Department of Mathematics

University of Toronto

APM441/MAT1501 Asymptotic and Perturbation Methods

Spring of 2016

Here current lecture notes will appear weekly. They will be based on Online textbook. So notes will be just references to sections of this textbook plus brief comments. Currently there are only placeholders. Usually each weekend (Sat or Sun) three new notes and a home assignment will be released covering the coming week and over next weekend (Fri or Sat) these notes will be finalized.

    Week 1 (January 11—15)

  1. 1.1. Introduction
    1.2. Asymptotic series etc
  2. 2.1. Laplace integrals
  3. 2.2. Laplace integrals. II. Multidimensional theory

    4. Week 2 (January 18—22)

  4. 2.3. Oscillatory integrals
    2.4. Oscillatory integrals. II. Multidimensional theory
  5. 2.5. Method of the steepest descent
  6. 3.1. Introduction and classification (for points of ODEs)

    7. Week 3 (January 25—29)

  7. 3.2. Ordinary points of differential equation
    3.3. Regular Singular Points of Differential Equation
  8. 3.4. Irregular Singular Points of Differential Equation
  9. 3.5. Some examples of nonlinear differential equations
    • Quiz 1 (January 28)
    • HA3: Problems 1--7; covered by Quiz 2 on Week 5

    10. Week 4 (February 01—05)

  10. 4.1. Regular perturbation theory
  11. 4.2. Singular perturbation theory
  12. 4.3. Singular perturbation theory. II
    4.4. Singular perturbation theory for PDEs

    13. Week 5 (February 08—12)

  13. Review
  14. Review
  15. 5.1. Preliminaries
    • Quiz 2 (February 09)
    • Quiz 3 (February 11)
    • HA4: Problems 1--?; covered by Quiz 4 on Week 7--not yet

    16. Reading Week (February 15—19)

    Week 6 (February 22—26)

  16. 5.2. Eikonal and Hamilton-Jacobi equations
  17. 5.2. Eikonal and Hamilton-Jacobi equations (end)
  18. 5.3. Transport equations
    • Test 1 (February 25)
    • HA5: Problems ?; covered by Quiz ? on Week ?

    Week 7 (Feb. 29— Mar.h 04)

  3. Week 8 (March 07—11)

  6. Week 9 (March 14—18)

  9. Week 10 (March 21—25)

  12. Week 11 (Mar. 28—Apr. 01)

  15. Week 12 (April 04—08)