Course Announcement

Math 6730 - Asymptotic and Pertubation Methods

Time: (Tenative) 12:55-2:20, Tuesday and Thursday

Place:LCB 215 (Tuesday), LCB 222 (Thursday)

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 names of the techniques include matched asymptotic expansions, time scale analysis, multiple-time scale analysis, averaging and homogenization. Applications will made to a variety of problems in the physical and life sciences.

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

    • Homework assignments will be posted and updated regularly at this .pdf file.

    Notes:

    Maple code for van der pol multiscaling analysis

    For more information contact J. Keener, 1-6089

    E-mail: keener@math.utah.edu