2006 Fall MATH 231-01
Bulletin Course Description Existence and uniqueness theorems for nonlinear systems, well-posedness, two-point boundary value problems, phase plane diagrams, stability, dynamical systems, and strange attractors. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title ORDINARY DIFF EQUATIONS Department MATH Course Number 2006 Fall 231 Section Number 01 Primary Instructor Schaeffer,David G Permission required? N
Prerequisites
Math 103 (Multiple-variable calculus), Math 104 (Linear
algebra), and Math 139 (Analysis). A previous course in
ODE is useful but not required.
Synopsis of course content
Theory for existence (local and global), uniqueness, and
continuous dependence on parameters.
Linear equations with constant or periodic coefficients.
Stability of equilibria and periodic orbits.
Bifurcation theory: Local (steady state and Hopf) and
global (homoclinic).
An example of chaos (The Lorenz attractor).
Textbooks
Hirsch, Smale, and Devaney, "Differential equations, dynamical systems, and an introduction to chaos"
Assignments
Eight to ten problem sets. (One extra class meeting per week, a recitation, will be devoted to problem solutions.)
Exams
Two take-home midterms plus an in-class final exam.
Term Papers
None.
Grade to be based on
Midterms: 35% each
Final: 30%
(Although much homework is assigned, it does not contribute directly to your grade.)
Additional Information
I welcome students outside of Mathematics. The format of
the course makes it fairly easy to accomodate a variety of
backgrounds. Please see me if you are concerned whether
your background will be sufficient for the course.
