Introduction to and motivation for a dedicated study of the kinetics of systems of particles.

Introduction

Generalized Newton's second law application to kinetics of systems of particles.

Newton's Second Law

Analysis of motion in a system of particles involving steady mass flow into or out of it.

Steady Streams of Particles

Analysis of motion in a system of particles gaining or losing mass.

Systems Gaining or Losing Mass

Work-Energy principle and conservation of energy, impulse-momentum principle and conservation of momentum, for a system of particles.

Energy and Momentum Methods

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

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

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

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

Max Engineering Tutorials

An academic and graduate engineer dedicated to explaining complex concepts in mathematics, computer science and engineering. I founded UniDrills to bring this vision to life, creating a world-class e-learning marketplace with a global outlook. I apply a first-principles approach to software architecture to build a professional and intuitive learning experience.

OAU, Ife

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

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

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

Engineering Mechanics

Dynamics

NUC CCMAS

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-systems-of-particles-engineering-mechanics

Meaning of the range of a linear map, with worked examples.

Range

Meaning of the kernel of a linear map, with worked examples.

Kernel

Definition, examples and general properties of linear maps.

Linear Maps

Matrix representation of a linear map, with worked examples.

Matrix Representation

Meaning and properties of the transition matrix between two bases of a vector space.

Transition Matrix

Definition of a map (also mapping or transformation) between two sets, notations and some general properties of maps.

Maps

Further operations on linear maps involving their definition and properties.

Operations on Linear Maps

Analysis of the vector space of all linear maps between two given vector spaces. Addition, scalar multiplication, composition and inverse of linear maps.

Algebra of Linear Maps

Welcome and course outline. Review of elementary matrix and linear vector space concepts.

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

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

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

Mathematical Methods II

Master the algebraic structures that underpin modern science and computation. This academic track delivers the complete NUC CCMAS MTH 204 curriculum, moving rigorously from abstract vector spaces to practical matrix theory. It provides the essential mathematical toolkit required for advanced problem-solving in high-demand STEM fields.

This programme is targeted at undergraduates in mathematics, engineering, and computer science requiring a firm grounding in linear structures. It also serves professionals in data science, cryptography, and machine learning needing a rigorous theoretical refresher on foundational concepts.

You will achieve competence in manipulating abstract vector spaces, determining basis and dimension, and analyzing linear transformations through their kernels and images. You will master matrix arithmetic, compute determinants, solve systems of linear equations using advanced methods, and apply techniques of eigenvalues and diagonalization. Completion establishes the critical foundation demanded for advanced studies in multivariate calculus, differential equations, and complex computational algorithms.

Linear Algebra I

linear-maps-transformations-linear-algebra

Linear Algebra

Meaning, operations and properties of eigenvalues and eigenvectors of matrices.

Eigenvalues and Eigenvectors

Diagonalization of matrices; evaluating polynomials and transcendentals of matrices.

Diagonalization of Matrices

Quadratic and canonical forms; transformations using symmetric matrices and orthogonal diagonalizing matrices.

Quadratic and Canonical Forms

Welcome and course outline. Review of elementary matrix concepts.

Diagonalization of symmetric matrices - orthogonal diagonalizing matrix, the Gram-Schmidt orthogonalization procedure, and related concepts.

Symmetric Matrices

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.

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

Advanced linear algebra is the mathematical backbone of modern data science, engineering, and physics. This learning track delivers the rigorous MTH 205 curriculum based on NUC CCMAS standards, focusing on sophisticated matrix analysis and practical computational methods critical for solving complex technical problems.

This programme is targeted at undergraduates in mathematics, engineering, and computer science requiring a deep command of advanced matrix theory. It is equally essential for data scientists and engineers seeking a rigorous theoretical foundation for machine learning algorithms, cryptography, and complex system modelling.

You will master matrix manipulations to solve linear systems and compute determinants and inverses efficiently using various methods including software like Python and MATLAB. You will gain competence in determining eigenvalues and eigenvectors, applying diagonalization to analyze the stability of dynamical systems, and working with quadratic and canonical forms. Completion establishes the critical mathematical expertise required for advanced studies in multivariate statistics, differential equations, and algorithmic development.

Linear Algebra II

eigenvalues-eigenvectors-and-diagonalization-of-matrices

Courses

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

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

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