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Gippsland First semester 2007 (Off-campus)

The unit covers several exact and approximate methods for solving ordinary and partial differential equations, with a particular focus on types of equations having physical applications. Topics include: phase plane analysis for critical points, linearisation of a nonlinear system, Green's functions, the Frobenius method, Bessel functions and Legendre polynomials, Sturm-Liouville theory, standard linear numerical methods for boundary value problems in two variables.

On completion of this unit, students will be able to: use separation of variables to obtain an analytic solution of a boundary value problem in two or more variables, involving a linear partial differential equation; apply transform methods to partial differential equations in two variables; solve simple Sturm-Liouville problems; give a qualitative description of the behaviour of a system in two variables, and deduce the behaviour of a nonlinear system from that of a related (linearised) system; apply simple numerical approximations to the solutions of boundary value problems in two variables; and select suitable solution methods and report on the conclusions drawn from an investigation of a differential equation(s) based model.

Examination (open book, 3 hours): 70%

Assignments: 30%

3 hours lectures and 1 hour tutorial, plus 8 hours private study per week

MAT1085; MAT2030 or MTH2010; MTH2032 or the pair MAT2047, MAT2077

MAA3021, MAA3072, MAT3022, MAT3031, MAT3026, GAS3621