# MTH3060 - Dynamical systems and boundary value problems

## 6 points, SCA Band 2, 0.125 EFTSL

#### 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