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.

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.

This course applies the principles of calculus to vector-valued functions. We move beyond static vectors to analyse how they change with respect to a parameter, such as time. The curriculum provides a rigorous treatment of vector differentiation, including specific rules for scalar and vector triple products. It then introduces vector integration, covering both anti-derivatives and the foundational concept of the line integral. Vector calculus is the essential language of dynamics and physics. Its primary application is kinematics - the mathematical description of motion. Engineers use these methods to model trajectories, velocities, and accelerations in mechanical, aerospace, and robotic systems. Physicists apply them to describe particle paths and force fields. These tools are non-negotiable for any study involving motion in two or three dimensions. Upon completion, you will be able to differentiate any vector-valued function and correctly apply the product rules. You will master the integration of vectors to solve initial-value problems, allowing you to determine position from acceleration or velocity. You will also gain the ability to set up and compute basic line integrals, a direct prerequisite for more advanced topics in vector analysis. This course is a mandatory component for undergraduate students in Engineering, Physics, and Applied Mathematics. It directly follows foundational courses in single-variable calculus and vector algebra (including products). It is also an essential module for computer science students focusing on 3D graphics or physics simulations, and a critical refresher for anyone preparing for advanced courses in fluid dynamics or electromagnetism.

This course provides the complete foundation in Two-Dimensional Coordinate Geometry, establishing the link between algebraic equations and geometric shapes. We systematically cover the algebraic definitions and analysis of straight lines and all four conic sections - the circle, ellipse, parabola, and hyperbola. The curriculum concludes by applying differential calculus to derive tangents and normals to these curves. Command of this geometry is essential for technical modelling in all physical sciences. These equations are used to define component paths in mechanical design and model trajectories in physics. For example, ellipses model orbits, and parabolas model projectile motion and reflector shapes. This course provides the indispensable toolkit for translating visual problems into computable algebraic forms. Upon completion, you will master calculating gradients and distances for straight lines and formulating their equations in various forms. You will derive and manipulate the algebraic equations for all conic sections. Furthermore, you will apply differentiation to find the equations of tangents and normals to any curve at a specified point. This course is mandatory for first-year undergraduate students in Engineering, Physics, and Applied Mathematics. It requires prior knowledge of basic algebra and differential calculus. This programme provides the necessary rigorous foundation in 2D spatial analysis, which is a critical prerequisite for advanced subjects like mechanics and multi-variable calculus.

This course provides a rigorous introduction to classical mechanics using the language of vectors. We cover the two main branches of the subject: dynamics, where you will analyze forces, equilibrium, work, energy, and moments; and kinematics, where you will describe the motion of particles using position, velocity, and acceleration. You will learn to analyze a wide range of scenarios, including projectile and circular motion. Mechanics is the science of how things move and interact, forming the foundation of all physical sciences and engineering. This course is designed to build your problem-solving intuition by applying vector principles to tangible, real-world scenarios. You will learn to model physical systems mathematically, providing a powerful framework for understanding the world around you. This programme is designed for students who have completed our introductory course on vector calculus. It is the ideal next step for first-year university students in physics, engineering, and other physical sciences. This course provides the essential foundation required before tackling more comprehensive topics in the main Engineering Mechanics learning track.