EMTH415-12S2 (C) Semester Two 2012
Special Topic in Engineering Mathematics

Description

Dynamical systems is the study of global, long-term behaviour of mathematical systems whose state evolves with time. Most of the systems studied arise from differential equations models of an applied problem from Physics, Biology, Economics, Chemistry, Engineering, etc. The aim of this course is to understand asymptotic behaviour using a combination of geometric reasoning, intelligent approximations, computer assistance and mathematical insight. This will be accomplished without grinding out the solutions of special classes of differential equations.

Topics covered: Overview of dynamics; flows on the line; one and two parameter bifurcations; 2d linear systems; phase plane for nonlinear 2d systems; limit cycles; Hopf bifurcations; applications; introduction to chaos in 3d flows.

Learning Outcomes

• to develop insight into the qualitative behaviour of the solutions to differential equations; in particular, the effects of nonlinearity
• to obtain a greater understanding of the use of differential equations in modelling physical systems; including the role of parameters, and the interplay between solutions to the model and experiments
• to apply relevant computational and geometric techniques to analyse systems of differential equations; and to communicate the mathematical results clearly and coherently

Pre-requisites

For further information see Mathematics and Statistics.