MA775 - ODEs - Spring 2014

MA775 - Ordinary Differential Equations - Spring 2014

MWF 11am-12pm in PSY B39

Contact Information

Instructor: Margaret Beck
Office: MCS 233
Phone: 617-358-3314
Email: mabeck -at- math.bu.edu
Office Hours: M 9-10:30, Wed 4-5:30, or by appointment

Announcements

None at the moment

Course Info

Syllabus and detailed course information: [.pdf] file
Grading: homework (70%; assigned every 1-2 weeks), and a final project (30%; details on syllabus)

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: fundamental solutions, matrix exponentials (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, ...

Books
The main book we will use is

C. Chicone, "Ordinary Differential Equations with Applications," Texts in Applied Mathematics, 34, Springer 2006, ISBN: 978-0387-30769-5.

You can access the entire book electronically here through the BU library. Another book that people have found useful in the past is

L. Perko, "Differential Equations and Dynamical Systems," Texts in Applied Mathematics, 7. Springer 2001, ISBN: 0-387-95116-4,

which is available phyiscally through the BU library.

Homework

Homework 1 (due Jan 27): [.pdf]
Homework 2 (due Feb 5): [.pdf]
Homework 3 (due Feb 19): [.pdf]
Homework 4 (due March 3): [.pdf]
Homework 5 (due March 24): [.pdf]
Homework 6 (due April 9): [.pdf]
Homework 7 (due April 23): [.pdf]