MA775 - Ordinary Differential Equations - Fall
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
- Local Nonlinear Theory: invariant manifolds, Hartman-Grobman, Poincare
- 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.
- Homework 1, due Tuesday, Sept 14
- Homework 2, due Tuesday, Sept 28
- Homework 3, due Thursday, Oct 7
- Homework 4, due Thursday, Oct 21
- Homework 5, due Thursday, Oct 28
- Homework 6, due Thursday, Nov 4
- Homework 7, due Thursday, Nov 11
- Homework 8, due Tuesday, Nov 23
Books and references:
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:
The main book we will use is
- J. Guckenheimer and P. Holmes, "Nonlinear
oscillations, dynamical systems, and bifurcations of vector fields."
Applied Mathematical Sciences, 42, Springer-Verlag, 1990, ISBN: 0-387-90819-6.
- S. N. Chow and J. K. Hale, "Methods of bifurcation
theory," Grundlehren der Mathematischen Wissenschaften [Fundamental
Principles of Mathematical Science], 251, Springer-Verlag, 1982, ISBN: 0-387-90664-9.
- Y. A. Kuznetsov, "Elements of applied
bifurcation theory," Applied Mathematical Sciences, 112, Springer-Verlag, 2004, ISBN: 0-387-21906-4.
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.
Instructor: Margaret Beck
Office: MCS 233
Email: mabeck -at- math.bu.edu
Office Hours: Tues 1:30-3, Wed 11-12, or by appointment