Methods of Asymptotic Analysis- Math 550/605
Office hours: By appointment (email usually works best)
PDE's: Review Exercises
March 21: choose project (inform instructor of your choice)
April 27: hand-in project
Suggestions for Projects
You may also choose your own project - subject to instructor approval!
Localized Perturbation References
Naeh, T.; Klosek, M. M.; Matkowsky, B. J.; Schuss, Z. A direct approach to the exit problem.
SIAM J. Appl. Math. 50 (1990), no. 2, 595--627.
Large deviation theory for stochastic difference equations, R. Kuske and J.B.Keller, EJAM 8
Additional WKB references (PS)
Long wavelength instabilities of square patterns, R. Hoyle, Physica D, 67(1993),
Domain Boundaries in Convection patterns, B. Malomed, A. Nepomnyaschy, M. I. Tribelsky,
Phys. Rev. A, 42,1990, 7244-.
Nonpotential effects in dynamics of fronts between convection patterns,
A. Hari and A. A. Nepomnyaschy, Phys. Rev. E, 61, 4835-.
Additional Pattern references (PS)
American options with dividends near expiry , J.D. Evans, R. Kuske, and Joseph B. Keller, Mathematical Finance, 2002.
No two students may choose the same paper.
Read the selected paper, and fill in ALL mathematical details as completely
Provide a summary of the paper in words, describing methods used and main results
Rules: Each project is to be independent student work
You must understand everything you have written down.
If there are some numerical results in the paper, discuss how they relate to
Score on the final project will be based on completeness and clarity of presentation
The difficulty level of the paper will also be taken into account.
Course Review Notes
Review of PDE's
Introduction to regular perturbation
Asymptotic evaluation of integrals
Boundary layer theory for ODE's
(550) Multi-scale analysis for ODE's
(605) WKB analysis (ODE's)
(605) WKB analysis (PDE's) (Thanks to M. Ward)
(550) Quasi-steady approximations:
(605)Bifurcation analysis for nonlinear boundary value problems
(605)Real Ginzburg-Landau equation
(605)Stability and 2D Ginzburg-Landau equation
(605) Free boundary problems
(605) Free boundary problems II