Differential equations are used to model dynamical phenomena as diverse as mechanical vibrations, chemical reaction kinetics, population fluctuations and epidemics. This course will develop some of the theory of systems of nonlinear ordinary differential equations, but the main emphasis will be on formulating differential equation models and interpreting their mathematical properties in the context of the application being modelled.
|First order equations. Linear systems: solution, stability and phase portraits. Nonlinear systems: stability of equilibra, phase protraits of planar systems. Bifurcations and transitions to chaos. Time series from differential equations.|