Asymptotic analysis and perturbation methods provide powerful techniques in applied mathematics for obtaining simple analytical forms to reliably approximate solutions to complicated problems in a range of different mathematical settings. This course will cover material on asymptotic expansions, 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)

Tues, Thurs 4:40-5:55pm, Room 259 Physics Building

- Problem Set 1
- Problem Set 2
- Problem Set 3
- Problem Set 4
- Problem Set 5
- Problem Set 6
- Problem Set 7, X=15
- Problem Set 8
- Problem Set 9

- Course outline/syllabus
- Review sheets
- Lecture notes
- Lecture 1: Introduction, Gaussian example
- Lecture 3: Solving algebraic equations, Maple worksheet
- Lecture 4: Basic methods for integrals
- Lecture 6: Watson's lemma
- Lecture 7: Exensions of Watson's lemma
- Lecture 8: Moving maxima
- Lecture 9: Review of contour integration, summary sheet
- Lecture 11: Steepest Descents, part 1
- Lecture 12: Steepest Descents, part 2
- Lecture 13: Local analysis of linear ODE, Maple worksheet
- Lecture 14: Irregular singular points
- (... all later notes put only on sakai...)