MTH3060 - Advanced ordinary differential equations

Leader(s): Dr Simon Clarke

Offered

Clayton Second semester 2009 (Day)

Synopsis

This unit examines two particular classes of ordinary differential equations: dynamical systems and boundary-value problems. The investigation of boundary-value problems considers Sturm-Liouville eigenvalues problems and orthogonal polynomials, shooting and direct matrix methods for the numerical investigation of boundary-value problems and iterative matrix methods. The second topic of dynamical systems considers analytical and numerical methods for planar autonomous systems, classification of critical points using eigenvalues and eigenvectors and perturbation methods for periodic and nearly periodic motion. Programming skills are developed in the context of the analytic and numerical investigation of advanced ordinary differential equations using MATLAB.

Objectives

On completion of MTH3060, students will have consolidated and extended their knowledge of the importance of differential equations in modelling, and the classification and analytic and numerical solution of ordinary differential equations.

Assessment

Examination (3 hours): 60%
Assignments and tests: 40%

Contact hours

Three 1-hour lectures and one 2-hour combined tutorial and computer laboratory class per week

Prerequisites

MTH2032 and MTH2051 or MTH3051