MTH3077 - Mathematical modelling

Leader: Dr Alistair Carr

Offered

Gippsland Second semester 2007 (Off-campus)

Synopsis

The unit examines several styles and purposes of mathematical modelling, as well as some of the elementary methods used to analyse the behaviour of continuous and discrete dynamical systems. Topics include: formulation and testing of models, selection of modelling approaches, stability analysis, asymptotic stability, limit cycles, bifurcation, sensitive dependance on initial conditions, chaotic solutions; qualitative and quantitative investigation of simple models drawn from the physical and biological sciences.

Objectives

On completion of this unit, student will be able to: describe the place of mathematical modelling in applying mathematics to real systems, analyse the stability and asymptotic stability of a simple continuous dynamical system using linearisation and/or Lyapunov methods, understand the characteristics of chaotic behaviour in both discrete and continuous dynamical systems, use several algebraic and graphical methods to investigate the behaviour of a discrete dynamical system in a single independent variable, apply elementary concepts from modern dynamical systems theory to simple models drawn from the biological and physical sciences, and make a detailed report of outcomes and conclusions drawn from a mathematical investigation.

Assessment

Examination (open book, 2 hours): 30%
Assignments: 70%

Contact hours

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

Prerequisites

MTH2010 and MTH2032