Many nonlinear equations do not have explicit solutions. This course shifts the focus from finding explicit solutions to discovering geometric properties of solutions. It also recognises that even a small amount of nonlinearity in a physical system can be responsible for very complicated chaotic behaviour.

The fact that nonlinear systems do not guarantee regular or predictable behaviour is having a major impact on many fields of science and engineering, as well as mathematics. The discovery of chaos in simple dynamical systems changes our understanding of physical processes and has many practical applications including the understanding of the dynamics of the weather and climate, excitable media such as cardiac tissue and nerve fibres, population dynamics, transport in complex flow fields, to mention a few.

This course introduces the fundamentals of nonlinear dynamics with applications to physics, engineering, biology, and chemistry. It takes an intuitive approach with emphasis on geometric thinking, analytic and computational methods and makes extensive use of software packages, such as Matlab.