Pre-requisite: 64613
This unit is broadly divided into three interrelated strands. A differential equation strand introduces basic dynamical systems theory which lays the foundation for chaos. It develops the theory of infinite series which then is used to introduce special functions for solutions of ODEs and the general Sturm-Louiville theory. An algebra strand establishes the basic structure of abstract vector spaces and of linear transformations to be able to solve linear problems in a convenient basis. Emphasises functional examples as it supports Sturm- Louiville theory, Fourier transform solutions, and later functional analysis. A modelling strand introduces the use of differential equations to mathematically model the dynamics of cars, gases and blood. The analysis is based upon conservation principles, and also emphasises mathematical and physical interpretation.