MAT3105 Harmony of Partial Differential Equations (FOSCI)

Semester 1 (ONC)Toowoomba (EXT)Toowoomba

Units 1.0 (Mathematics) Band 2

Pre-requisite: MAT2100

Synopsis

This course establishes properties of the basic partial differential equations (PDEs) that arise commonly in applications such as the heat equation, the wave equation and Laplace's equation. It also develops the mathematical tools of Fourier transforms and special functions necessary to analyse such PDEs. The theory of infinite series is used to introduce special functions for solutions of ODEs and the general Sturm-Louiville theory. These methods are implemented in computer algebra. A modelling part introduces the use of partial 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. This course is offered only in even numbered years.