a mandatory prerequisite for the study of calculus and provides an essential foundation for financial modelling and algorithm 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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This course covers two critical topics in discrete mathematics: the principle of mathematical induction as a formal proof technique, and the binomial theorem for expanding powers of binomials. The course structure directly links the proof method to one of its most important applications in algebra.

These topics are the foundation of algorithm verification, probability theory, and statistics. Mathematical induction is a core technique for proving algorithm correctness and establishing formulas for series. The binomial theorem is a powerful tool used directly in statistics for the binomial distribution and in financial mathematics.

By the end of this course, you will be able to apply the principle of mathematical induction to prove mathematical statements, solve complex counting problems using permutations and combinations, and use the binomial theorem to expand any binomial expression for a positive integer exponent.

This course is for first-year university students and is a fundamental prerequisite for computer science, statistics, and probability theory. It provides essential skills for competitive mathematics and advanced algebraic studies.

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This course provides a complete introduction to the complex number system, from the definition of the imaginary unit to the Argand diagram and polar form. It then covers De Moivre’s theorem and its application to finding the nth roots of unity. This material extends algebra into two dimensions and provides essential tools for advanced mathematics.

Complex numbers are an essential tool in engineering and the physical sciences. They are used extensively in electrical engineering to analyse AC circuits, in signal processing for Fourier transforms, in quantum mechanics to describe wave functions, and in fluid dynamics. This course provides the practical foundation for these applications.

By the end of this course, you will be able to perform all arithmetic operations on complex numbers, represent them on an Argand diagram, convert between Cartesian and polar forms, apply De Moivre’s theorem to find powers of complex numbers, and calculate the nth roots of unity.

This course is designed for first-year university students of mathematics, physics, and engineering. It is a critical prerequisite for the study of electrical circuits, signal processing, quantum mechanics, and any field that uses wave analysis or advanced vector mathematics.

introduction-to-complex-numbers-mathematics-undergraduate

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.

trigonometry-mathematics-undergraduate-foundation

Master the mathematics every scientist, engineer, and computer scientist must know. This track covers the NUC Core syllabus for MTH 101: Elementary Mathematics I. From set theory and sequences to trigonometry and complex numbers, you will gain the exact tools used in higher mathematics, algorithm design, data analysis, physics, and engineering.

This programme is for first-year university students in mathematics, computer science, engineering, or physics, as well as serious learners preparing for undergraduate study. It also serves professionals who need a rigorous mathematical foundation for technical fields.

By the end, you will handle formal set notation, progressions, quadratic models, combinatorics, induction proofs, binomial expansions, trigonometric analysis, and complex arithmetic. You will be equipped to solve real problems in science, engineering, computing, and finance, and ready for advanced study in calculus, statistics, and applied mathematics.

Our goal is to create a generation of confident problem-solvers by making mathematics and science accessible, enjoyable and inspiring for students everywhere. Our mission is to help students excel academically while nurturing curiosity and a deep appreciation for mathematics and science.

Numeric Academy

I am passionate about transforming mathematical struggles into success. I focus on clarity, confidence, and results. Known for turning struggling students into top achievers, my method combines core concept mastery with intensive problem-solving. Many of my students thrive at leading universities worldwide.

Elementary Mathematics I

Algebra and Trigonometry

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.

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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.

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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.

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