The majority of the module is concerned with providing techniques for solving selected classes of ordinary differential equations (ODEs) relevant to the analysis of engineering topics. This module also provides the basic calculus to help analyse engineering problems in two- or three-dimension and special solutions of partial differential equations relevant to engineering applications. The module will cover:

• Vector Calculus
• Multiple Integrals
• Fourier Series and Periodic Functions
• Homogeneous (revision), Inhomogeneous (forced) and Systems of ODEs
• Application of Fourier Series
• Laplace Transform
• Separation of Variable Technique for PDEs.

This module aims to introduce vector differential calculus operators commonly used in the fundamental analysis of two- or three dimensional advanced engineering problems. To understand, apply and manipulate standard techniques for solving important classes of ordinary differential equations and the calculus relevant to analysing core engineering models. The fundamental concepts for solving partial differential equations relevant to modelling of thermodynamic, fluid or elastic problems is introduced and illustrated by obtaining fundamental solutions using techniques developed within the module.