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Fall 2005 Math 634

What, When, and Where:

Course Description:

Theory of Ordinary Differential Equations: Initial-value problems, existence and uniqueness of solutions, linear and nonlinear theory, stability theory, invariant manifold theory, bifurcation theory, and boundary-value problems.

Text:

Lecture notes and handouts

Lectures:

MWF 10:00-10:50 133 TMCB

Office Hours:

MWF 11:00-11:50 306 TMCB

Grading Scheme:

50% Homework Assignments
25% Midterm Exam (take-home)
25% Final Exam (take-home)

Course Schedule: (subject to change)

Aug 29 Normed Linear Spaces I
Aug 31 Normed Linear Spaces II, Completeness
Sep 02 Banach Spaces
Sep 05 Labor Day
Sep 07 Contraction Mapping Principle
Sep 07 Bounded Linear Operators I
Sep 12 Bounded Linear Operators II; Differentiation I
Sep 14 Differentiation II
Sep 16 Inverse Function Theorem
Sep 19 Implicit Function Theorem
Sep 21 Existence and Uniqueness for IVP
Sep 23 Extension Theorem
Sep 26 Continuous Dependence on Parameters
Sep 28 General Linear Systems
Sep 30 Finite Dimensional Linear Systems
Oct 03 Variation of Constants
Oct 05 Review: Spectral Theory
Oct 07 Review: Spectral Theory II
Oct 10 The Resolvent
Oct 12 Local Properties
Oct 14 Spectral Resolution
Oct 17 Spectral Decomposition I
Oct 19 Spectral Decomposition II
Oct 21 Class Cancelled
Oct 24 Overview of Stability
Oct 26 Guest Lecture: Controls I
Oct 28 Guest Lecture: Controls II
Oct 31 Stability I
Nov 02 Stability II
Nov 04 Lyapunov for Rest Points I
Nov 07 Lyapunov for Rest Points II
Nov 09 Lyapunov for Rest Points III
Nov 11 Lyapunov for Rest Manifolds I
Nov 14 Lyapunov for Rest Manifolds II
Nov 16 Lyapunov for Rest Manifolds III
Nov 18 Lyapunov Functions
Nov 21 Guest Lecture: Discrete Systems
Nov 22 Guest Lecture: Discrete Systems II

Assignments:

Assignment #1 (Due 09/19/05)
(pdf)

Assignment #2 (Due 10/17/05)
(pdf)