units

MTH3066

Faculty of Science

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Monash University Handbook 2010 Undergraduate - Unit

6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL

LevelUndergraduate
FacultyFaculty of Science
OfferedNot offered in 2010
Coordinator(s)Dr Alistair Carr

Synopsis

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.

Objectives

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.

Assessment

Examination (open book, 3 hours): 70%
Assignments: 30%

Contact hours

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

Prerequisites

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

Prohibitions

MAA3021, MAA3072, MAT3022, MAT3031, MAT3026, GAS3621