MA775 - Ordinary Differential Equations - Fall 2010

Lectures: Tuesdays and Thursdays, 11am - 12:30pm, PRB 146

Content of Course:

This course is a graduate level introduction to the mathematical theory of ordinary differential equations. The basic outline for the course is

  • Introduction: existence and uniqueness, flows, first examples
  • Linear Theory: semigroups, spectral theory, Floquet theory, exponential dichotomies
  • Local Nonlinear Theory: invariant manifolds, Hartman-Grobman, Poincare maps
  • Global Nonlinear Theory: Hamiltonian dynamics, Gradient flows and Lyapunov functions, Poincare-Bendixson
  • Bifurcations: saddle node, pitchfork, transcritical, Hopf, normal forms
  • Additional topics (if time permits): forced osciallations, averaging, Melnikov theory, extensions in infinite dimensions, ...

  • Here is your final. Some remarks:
    • It is due by noon on Monday, December 13. (Note: no late papers will be accepted.) Please give it to me directly, put it in my mailbox, slide it under my door, or scan it and email it to me by noon.
    • You may not discuss the final with anyone. It is open book, however, so you may use your notes, book, etc. If you get stuck you can come ask me for a hint, but please do not discuss it with anyone else.
    • We have not covered the material for the last problem, #7, yet. We should get to this on Thursday, Dec 2.
  • There will be no class or office hours on Tuesday, November 30.


Books and references:

The main book we will use is

Unfortunately, the BU library does not have a copy of this book. Although you may find it useful to purchase a copy, you are certainly not required to do so. Other books that you might find interesting and/or useful are:


A .pdf file of the syllabus can be found here. Your grades will be based upon homework assignments (70%), given approximately every one-two weeks, and a take-home final exam (30%). You are encouraged to work together on the homework, but you must work independently on the take-home final.

Contact Information

Instructor: Margaret Beck
Office: MCS 233
Phone: 617-358-3314
Email: mabeck -at-
Office Hours: Tues 1:30-3, Wed 11-12, or by appointment