Computational and Applied Mathematics
Math 579
-- Singular Perturbations -- Spring 2003
Course Number: 60724
Instructor: Charles Tier e-mail:
tier@uic.edu
Time: 3-4:15 MW Room: 313 TH
Office: 720 SEO Phone: 312-996-2442
Course Web Page: www.math.uic.edu/~tier/Math579
Description
The course deals with perturbation methods (regular and singular) which are used
to systematically construct approximations to problems (e.g. ODE and PDE) which
are otherwise intractable. The approximations are analytic and often provide
important insight into the behavior of the solution. This is in contrast to numerical
solutions which can provide extremely accurate results yet not provide sufficient
information about the solution. The purpose of the course is to survey important
perturbation methods. These methods will be contrasted with numerical methods
and it will be illustrated
how the perturbation and numerical methods often complement one another.
Text and References
- Text: M.H. Holmes, Introduction to Perturbation Methods,
Springer-Verlag, 1995.
- Reference: E. Bender and D. Orszag, Advanced Mathematical
Methods for Scientists and Engineers, Wiley.
Tentative Topics
- introduction to asymptotic approximation
- matched asymptotic expansions; boundary layer expansions
- method of multiple scales - slowly varying coefficients
- WKB method
- bifurcation and stability
Prerequisites: background in differential equations (ODE and PDE) or consent
of instructor.
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