NUC CCMAS

This course provides a rigorous foundation in the concept of functions, the building block of calculus. We begin with the real number system - rationals, irrationals, intervals, and infinity - before defining real-valued functions, their domains, and ranges. You will systematically study all key function families: polynomial, rational, algebraic, piecewise-defined, and transcendental, including exponential, logarithmic, trigonometric, and hyperbolic types.

A command of functions is essential for all technical and quantitative disciplines. These principles are directly applied in physics to model motion, in economics for supply-demand curves, in engineering for signal processing, and in computer science to analyse algorithm complexity. This course delivers the core mathematical tools required for effective modelling and problem-solving in these fields and beyond.

By the end of this course, you will be able to: calculate the domain and range of any given function; classify functions and identify their fundamental properties; analyse functions for key characteristics like symmetry (odd and even); and accurately construct graphs for a wide range of standard and piecewise-defined functions directly from their equations.

This course is designed for first-year undergraduates in science, technology, engineering, mathematics (STEM), and economics. It is also critical for any student preparing for advanced calculus or for professionals who require a solid mathematical base for roles in finance, data science, or technical research.

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Single-Variable Calculus

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

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

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

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

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

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

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

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


continuity-of-functions-single-variable-calculus

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

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

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

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


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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.

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Multivariable Calculus

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

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

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

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

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Linear Algebra

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

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

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

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

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Vectors

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!

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Calculus

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.

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.

Engineering Mathematics I

OAU, Ife

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

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

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

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Introductory Abstract Algebra

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.

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This course focuses on mappings???one of the core tools in modern mathematics and abstract algebra.

We cover functions, injectivity, surjectivity, bijections, and composition. You'll see how mappings connect sets, preserve structure, and lay the groundwork for understanding homomorphisms in algebraic systems.

Straightforward, precise, and built for learners taking their first steps into abstract algebra.

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This course introduces binary operations???the basic building blocks of algebraic structures.

We explore how operations combine elements of a set, and what it means for them to be associative, commutative, or have an identity or inverse. These ideas form the core of how structures like groups and rings are defined.

Clear, hands-on, and designed for anyone beginning their journey into abstract algebra.

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This course introduces groups???one of the fundamental structures in abstract algebra.

We cover the group axioms, explore classic examples like integers under addition and symmetry groups, and show how groups model structure and transformations in math.

Clear, focused, and designed for learners new to abstract algebra.

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This course dives into subgroups???key pieces within groups that reveal deeper structure.

You???ll learn how to identify subgroups, understand their properties, and see why they matter in the bigger picture of group theory. We???ll also explore examples and criteria that help recognize subgroups quickly.

Clear, practical, and perfect for first-time learners ready to explore group structures more deeply.

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This course explores homomorphisms???the maps that connect algebraic structures while preserving their operations.

You???ll learn what makes a function a homomorphism, see examples between groups and rings, and understand how these mappings reveal similarities and relationships between structures.

Clear, focused, and designed for first-time learners ready to deepen their understanding of algebraic connections.

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This course introduces rings and fields???two central structures in abstract algebra.

You???ll learn how rings extend the idea of groups with two operations, and how fields bring in the familiar arithmetic of fractions and equations. We explore key examples like integers, polynomials, and modular systems.

Simple, structured, and made for first-time learners building up their algebra toolkit.

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This course brings in elementary number theory as a foundation for abstract algebra.

We cover divisibility, prime numbers, greatest common divisors, modular arithmetic, and congruences???all with a focus on the ideas that connect naturally to groups, rings, and fields.

Clean, intuitive, and designed for learners building a solid entry point into algebra through number theory.

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Master the foundational structures of modern mathematics. This learning track provides a direct path through abstract algebra, from basic sets to groups, rings, and fields. It delivers the analytical framework essential for advanced theoretical work.

This programme is for undergraduate students in mathematics, computer science, or theoretical physics. It is also essential for professionals requiring a rigorous grasp of algebraic structures for work in cryptography, algorithm design, or quantum computing.

Construct rigorous proofs and analyse the properties of groups, rings, and fields. This programme directly prepares you for postgraduate studies in pure mathematics and for advanced technical roles in cryptography and algorithm theory.

Introduction to Abstract Algebra

UI, Ibadan

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.

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Advanced Calculus

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

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

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

Real Analysis

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

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

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

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

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This course provides a rigorous introduction to the differential geometry of curves in three-dimensional space. Using the tools of vector calculus, you will learn to analyze the intrinsic properties of a curve at any point. We will explore key concepts such as arc length, curvature, and torsion, and define the moving T-N-B frame (tangent, normal, and binormal vectors) using the celebrated Frenet-Serret formulas.

How can we mathematically describe the precise twisting and turning of a curve in space? Differential geometry provides the elegant and powerful answer. This field is not just abstract; its principles are fundamental to understanding the shape of DNA, designing paths for robotics, and creating realistic motion in computer graphics. This course reveals the beautiful mathematics behind the shapes that define our world.

This programme is designed for students who have completed our introductory course on vector calculus and wish to explore a beautiful application of its principles. It is ideal for students of mathematics, physics, and computer science with an interest in geometry and abstract structures. This course will sharpen your analytical skills and provide a solid foundation for more advanced studies in geometry and topology.

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Vector analysis is the mathematical backbone of classical mechanics, electromagnetism, and fluid dynamics. This learning track delivers the complete NUC CCMAS MTH 210 curriculum, rigorously progressing from fundamental vector algebra to the advanced differential and integral calculus of scalar and vector fields used in complex engineering and scientific modelling.

This programme is targeted at undergraduates in engineering, physics, mathematics, and computer science. It provides the essential mathematical toolkit for students entering disciplines that rely on applied mathematics and spatial analysis, and serves as a rigorous refresher for professionals needing to solidify their command of vector principles.

You will master the full spectrum of vector operations including dot, cross, and triple products, and apply them to solve geometric problems and vector equations. You will acquire the skills to analyze the differential geometry of curves using the Frenet-Serret framework and apply the powerful gradient, divergence, curl, and Laplacian operators in various coordinate systems. Completion establishes the critical mathematical foundation demanded for advanced studies in continuum mechanics, electrodynamics, and theoretical physics.

Vector Analysis

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

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

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.

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

linear-maps-transformations-linear-algebra

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

Abstract algebra is the structural foundation of modern advanced mathematics. This track delivers the complete NUC CCMAS MTH 203 curriculum, rigorously transitioning you from computational arithmetic to abstract mathematical reasoning. It provides the necessary prerequisite framework for understanding complex mathematical systems and their applications.

This programme is targeted at undergraduate students in mathematics, computer science, and physics requiring a firm grounding in fundamental algebraic structures. It also serves professionals in fields like cryptography or theoretical computer science who need a rigorous theoretical refresher.

You will master the precise definitions, properties, and relations of core algebraic structures, including groups, subgroups, rings, and fields. You will gain competence in constructing formal proofs using set theory and logic, and understand how homomorphisms preserve mathematical structure. Completion establishes the critical theoretical base demanded for advanced studies in algebra, coding theory, and algorithm design.

Sets, Logic and Algebra I

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.

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Mathematical Methods

Definitions of differential equations and related terminologies, identification of different differential equations and their solutions.

introduction-to-differential-equations-mathematical

This course breaks down the key types of first-order ordinary differential equations (ODEs) ??? separable, homogeneous, exact, linear, and more ??? plus how to handle tricky non-homogeneous and inexact ones by transformations.

You???ll also learn how to reduce certain higher-order equations into first-order ones you already know how to solve.

The course is straight to the point, method-focused, and designed to build your confidence with step-by-step explanations and examples.

If you're a science, engineering, or math student or professional who wants clarity without fluff, this is for you.

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Solutions and applications of linear ordinary differential equations.

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Solutions and applications of systems of ordinary differential equations.

systems-of-linear-ordinary-differential-equations

Mastering differential equations is essential for modelling dynamic systems in science and engineering. This learning track delivers the complete MTH 202 curriculum based on NUC CCMAS standards, equipping you with the mathematical command to describe motion, analyse electrical circuits, and predict rates of change across physical phenomena.

This programme is targeted at undergraduates in mathematics, physics, engineering, and chemistry who possess a strong background in single and multivariable calculus. It also serves professionals requiring a rigorous, method-focused refresher on fundamental mathematical modelling tools.

You will achieve competence in classifying equations and deploying solution methods for first-order, reducible higher-order, and general linear ordinary differential equations. You will learn to solve systems of linear ODEs and apply these techniques directly to real-world physical and technical problems. Completion establishes the necessary foundation for advanced studies in partial differential equations, control theory, and advanced physics.

Learning Tracks

GET 209: Engineering Mathematics I

MTH 205: Introduction to Abstract Algebra

MAT 223: Real Analysis

MTH 210: Vector Analysis

MTH 205: Linear Algebra II

MTH 204: Linear Algebra I

MTH 203: Sets, Logic and Algebra I

MTH 202: Elementary Differential Equations