## Math 553: Asymptotic Analysis and Perturbation Methods
(Fall 2020) [18164/18165]

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)

#### Prerequisites

Background in ordinary differential differential equations (Math 353, 356 or
higher), basic background in multi-variable calculus (line integrals or
contour integrals from complex variables).

#### Schedule

Wed, Fri 3:30-4:45pm, Online (Zoom) and
Room 119 Physics (in-person)

#### Instructor

Thomas Witelski, Professor, Dept of Math

####
Problem sets

#### Course materials

- Course outline/syllabus

- Lecture notes and Review sheets
- See resources folder in Sakai
- Last lecture day: Friday November 13, 2020

Problems accessing the sheets?
All materials are posted at the Duke
Sakai website (class members only) or
access locally from any *.duke.edu computers or
try
Duke OIT VPN (Start VPN @ portal.duke.edu).