OAU, Ife

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

Engineering Mechanics

Kinematics of Particles - Engineering Mechanics (Undergraduate Advanced)

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

Kinetics of Particles by Newton's Second Law - Engineering Mechanics (Undergraduate Advanced)

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

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

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

Kinetics of Systems of Particles - Engineering Mechanics (Undergraduate Advanced)

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

2D Kinematics of Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

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

2D Kinetics of Rigid Bodies by Newton's Second Law - Engineering Mechanics (Undergraduate Advanced)

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

2D Kinetics of Rigid Bodies by Energy and Momentum Methods - Engineering Mechanics (Undergraduate Advanced)

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

Introduction to Dynamic Systems and Vibration - Engineering Mechanics (Undergraduate Advanced)

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.

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

Olowojaye Rufus

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.

Engineering Mechanics II

Dynamics

MEE 206: Engineering Mechanics II - Dynamics

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

Calculus

Calculus of Scalar and Vector Fields (Undergraduate Advanced)

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

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

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

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

complex-numbers-mathematical-methods-undergraduate

Mathematical Methods

Complex Numbers - Mathematical Methods (Undergraduate Advanced)

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

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

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

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

- Perform operations on vectors using linear combinations and scalar multiplication

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

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

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

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

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

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

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

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

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

linear-vector-spaces-linear-algebra-undergraduate

Linear Algebra

Linear Vector Spaces - Linear Algebra (Undergraduate Advanced)

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

linear-maps-transformations-linear-algebra

Linear Maps (Transformations) - Linear Algebra (Undergraduate Advanced)

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

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

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

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

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

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

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

Eigenvalues, Eigenvectors and Diagonalization of Matrices - Linear Algebra (Undergraduate Advanced)

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

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

Mathematical Methods II

MTH 202: Mathematical Methods II

University

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

Statics of Particles - Engineering Mechanics (Undergraduate Advanced)

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

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

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

Equilibrium of Rigid Bodies - Engineering Mechanics (Undergraduate Advanced)

Analysis of trusses, frames and machines.

analysis-of-structures-engineering-mechanics

Analysis of Structures - Engineering Mechanics (Undergraduate Advanced)

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

Dry Friction - Engineering Mechanics (Undergraduate Advanced)

Analysis of centroids and moments of inertia.

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

Centroids and Centres of Gravity - Engineering Mechanics (Undergraduate Advanced)

Analysis of the second moments of areas and its applications.

moments-of-inertia-engineering-mechanics-undergraduate

Moments of Inertia - Engineering Mechanics (Undergraduate Advanced)

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

method-of-virtual-work-engineering-mechanics

Method of Virtual Work - Engineering Mechanics (Undergraduate Advanced)

Statics decides if a structure stands or fails. This track teaches force calculation, support reactions, and equilibrium analysis for stable engineering systems. You will move from particle resolution to full structural modelling. The curriculum delivers the exact mathematical foundation required for real design work.

This programme is for first and second-year engineering undergraduates. It suits mechanical, civil, aerospace, and structural students, plus polytechnic learners. You only need basic physics and vector algebra. The sequence provides the precise calculation methods your degree demands.

You will finish able to resolve two and three dimensional forces, compute moments and couples, and solve rigid body equilibrium problems. You will calculate truss loads, evaluate friction in screws and belts, locate centres of gravity, and verify systems using virtual work. These results secure high grades in advanced mechanics modules and prepare you for structural design, machine engineering, and civil site roles.

Engineering Mechanics I

Statics

Engineering Mechanics I - Statics

Real-valued functions form the base of all advanced calculation in engineering and physics. This course maps the complete structure of these functions from first principles. You will cover number systems, the split between rational and irrational values, and exact interval notation. You will examine function behaviour at infinity. The work moves straight to domain and range analysis, supported by worked examples that lock the theory in place. You will classify polynomial, rational and algebraic forms. You will handle piecewise definitions, odd and even symmetry, and transcendental forms covering exponential, logarithmic, trigonometric and hyperbolic families.

Engineers and analysts use these functions daily to build accurate models and predict system results. You will apply domain rules to stop calculation errors in structural design. You will deploy exponential and logarithmic rules for signal processing and financial modelling. Trigonometric and hyperbolic functions govern wave analysis, circuit simulation and mechanical vibration studies. Correct use of piecewise and odd-even rules simplifies computer algorithms and cuts processing time. Mastery of this material removes guesswork and supplies reliable mathematical tools for real technical tasks.

You will leave able to find the exact domain and range of any function without external aid. You will group functions into algebraic, transcendental or piecewise types by quick inspection. You will adjust exponential, logarithmic and trigonometric expressions using standard identities. You will recognise odd and even symmetry to reduce integration workload. You will switch between direct and inverse forms of trigonometric and hyperbolic functions. You will solve combined problems that merge multiple function types into a single analytical framework.

This course targets undergraduates and graduate students who need advanced calculus for examination success. It suits engineering, physics and computer science students who require strict mathematical training. Learners who finished secondary school mathematics can still use the structured examples to build a solid base. Professionals returning to technical work will refresh core concepts rapidly. The clear progression and focused practice allow any serious student to command real-valued functions for academic or industrial use.

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

Advanced Calculus

Real-Valued Functions - Advanced Calculus (Undergraduate Advanced)

Limits dictate how mathematical models predict exact behaviour at critical points. This course covers formal and informal definitions of finite and infinite limits. You will study direct substitution, algebraic factorisation, conjugate multiplication, the squeeze theorem, and piecewise function analysis. The material handles indeterminate forms through derivative ratio techniques and rationalisation. Each method includes repeated worked examples to fix the procedure in your mind.

Engineers and analysts use limit evaluation to calculate instantaneous speed, stress thresholds in structures, and signal decay rates. Financial planners apply these rules to compound interest and market trend forecasting. Computer simulation software relies on accurate limit logic to prevent calculation crashes and rounding errors. Mastery of this material gives you reliable tools for real technical modelling and removes guesswork from system analysis.

You will construct formal proofs for finite and infinite limits using strict logical bounds. You will select the correct evaluation method from substitution, algebra, or derivative rules without hesitation. You will resolve indeterminate forms and apply boundary checks to complex piecewise cases. You will verify every answer through graphical inspection and numerical approximation. You will gain complete control over the transition points of any real function.

This course targets university students and postgraduate researchers in engineering, physics, or mathematics. Advanced secondary school students with strong algebra skills will secure a clear advantage before university entry. Professionals preparing for technical exams will rebuild their analytical foundation. The structured progression and repeated practice ensure that any disciplined learner can apply limit theory to academic or industrial problems.

limits-of-functions-single-variable-calculus

Limits of Real-Valued Functions - Advanced Calculus (Undergraduate Advanced)

Continuity ensures that a function behaves predictably without sudden jumps or breaks. This course defines continuity at interior points, endpoints, and across entire intervals. You will identify standard continuous functions and test them through repeated worked examples. The material classifies discontinuities, with specific focus on removable gaps that can be repaired. You will study the max-min theorem and the intermediate-value theorem to understand how continuous functions guarantee specific outputs within a range.

Engineers rely on continuity to model physical systems where sudden changes cause failure. Structural analysis requires smooth stress distributions to prevent material fracture. Electrical circuit design depends on continuous current flow for stable operation. Computer graphics algorithms use continuity to render smooth curves and surfaces without visual artifacts. Financial models assume continuous price movements to calculate risk and option values accurately. Mastery of these concepts prevents calculation errors in simulation software and real-world design tasks.

You will determine if a function is continuous at any given point or interval. You will distinguish between removable and non-removable discontinuities using limit analysis. You will apply the max-min theorem to find absolute extrema on closed intervals. You will use the intermediate-value theorem to prove the existence of roots and solutions. You will verify continuity for composite functions and piecewise definitions. You will gain the ability to spot and fix breaks in mathematical models.

This course targets undergraduates and graduate students in mathematics, engineering, and physics. It suits students preparing for advanced calculus examinations or research projects. Secondary school leavers with strong algebra skills can use this material to bridge the gap to university-level analysis. Professionals returning to technical work will refresh their understanding of function behaviour. The clear structure and practical examples allow any disciplined learner to master continuity for academic or industrial application.

continuity-of-functions-single-variable-calculus

Continuity of Real-Valued Functions - Advanced Calculus (Undergraduate Advanced)

Differentiation measures how a function changes at any given point. This course moves from the basic slope of a line to advanced derivative theory. You will define differentiability at a point and on an interval. You will link differentiability to continuity to spot where functions break. The material covers standard rules for sums, products, quotients, and composites. You will study Rolle's theorem and the mean-value theorem to understand function behaviour between points. The course extends to higher-order derivatives using Leibniz's formula. You will finish with Taylor and Maclaurin series to approximate complex functions with polynomials.

Engineers use derivatives to calculate velocity, acceleration, and force in moving systems. Electrical engineers apply these rules to analyse current change in circuits. Economists use differentiation to find marginal cost and maximise profit. Computer scientists deploy Taylor series for fast approximation in graphics and machine learning algorithms. Mastery of these tools allows you to model real-world dynamics with precision. You will gain the ability to predict system responses and optimise designs without relying on trial and error.

You will determine if a function is differentiable at any point or interval. You will apply product, quotient, and chain rules to differentiate complex expressions. You will use Rolle's theorem and the mean-value theorem to prove existence of critical points. You will compute higher-order derivatives and apply Leibniz's formula for product terms. You will construct Taylor and Maclaurin polynomials to approximate functions near a centre. You will estimate error bounds for these approximations. You will solve applied problems that merge multiple differentiation techniques.

This course targets undergraduates and graduate students in mathematics, engineering, and physics. It suits students preparing for advanced calculus examinations or research projects. Secondary school leavers with strong algebra skills can use this material to bridge the gap to university-level analysis. Professionals returning to technical work will refresh their understanding of rate of change. The clear structure and repeated practice ensure that any disciplined learner can master differentiation for academic or industrial application.

differentiability-and-derivatives-of-functions

Differentiability of Real-Valued Functions - Advanced Calculus (Undergraduate Advanced)

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

Convergence of Infinite Sequences and Series - Advanced Calculus (Undergraduate Advanced)

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

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

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

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

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

Real Analysis

Analysis of Infinite Sequences and Series - Real Analysis (Undergraduate Advanced)

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

Partial Differentiation and Its Applications - Multivariable Calculus (Undergraduate Advanced)

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

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

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

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

introduction-to-numerical-methods-undergraduate-foundation

Numerical Methods

Introduction to Numerical Methods (Undergraduate Foundation)

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

Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

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

MTH 201: Mathematical Methods I

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