Methods of Applied Mathematics

(3 Credits)

Convergent and divergent asymptotic series. Asymptotic expansion of integrals: steepest descents, Laplace principle, Watson?s lemma, and methods of stationary phase. Regular and singular perturbations of differential equations, the WKB method, boundary-layer theory, matched asymptotic expansions, and multiple-scale analysis. Rayleigh-Schr?dinger perturbatioConvergent and divergent asymptotic series. Asymptotic expansion of integrals: steepest descents, Laplace principle, Watson?s lemma, and methods of stationary phase. Regular and singular perturbations of differential equations, the WKB method, boundary-layer theory, matched asymptotic expansions, and multiple-scale analysis. Rayleigh-Schr?dinger perturbation theory for linear eigenvalue problems, summation of series, Pade approximation, averaging methods, renormalization groups, weakly nonlinear waves, and geometric optics.