Differential equations
Dr Alistair Carr
6 points * First semester * 4 hours per week * Gippsland/Distance (odd-numbered years only) * Prerequisites: GAS1612, GAS2612, GAS2622, GAS2621 (and subject GAS2623 is desirable) * Prohibition: MAA3021, MAA3072
Objectives The objectives of this subject are for students to master the technique of `separation of variables' for linear partial differential equations in two or more independent variables, and to be aware of the (Sturm-Liouville) properties of eignfunctions that commonly arise in this context; to be able to use Bessel functions and Legendre polynomials, and to construct a Green's function for an ordinary differential equation solved on a finite domain; to be able to use standard transforms (eg Laplace, Fourier) in solving partial differential equations in two or three independent variables, and to use elementary numerical approximation algorithms for partial differential equations in two variables; to understand the qualitative behaviour of a system near equilibrium, and the stability analysis that can be based on linearisation of a nonlinear system near equilibrium.
Synopsis This subject aims to treat several advanced methods for solving ordinary and partial differential equations with physical applications, and the use of numerical approximations where appropriate. Topics include the Frobenius method, Bessel functions and Legendre polynomials; Sturm-Liouville theory; use of integral transforms; Green's functions; phase plane analysis of critical points; numerical methods for partial differential equations. On-campus students are offered lectures and tutorials, supplemented by practice assignments and study guides. One of the assessment assignments is a long essay on a technical, historical or `applications' topic.
Assessment Two assessment assignments: 40% * Examination: 60%
Prescribed texts
O'Neil P Advanced engineering mathematics 4th edn, Wadsworth, 1995
Recommended texts
Borrelli R L and Coleman C S Differential equations - a modeling approach Prentice-Hall, 1987
Haberman R Elementary applied partial differential equations Prentice-Hall, 1983
Huntley I D and Johnson R M Linear and non-linear differential equations Ellis Horwood, 1983
James G and others Advanced modern engineering mathematics Addison-Wesley, 1993
Kreyszig E Advanced engineering mathematics 7th edn, Wiley, 1993
| Published by Monash University, Clayton, Victoria
3168 Copyright © Monash University 1996 - All Rights Reserved - Caution Authorised by the Academic Registrar December 1996 |