TEC1803 Differential equations and numerical methods

This unit introduces the fundamental concepts of ordinary differential equations (ODEs) and numerical methods, with a focus on technology-driven applications. You will learn analytical methods for solving first- and second-order ODEs, including Laplace transform techniques, and apply them to dynamic systems, electrical circuits, thermal responses, and control processes. The unit also covers numerical methods such as root-finding, interpolation, numerical differentiation and integration, matrix algebra, and numerical solutions for initial-value and boundary-value problems. In addition, you will be introduced to the finite difference method for approximating solutions to partial differential equations (PDEs) in engineering contexts such as heat transfer, fluid flow, and electrodynamics. Through theoretical study and computational exercises, this unit develops the mathematical understanding and problem-solving skills needed for the modelling, simulation, and optimisation of real-world technological systems.