MATH 435: Ordinary Differential Equations

Description

A second course in ordinary differential equations. Existence, uniqueness, and continuation of solutions of ODE. Linear systems, fundamental matrix, qualitative methods (phase plane). Dependence on initial data and parameters (Gronwall's inequality, nonlinear variation of parameters). Stability for linear and nonlinear equations, linearization, Poincare-Bendixson theory. Additional topics may include regular and singular perturbation methods, autonomous oscillations, entrainment of forced oscillators, and bifurcations.

Detailed Syllabus

Textbook

Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith.

Grading

There will be two midterms and a final. The grade will be based on Homework (45%), Midterm 1 (15%), Midterm 2 (15%) and the final exam (25%). These percentages notwithstanding, attendance is required and participation is expected.

Schedule of Homework Exercises

Number Date Assigned Assignment Date Due
1 1/18 First Homework Assignment
(Note there will be no class Monday 1/18, in honor of Dr. Martin Luther King Junior day.)
1/25
2 2/1 Second Homework Assignment 2/8
3 2/15 Third Homework Assignment 2/22
In-class Midterm 1 2/26
3/6 SPRING BREAK 3/14
4 3/15 Fourth Homework Assignment 3/24
5 3/29 Fifth Homework Assignment 4/5
In-class Midterm 2 4/9
6 4/16 Sixth Homework Assignment 4/26
Final Exam 8:30-11:30 a.m. 4/30


Contact Prof. Thomas.

Updated: January 11, 2010