|Faculty or Section :||Faculty of Health, Engineering and Sciences|
|School or Department :||School of Mathematics, Physics & Computing|
|Student contribution band :||Band 1|
|Grading basis :||Graded|
|Version produced :||23 May 2022|
Pre-requisite: ENM2600 or MAT2100 or MAT2500
This course develops methods needed to apply the mathematics of partial differential equations. An understanding of their qualitative behaviour provides a structure for the analysis of wide-ranging problems. The methods of systematic approximation introduced with Fourier series and power series. The application of conservation principles in mechanics enable the modelling of physical problems as partial differential equations. Nonlinear partial differential equations (PDEs) are important for modelling numerous real-life processes; some basic nonlinear PDEs are introduced.
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-Liouville theory. 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. Nonlinear PDEs are introduced and discussed.
The on-campus offering of this course is normally available only in even numbered years. The external offering of this course is available yearly.