Mathematics 204, Ordinary differential equations Fall 2008

Professor: Richard Borcherds

Office hours: Tuesday, Thursday 2:00-3:30 927 Evans Hall

This class meets in 81 Evans Hall, TuTh 9:30-11:00. The first lecture is on Thursday Aug 28, the last lecture is on Tuesday Dec 9, and there are holidays on Nov 11 and Nov 27. This is the course home page (address /~reb/204/). The course control number is 54913.

Catalogue Description: Mathematics 204

Course Format: Three hours of lecture per week.

Prerequisites: 104.

Description:Rigorous theory of ordinary differential equations. Fundamental existence theorems for initial and boundary value problems, variational equilibria, periodic coefficients and Floquet Theory, Green's functions, eigenvalue problems, Sturm-Liouville theory, phase plane analysis, Poincare-Bendixon Theorem, bifurcation, chaos.

This course

Textbook:

E. Coddington, N. Levinson, Theory of ordinary differential equations. ISBN-13: 978-0898747553 Amazon Abebooks (This is not the same as "Introduction to ordinary differential equations" by Coddington.)

Recommended Reading: E.L. Ince, Ordinary Differential Equations, Dover Publications, 1958, ISBN 0486603490 Abebooks Amazon

Links related to the course:

Grading:

Grading will be based on homework and a takehome final, that will be closely based on homework questions.

Suggested homework (due 1 week after it is set):

  1. Aug 28 No homework.
  2. Sep 2 No homework.
  3. Sep 4 Chapter 1, problems 1, 10, 11
  4. Sep 9 Chapter 1, problems 2, 3
  5. Sep 11 Chapter 1, problems 12
  6. Sep 16 Chapter 2, problems 4, 5
  7. Sep 18 Chapter 3, problems 40, 41
  8. Sep 23 Chapter 3, problems 1,2
  9. Sep 25 Chapter 3, problems 18,26
  10. Sep 30 Chapter 3, problems 16, 17
  11. Oct 2 Chapter 4, problems 5, 6
  12. Oct 7 Chapter 4, problems 8,9
  13. Oct 9 Chapter 4, problems 10, 11
  14. Oct 14 Chapter 4, problems 7, 12 Oct 21 Chapter 5, problem 4
  15. Oct 23 Chapter 5 problem 2
  16. Oct 28 Chapter 5, problem 5
  17. Oct 30 Chapter 7, problems 1,2
  18. Nov 4 Chapter 7, problems 3, 13
  19. Oct 6 (No homework)
  20. Nov 13 Chapter 7, problems 5, 6
  21. Nov 18 Chapter 7, problems 4, 15
  22. Nov 20 Describe the spectum of the Sturm-Liouville problem of the real line for the potential given by V(x) = -U for |x|< 1, V(x)=0 otherwise. In other words find the spectrum corresponding to u'' -V(x) u. How many eigenvalues are there? What is the continuous part of the spectrum?
  23. Nov 25 Chapter 9, Problem 3.
  24. Dec 2 Chapter 10, Problem 4
Final exam