Instructor:
|
Dr. Patrick Nelson
East Hall 5860
tel: 763-3408
fax: 763-0937
pwn@umich.edu
office hours: Tuesday, 10:00 - 11:00; Thursday, 3:00-4:00
|
Course Description
This is an introduction to methods of asymptotic analysis including asymptotic expansions for integrals and solutions of ordinary and
partial differential equations. The prerequisites include linear algebra, advanced calculus and complex variables. Math 556 is not a prerequisite.
This course is a core course for the Applied and Interdisciplinary Mathematics (AIM) graduate program.
Textbook
- Advanced Mathematical Methods for Scientists and Enginners , Bender and Orszag McGraw-Hill,
Mathematical Concepts to be covered
- Method of Dominant Balance
- Frobenius Methods
- Approximate solutions to Non-linear differential equations
- Phase-space interpretation
- Stationary Phase, Steepest descent
- Laplace's method
- Regular and singular perturbation methods
- Boundary layer theory
- WKP
- Multiple scales
Homeworks
The main purpose of this class is to present and explain mathematical methods for obtaining approximate analytical
solutions to differential equations that cannot be solved exactly.Ê My objective is to help students build upon the skills necessary
to analyze equations that they will encounter in their work. Applications will be emphasized and will come from areas of
Physics, Engineering, Medicine, and the Life Sciences.
Grading
Homework assignments will count as 1/2 of grade evaluation. There will also be two quizzes
and each will count for 1/4 of the grade.