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Course Announcement

Math 6730 - Asymptotic and Perturbation Methods

Time: 2-3:20pm T,TH

Place: LCB 222

Makeup sessions: Oct 8, Oct 22, Dec 3 in LCB 222 3:40-5:00 pm

## Course Description:

In this course, we will discuss the 4 basic problems of singular
perturbation theory, namely singular boundary value problems, singular
initial value problems, multiple time scale problems, and multiple
space scale problems. The specific names of the techniques are matched
asymptotic expansions, multiple-time scale analysis,
averaging, and homogenization. Applications will made to a variety of
problems in the physical and life sciences, including fluid dynamics, enzyme kinetics, cardiac electrophysiology, and many more.
In addition to covering the theory for these methods and applications, we will make extensive use of Maple to do explicit calculations.
A more detailed outline of the course is contained in
this
.pdf file
## Text:

M. Holmes, Introduction to Perturbation Methods

## Other References:

J. D. Kevorkian and J. D. Cole, Perturbation Methods in Applied
Mathematics, Springer, ISBN 0-387-90507-3
J. D. Cole, Perturbation Methods in Applied
Mathematics, Ginn-Blaisdell
M. van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press
K. W. Chang and F. A. Howes, Nonlinear Singular Perturbation
Phenomena: Theory and Application, Springer, ISBN 0-387-96066-X
D. R. Smith, Singular perturbation theory, Cambridge, ISBN
0-521-30042-8
J. P. Keener, Principles of Applied Mathematics, Perseus, 1998, second edition, chapters 10 and 11.

Class Schedule:
Homework assignments will be posted and updated regularly at
this
.pdf file, and the solution to previous exercises are posted here.

Notes:

Maple
code for regular perturbation of gravitational trajectory

Maple
code for higher order matching

Maple
code for problem with multiple boundary layers

Notes on corner layer analysis

Notes on quasi-steady state analysis

Notes on rapid equilibrium approximation for Michaelis-Menten dynamics

Maple
code for van der pol multiscaling analysis

Maple
code for forced Duffing equation multiscaling analysis

Notes on averaging the pendulum equation

For more information contact J. Keener, 1-6089

E-mail: keener@math.utah.edu