Methods of applied mathematics

This unit covers the key principles to approximate and understand solutions of linear, weakly nonlinear, and strongly nonlinear equations by asymptotic analysis and dynamical systems theory. The main topics are: local analysis of linear ODEs, including irregular singular points and asymptotic series; asymptotic expansion of integrals, including stationary phase and steepest descent; introduction to regular/singular perturbation series; matched asymptotic expansion; multiple scale analysis, WKB theory; dynamical systems theory, including bifurcation, stability, and an introduction to chaos.