| Date | Chapter | Lecture | DDS | HW | Problems | Due |
|---|---|---|---|---|---|---|
| 11-Jan | 1: Modeling | Models | 1.2-1.4 | #1 | Ch1: 2,3,4,7,10 Ch2: 1,6,7,9 |
1/25/10 |
| 13-Jan | Phase Plane, Nullclines | 1.5-1.7 | ||||
| 15-Jan | 2: Linear Systems | Matrix ODEs | 2.1 | |||
| 18-Jan | HOLIDAY | |||||
| 20-Jan | 2D Systems, Exponentials | 2.2-2.3 | ||||
| 22-Jan | etA for Complex | 2.4-2.5 | ||||
| 25-Jan | Uniqueness, etA for Multiple | 2.6 | HW 1 Due | |||
| 27-Jan | Stability | 2.7 | #2 | Ch 2: 12,14,15abf,19,23 Ch 3: 4,5,8 |
2/12/10 | |
| 29-Jan | Floquet Theory I | 2.8 | ||||
| 1-Feb | Floquet Theory II | 2.8 | ||||
| 3-Feb | 3: Existence & Uniqueness | Function Space Preliminaries | 3.1-2 | |||
| 6-Feb | Existence & Uniqueness | 3.3 | ||||
| 8-Feb | Existence & Uniqueness II | |||||
| 10-Feb | Dependence upon initial conditions | 3.4 | ||||
| 12-Feb | Maximal Interval of Existence | 3.5 | HW 2 Due | |||
| 15-Feb | 4: Dynamical Systems | Flows & Vector Fields | 4.1-2 | Project selection | ||
| 17-Feb | Global Existence & Linearization | 4.3-4 | #3 | Ch 3: 10,11 Ch 4: 1a, 2c,3a-d,5, 8b, 9 |
3/1/10 | |
| 19-Feb | Stability | 4.5 | ||||
| 22-Feb | Lyapunov Functions | 4.6 | ||||
| 24-Feb | Conjugacy | 4.7 | ||||
| 26-Feb | Conjugacy II | 4.7 | ||||
| 1-Mar | Hartman-Grobman, Omega Limits | 4.8-9 | HW 3 Due | |||
| 3-Mar | Omega Limits, Attractors | 4.9-10 | #4 | Ch 4:12,15,18
Ch 5:1,3,4,9 |
3/17/10 | |
| 5-Mar | 5: Invariant Manifolds | Heteroclinic Orbits | 5.1-2 | |||
| 8-Mar | Stable Manifolds I | 5.3 | ||||
| 10-Mar | Stable Manifolds II | 5.4 | ||||
| 12-Mar | Center Manifolds | 5.6 | ||||
| 15-Mar | NO CLASS | (out of town) | ||||
| 17-Mar | 6: Nonhyperbolic Equilibria | 6.1-2 | HW 4 Due | |||
| 19-Mar | Centers | 6.3 | Project Proposal Due | |||
| 22-Mar | SPRING BREAK | |||||
| 24-Mar | SPRING BREAK | |||||
| 26-Mar | SPRING BREAK | |||||
| 29-Mar | 7: Chaos | Defining Chaos | 7.1 | #5 | Ch 7:5,6,7,9,11abd | 4/12/10 |
| 31-Mar | Lyapunov Exponents I | 7.2 | ||||
| 2-Apr | Lyapunov Exponents II | |||||
| 5-Apr | Strange Attractors | 7.3 | ||||
| 7Apr | Fractals, Dimension | |||||
| 9-Apr | 8: Bifurcation Theory | Saddle-Node, Non-bifuraction theorem | 8.1-2 | |||
| 12-Apr | Unfolding | 8.3 | HW 5 Due | |||
| 14-Apr | Saddle-Node Theorem | 8.4 | #6 | Summarize your quadratic system | 4/23/10 | |
| 16-Apr | Saddle-Node in R^n | 8.6 | ||||
| 19-Apr | Hopf Bifurcation | 8.8 | ||||
| 21-Apr | Codimension Two | 8.9-8.10 | ||||
| 23-Apr | Takens Bogdanov | 8.9-8.10 | HW #6 Due | |||
| 2-Apr | Homoclinic bifurcations | 8.11 | ||||
| 28-Apr | Presentations | Fox, Bowen, Hougland | ||||
| 30-Apr | Skardal, Lieb, Martin | Project Due | ||||
| 1-May | Final Exam | Project Presentations | 1:30-4:30 | (May be extended to 5:30) |