USQ Logo
The current and official versions of the course specifications are available on the web at https://www.usq.edu.au/course/specification/current.
Please consult the web for updates that may occur during the year.

MAT3105 Harmony of Partial Differential Equations

Units : 1
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

Requisites

Pre-requisite: ENM2600 or MAT2100 or MAT2500

Overview

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.

Course offers

Semester Mode Campus
Semester 1, 2022 On-campus Toowoomba
Semester 1, 2022 Online
Date printed 23 May 2022