Modelling and Analysis of Continuous Real-World Problems will introduce a number of key methods for studying continuum models. Each week we start from real-world problems and show how to derive the corresponding mathematical model. We then use these models as vehicles to demonstrate the relevant analytical and computational methods. At the end of each week, the students will have the complete set of tools needed to set up, analyse and solve a class of mathematical models.
Prof. Colin Please
Diffusion problems arising in heat flow, chemical reactions, pattern formation, and thermal runaway. Conservation laws; well-posedness; separation of variables; transforms; similarity solutions; nonlinear equilibria; linear stability.
Elastic waves; acoustics; Stokes waves; electromagnetism; optics. Method of characteristics; separation of variables; eigenvalue problems; resonance; high-frequency asymptotics.
River flow; porous-medium flow; two-phase flow. Shocks, causality, regularization, weakly nonlinear theory.
Capillary statics; elasticity; buckling; liquid crystals; Calculus of variations; bifurcations; weakly nonlinear analysis.