Course notes will be distributed to registered students. In addition the following
references are excellent.
Here is a timetable of lecture topics. The last column shows activities for the week.
This schedule may be updated as the semester progresses.
| Lecture |
Date |
Topics |
Due Dates |
| 1 |
Sept 8 |
Introduction: nonlinear ODEs; nonlinear phenomena; phase portraits |
|
| 2 |
Sept 15 |
Mathematical background |
|
| 3 |
Sept 22 |
Existence and uniqueness of solutions |
Homework 1 |
| 4 |
Sept 29 |
Comparison lemma, Continuity w.r.t. ic's; finite escape time; limit sets |
Quiz 1 |
| 5 |
Oct 6 |
Invariant sets; Nagumo theorem, stability definitions |
|
| |
Oct 13 |
Thanksgiving |
|
| 6 |
Oct 20 |
Lyapunov stability theory, Barbashin-Krasovksii theorem |
Homework 2 |
| |
Oct 27 |
Fall Break |
|
| 7 |
Nov 3 |
Exponential stability, nonautonomous systems, converse theorems |
Quiz 2 |
| 8 |
Nov 10 |
LaSalle Invariance Principle; Barbalat's Lemma |
Project Proposal |
| 9 |
Nov 17 |
Stability of perturbed systems |
Homework 3 |
| 10 |
Nov 24 |
Advanced topics |
Quiz 3 |
| 11 |
Dec 1 |
Advanced topics |
|
| |
Dec 15 |
Final Project |
|
Homework will be submitted on Quercus by 5pm on the due date.