Mathematics 233: Asymptotics and Perturbation Methods (Fall 2003)

Instructor

Description

Asymptotic analysis and perturbation methods provide powerful techniques in applied mathematics for obtaining simple analytical forms for 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, 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.

Graduate students from the mathematics department interested in applied math often take this course in their second year, though first year students can also take it if their schedule permits. Likewise students from other departments are encouraged to consider the course. This course would be helpful to those students planning on taking Math 281 (PDE II) this term and considering Math 229 (Modeling) in the future.

Textbooks

(Required) Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory by C. M. Bender and S. A. Orszag, Springer Verlag
(Recommended) Introduction to Perturbation Techniques, A.H Nayfeh, John Wiley Inc.

Prerequisites

Background in ordinary differential equations (Math 131 or higher), background in complex variables -- contour integrals (Math 114, Math 181 or higher).

Course Website

For more information see http://www.math.duke.edu/~witelski/233

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