MAST 30030

Applied Mathematical Modelling

This subject demonstrates how the mathematical modelling process naturally gives rise to certain classes of ordinary and partial differential equations in many contexts, including the infectious diseases, the flow of traffic and the dynamics of particles and of fluids. It advances the student’s knowledge of the modelling process, as well addressing important mathematical ideas in deterministic modelling and the challenges raised by system nonlinearity. Infectious disease models and other contexts leading to systems of autonomous first-order differential equations; initial value problem, phase space, critical points, local linearization and stability; qualitative behaviour of plane autonomous systems, structural stability; formulation, interpretation and critique of models. Conservation laws and flux functions leading to first-order quasilinear-linear partial differential equations; characteristics, fans, shocks and applications including modelling traffic flow. Introduction to continuum mechanics: basic principles; tensor algebra and tensor calculus; the ideal fluid model and potential flow; the Newtonian fluid, Navier-Stokes equations and simple solutions.