Description

This course is about the asymptotic and perturbation methods in applied mathematics. After the study of this course, the students will be equipped with strong ability in applied analysis techniques to handle various models in science and engineering.
The topics will include

1. Asymptotic expansions, regular perturbation theory, and eigenvalue perturbation theory.
2.  Asymptotic evaluation of integrals, including Laplace's method and the method of stationary phase for oscillatory integrals
3. Local analysis and the matched asymptotic method for Ordinary differential equations.
4. Singular perturbation methods and boundary layer theory, with applications from reaction-diffusion theory, fluid flow, heat transfer, etc.

Prerequisites

Math 4160 (PDE), Math 3111(Complex analysis) or equivalent are recommended.

Recommended references

The instructor usually teach this course based on his/her lecture notes. References about this course are given below

• Bender, C. M., Orszag, S. A. : Advanced Mathematical Methods for Scientists and Engineers.
• Copson, E.: Asymptotic Expansions.
• deBruijn, N.: Asymptotic Methods in Analysis.
• Erdelyi, A.: Asymptotic Expansions.
• Murray, J.: Asymptotic Analysis.
• Olver, F.: Asymptotics and Special Functions.
• Sirovich, L.: Techniques in Asymptotic Analysis.