Authorised by Academic Registrar, April 1996
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 review of techniques for solving ordinary differential equations; the power series method and Frobenius solutions; Bessel functions and Legendre polynomials; Sturm-Liouville theory - separation of variables and the use of integral transforms for linear partial differential equations in two or more independent variables; Green's functions for ordinary differential equations; use of the phase plane and analysis of critical points for linear and non-linear systems; introduction to numerical methods for partial differential equations. On-campus students are offered lectures and tutorials, supplemented by assignments and study guides. Some assignment work is corrected but does not count directly towards assessment grades. One of the assessment assignments is a long essay on a technical, historical or `applications' topic.
Assessment Two assessment assignments: 40% + Examination: 60%