Asymptotic analysis and perturbation methods provide powerful techniques for obtaining simple analytical forms to reliably represent solutions to complicated problems in a range of different applied and mathematical settings.
This course will cover material on constructing asymptotic expansions for the solution of nonlinear algebraic equations, regular and singular perturbations problems, perturbations of matrix eigenvalue problems, asymptotics of integrals (Fourier and Laplace transforms), and solutions of differential equations (WKB theory, eigenvalue problems, multiple-scale analysis, boundary layers, and matched asymptotic expansions).
Textbook:
Advanced Mathematical Methods for Scientists and Engineers by
C.M. Bender and S. A. Orszag, Springer.com (1999)