Mathematics 557 – Advanced Topics in Applied Math: Asymptotic Methods

Instructor: Nelson

TuTh 8:30-10

3 credits

Required Text: Bender and Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory Other Text (not required): Kevorkian, Multiple Scales and Singular Perturbation Methods This is an introduction to methods of asymptotic analysis including asymptotic expansions for integrals and solutions of ordinary and partial differential equations. This course is a core course for the Applied and Intersciplinary Mathematics (AIM) graduate program. Content: Topics include stationary phase, steepest descent, characterization of singularities, method of dominant balance,, regular and singular perturbation problems, boundary layers, multiple scales, WKB method. Additional topics include non-linear stability theory, bifurcations, applications in physics, engineering and biology.