Course Announcement

Math 6730 - Asymptotic and Perturbation Methods

Time: 2-3:20pm T,TH

Place: CSC 12

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

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