modules

Most mathematical problems in engineering and science lead to systems of nonlinear equations that cannot be solved with pencil and paper, and where a numerical approach does not give a complete answer. In this module you will use theory and mathematical methods from Stages 1 and 2 (calculus, dynamics, differential equations, numerics and scientific computing) to solve realistic problems as they occur in nonlinear dynamics in engineering and science.

In this module you will gradually assemble a toolbox of small programs (in MATLAB) and then use these programs to study nonlinear dynamical systems with complicated behaviour (for example, chaos) and transitions between behaviours (bifurcations) as parameters are changed. In the end you will have solved some fairly complex problems from scratch, using tools developed and written by yourself during the module. For example, you will have proved (or, at least given robust numerical evidence for) the existence of chaos in the forced pendulum and examined the dynamics of some neuron models. Half of the contact time will be supervised lab sessions during which you will get support to get started on the problems.  Additional programming experience is recommended for students taking this module.

 

Pre-requisites: MTH2005 Modelling: Theory and Practise OR MTH1003 Mathematical Modelling