LECTURER : M. Gandhi
Exposure to the notion of metric spaces, limits, compactness and continuity of functions would be advantageous.
In this module you’ll gain an introduction to the modern theory of dynamical systems, a study of systems that evolve with time. This theory originated at the end of the 19th Century, and has led to the development of a rich and powerful field with applications in many branches of science and engineering. The mathematical core of the module is in understanding the behaviour of individual time-evolutions of systems that can be described with ordinary differential equations and iterated maps. Notable, the core also would include a generous introduction to Chaos theory. The study of a few applications is also included.
Ordinary differential equations and iterated maps as dynamical systems. Geometric representation of trajectories. Limiting behaviour of trajectories in linear and nonlinear systems. Equilibria of linear systems and linearisation of hyperbolic equilibria of nonlinear systems. Invariant sets and attractors. Bifurcation and Chaos in nonlinear maps. Notions of stability. Some applications of dynamical systems in modelling.
References will be provided
To be finalized
TWO class tests and ONE final examination.
Last Modified: Thu, 02 Jul 2015 20:38:45 SAST