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

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

Introduction

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

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

Shapes of Molecules

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

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

Hybridization Theory

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

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

Intermolecular Forces

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

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

Types of Bonds

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

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

Conclusion

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

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

Lewis Structures

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

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

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

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

Our mission is to simplify complex concepts by teaching from first principles. We go beyond simple problem-solving to build a deep, foundational understanding of the "why" behind the "how."

Our content is meticulously designed for undergraduates navigating the rigorous curricula of top engineering and physical science programmes in Nigeria and globally.

As a core academic partner on UniDrills, we are committed to upholding the highest standards of clarity, precision, and professional excellence in education.

Max Engineering Tutorials

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

NUC CCMAS

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

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

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

General Chemistry I

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

Chemistry

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

Equations in One Variable (1)

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

Integration (1)

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

Integration (2)

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

Equations in One Variable (2)

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

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

??? Distinguish between analytical and numerical solutions.

??? Identify problems best suited for numerical methods.

??? Recognise key sources of numerical error.

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

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

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

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

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

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.

OAU, Ife

This learning track delivers the complete mathematical toolkit required for a university-level science, engineering, or computing degree. It systematically covers the entire MTH 201 curriculum, building from the foundational principles of single-variable calculus - functions, limits, continuity, and differentiability - to the advanced methods of multivariable calculus, infinite series, numerical methods, and ordinary differential equations. This is the definitive preparation for advanced quantitative study.

This programme is designed for second-year students offering MTH 201 at Obafemi Awolowo University, Ile-Ife, Nigeria. It is also helpful for any student in a STEM field - including physics, engineering, and computer science - who requires a rigorous and comprehensive command of calculus and its applications.

This track delivers a full skill set in mathematical analysis and applied problem-solving. Graduates will be able to solve a wide range of problems, from optimising multivariable functions to modelling dynamic systems with differential equations and testing the convergence of infinite series. This programme directly prepares students for success in advanced courses in vector calculus, partial differential equations, and real analysis, providing the necessary foundation for a career in engineering, data science, or theoretical physics.

Mathematical Methods I

introduction-to-numerical-methods-undergraduate-foundation

Numerical Methods

This chapter establishes the course's core philosophy. We define the modern developer's mindset, outline our practical, tool-centric teaching approach, and address the role of AI in professional workflows. This is the strategic overview for the entire course.

You will grasp the course structure, its practical, tool-focused philosophy, and the professional's approach to using AI in modern development.

To build for the web, you must understand its architecture. This chapter explains the sequence of events that delivers a website to a browser, covering the key components, protocols, and addressing systems that make it work. This knowledge is non-negotiable for any technical professional.

By the end, you will be able to: explain the client-server request-response model, define the roles of HTTP and DNS in communication, and trace the journey of a URL from keyboard to a page rendering on screen.

How the Web Works

Graphical interfaces are for consumption; the command line is for production. This chapter introduces the command-line interface (CLI), the tool developers use to navigate systems and manage files with superior speed and control. Proficiency here is a non-negotiable professional competency.

You will master the essential commands for file system management. This includes orienting yourself within the terminal, navigating directories, and performing all core creation, manipulation, and deletion operations on files and folders.

The Command Line

Your editor is an active development tool, not just a place for typing. This chapter focuses on configuring Visual Studio Code for professional efficiency, transforming it from a default program into a powerful environment that automates tasks and accelerates your workflow.

By the end of the chapter, you will: install and set up the editor, use the integrated terminal for a seamless workflow, automate code formatting for consistency, and leverage AI tools like GitHub Copilot to improve productivity.

Code Editing with VS Code

Version control is the professional standard for managing software projects. This chapter covers Git for tracking local history and GitHub for remote collaboration and backup. Proficiency with these tools is a non-negotiable industry requirement for any developer.

You will master the core version control workflow. This includes creating a local Git repository, saving snapshots of your work using the stage-and-commit process, and synchronizing that history with a remote GitHub repository.

Git and GitHub

This concluding chapter consolidates your achievements and directs you to the next stage. We will review the foundational skills you have mastered, place them within a professional context, and provide a clear path forward to ensure your learning momentum continues.

By the end of the chapter, you will: review the core web concepts and the professional toolkit; understand how advanced tools build upon this foundation; and identify the HTML5 course as your immediate next step.

Your Path Forward

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.

Beginner

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

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

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

Modern Web Development Foundations

beginner-modern-web-development-foundations

From Zero to Your First Interactive Website

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

Web Development

Understanding the mean-value and Rolle's theorems.

Theorems on Differentiable Functions

Higher-order derivatives of differentiable functions - meaning, proof of Leibniz's formula and its applications.

Higher-Order Derivatives

Meaning of the differentiability of real-valued functions at a point; illustration by slope of a straight line.

Taylor and Maclaurin series expansion of differentiable functions.

Taylor and Maclaurin Series

Differentiability on an interval and the meaning of derivatives; relating differentiability and continuity of a function.

Derivatives

How to find the derivatives of real-valued functions; rules of derivatives of sums, products and quotients of functions and their proofs.

Rules of Differentiation

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.


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 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

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

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

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

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

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

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

Real Analysis I

differentiability-and-derivatives-of-functions

Single-Variable Calculus

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

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

Theorems on Continuous Functions

Various types of discontinuities - meaning and examples.

Types of Discontinuity

Examples of continuous functions, worked problems on continuity.

Continuous Functions

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

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

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

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


continuity-of-functions-single-variable-calculus

Analysis of motion of particles by relating the linear momentum of the body with the impulse of the forces applied on it.

Linear Impulse and Momentum

Analysis of motion of a particle by relating the kinetic energy of the body with work done by the external forces acting on it.

Work and Energy

A study of collision of particles and their motion before and after collision.

Impact

Analysis of motion of particles under conservative forces by considering the conservation of mechanical energy in the system.

Conservation of Energy

Definition of work. Determining the work done by a force under various conditions.

Work

Welcome to the course and course outline. Review of kinematics and kinetics of particles concepts.

Determining instantaneous power, average power, and efficiency of a force by the principle of work and energy.

Power and Efficiency

Introduction to angular momentum, relation between angular momentum and moment of a force, principle of angular impulse and momentum, conservation of angular momentum.

Angular Impulse and Momentum

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

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

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

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

Engineering Mechanics

Dynamics

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

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

Transformation of coordinates by rotation.

Coordinates Transformation

Equations of circles, ellipses, parabolas and hyperbolas.

Second-Degree Plane Curves

Three-dimensional rectangular coordinates system, graphs.

Three-Dimensional Rectangular Coordinates

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

Two-Dimensional Rectangular Coordinates

Direct classification of quadric surfaces.

Classifying Quadric Surfaces I

Classification of quadric surfaces by variable substitution.

Classifying Quadric Surfaces II

The polar, cylindrical and spherical coordinates systems.

Other Coordinates Systems

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

Quadric Surfaces

Learn to analyze the three-dimensional Euclidean space using coordinates and equations with pin-point precision.

Designed for students, researchers, and professionals in fields such as engineering, computer graphics, physics, astronomy, medicine, biology, architecture, and building technology, this course provides a thorough understanding of coordinate systems, equations, and quadric surfaces.

On completing this course, you will have mastered:

- One-dimensional coordinate system and locating points

- Two-dimensional coordinate system, lines, and curves

- Conic sections and their equations

- Three-dimensional coordinate system and quadric surfaces

- Computer-aided visualization using Geogebra

- Coordinate transformation and rotation

- Equations in polar, cylindrical, and spherical coordinates

Throughout the course, you'll engage with high-quality video lessons, completely-solved examples, free-hand sketching techniques, and computer-aided visualizations. Multiple-choice quizzes will keep you focused and help reinforce your learning.

Prerequisites:

This course is designed for first-year undergraduate students in engineering and sciences. Prior knowledge of basic trigonometric ratios, determinants, and elementary row operations on matrices is helpful but not required, as the course is designed to be accessible to learners with varying backgrounds.

Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

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

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

Engineering Analysis I

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

Analytic Geometry

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

Proving Limits Involving Infinity

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

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

Evaluating Finite Limits (1)

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

Evaluating Limits at Infinity

How to prove that a given finite limit as x approaches a finite value is correct, using the formal or epsilon-delta definition.

Proving Finite Limits

Other methods of evaluating finite limits - L???H??pital???s rule, use of known special limits, squeeze theorem, limits of piecewise-defined functions, etc.

Evaluating Finite Limits (2)

Intuitive methods of evaluating finite limits of real-valued functions.

Evaluating Finite Limits (3)

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

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

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

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

limits-of-functions-single-variable-calculus

Analysis of frames under various loading conditions.

Frames

Analysis of machines under various loading conditions.

Machines

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

Planar Trusses (1)

Analysis of planar trusses by the method of sections.

Planar Trusses (3)

Analysis of planar trusses by the method of joints.

Planar Trusses (2)

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

Space Trusses

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

Analysis of trusses, frames and machines.

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

analysis-of-structures-engineering-mechanics

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

Moment About a Point in Three Dimensions

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

Moment About an Axis

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

Moment About a Point in Two Dimensions

Simplifying general systems of forces and couples on rigid bodies.

General Systems of Forces

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

Couples

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

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

Moment of a Force

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

Force-Couple Systems

Simplifying systems of forces on rigid bodies involving distributed loads.

Distributed Loads

This course is a comprehensive guide to the effects of forces on rigid bodies, a critical topic in engineering mechanics. It moves beyond particles to analyse systems where the point of application of a force is crucial, introducing the concepts of moments and couples. The material covers the calculation of moments in two and three dimensions, the properties of couples, and the methods for reducing complex force systems into simpler, statically equivalent systems.

Understanding moments is fundamental to all structural and mechanical analysis. These principles are used to calculate the bending and twisting stresses in beams, shafts, and machine components, and to ensure the rotational stability of structures and vehicles. A command of this subject is non-negotiable for designing any object intended to withstand real-world loads without failing or rotating unintentionally.

By the end of this course, you will be able to calculate the moment of a force about any point or axis using both scalar and vector methods. You will also be able to determine the moment of a couple, and reduce any complex system of forces and couples acting on a rigid body to its simplest equivalent form, such as a single resultant force and couple moment at a specified point.

This course is for undergraduate students in any engineering discipline who have already completed a course on the statics of particles. It is the direct prerequisite for the study of the equilibrium of rigid bodies, and is a necessary foundation for advanced courses in dynamics, mechanics of materials, and structural analysis.

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

Meaning and identification of reflexive relations.

Reflexive Relations

Meaning and properties of the empty relation.

Empty Relation

Introduction to ordered pairs, Cartesian products and relations.

Meaning and identification of symmetric relations.

Symmetric Relations

Meaning and identification of equivalence relations.

Equivalence Relations

Meaning and identification of transitive relations.

Transitive Relations

Meaning and calculation of equivalence classes for a given equivalence relation.

Equivalence Classes

Meaning and examples of congruence relations and residue classes.

Congruence and Residue Classes

Meaning and properties of partially-ordered sets.

Partially-Ordered Sets

Lattices

This course builds up a key part of the foundation for abstract algebra???relations.

We explore equivalence relations, partitions, orderings, and how they help us organize and understand mathematical structures. These ideas connect directly to how we define and work with algebraic systems like groups and rings.

Clear, focused, and made for first-time learners stepping into abstract algebra.

Courses

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

Introduction to Numerical Methods (Undergraduate Foundation)

An Introduction to Modern Web Development Concepts and Tools (Professional Practice)

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

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

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

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

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

Analysis of Structures - Engineering Mechanics (Undergraduate Advanced)

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

Relations - Introductory Abstract Algebra (Undergraduate Advanced)

Chemical Equilibria and Acid-Base Chemistry (Undergraduate Foundation)