MTH3060 - Dynamical systems and boundary value problems

Leader: Dr Simon Clarke

Offered

Clayton Second semester 2007 (Day)

Synopsis

This unit examines dynamical systems and boundary-value problems. The first topic of dynamical systems considers analytical and numerical methods for planar autonomous systems, elementary bifurcation theory and perturbation methods and the chaotic dynamics of a pendulum. 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. Programming skills are developed in the context of advanced ordinary differential equations using MATLAB.

Objectives

On completion of MTH3060, students will strengthen their awareness of the importance of differential equations in the modelling of real systems; will have consolidated, strengthened and extended their knowledge of: the solution and classification of linear dynamical systems using eigenvalue and eigenvector methods; the analytic solution of linear Sturm-Liouville boundary-value problems using regular and singular power series methods and orthogonal polynomials; numerical techniques for the solution of nonlinear dynamical systems and linear boundary-value problems; will also have developed an awareness of: qualitative methods for nonlinear dynamical systems; perturbation methods for differential equations; the nature of chaotic dynamics; and will have developed problem solving skills in applied mathematical methods and numerical programming and computational mathematics skills.

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