| Week |
Date |
Sections |
Topics covered |
homework problems |
Due |
| 1 |
27-Aug |
1 |
Terminology |
|
|
| |
29-Aug |
2.2,2.4 |
One-dimensional flows, fixed points, stability |
|
|
| |
31-Aug |
|
Chaos: the video |
|
|
| 2 |
3-Sep |
no class |
|
Labor Day |
|
| |
5-Sep |
2.4,2.8 |
Discussion groups |
|
|
| |
7-Sep |
2.8 |
Linear stability. Numerics |
|
|
| 3 |
10-Sep |
3.1,3.2 |
Bifurcations (saddle node and transcritical) |
|
|
| |
12-Sep |
|
HW presentations |
|
|
| |
14-Sep |
3.3,3.4 |
Bifurcations (transcritical, pitchfork) |
|
|
| 4 |
17-Sep |
3.5,3.6 |
Bead on a wire |
|
|
| |
19-Sep |
3.6 |
Catastrophe (cusp bifurcations) |
|
|
| |
21-Sep |
10.1 |
Fixed points and cobwebs |
|
|
| 5 |
24-Sep |
10.2 |
More on bifurcations. Logistic map |
|
|
|
26-Sep |
|
HW presentations |
|
|
|
28-Sep |
10.3 |
Logistic map - computer lab |
|
|
| 6 |
1-Oct |
10.4 |
Period doubling |
|
|
| |
3-Oct |
10.5 |
Period 3. Chaos |
|
|
| |
5-Oct |
10.6 |
Lyapunov exponents |
|
|
| 7 |
8-Oct |
10.7 |
Chaos and binary shift |
|
|
| |
10-Oct |
3.5 |
Periodic windows |
|
|
| |
12-Oct |
3.6 |
Renormalization |
|
|
| 8 |
15-Oct |
3.7 |
More on renormalization |
|
|
| |
17-Oct |
3.8 |
HW presentations |
|
|
| |
19-Oct |
5.1,5.2 |
Classification of linear systems |
|
|
| 9 |
22-Oct |
5.3 |
Love affairs |
|
|
|
24-Oct |
|
Homework presentation (renormalization, step II) |
|
|
| |
26-Oct |
5.2 |
More on linear systems |
|
|
| 10 |
29-Oct |
6.1 |
The phase plane. A clinical model |
|
|
| |
31-Oct |
6.1,6.2 |
Linear systems. Nullclines |
|
|
| |
2-Nov |
6.3,6.5 |
Linearization about fixed points. Conservative systems |
|
|
| 11 |
5-Nov |
7.1,7.2 |
Limit cycles. Gradient systems and Lyapunov functions |
|
|
| |
7-Nov |
7.4,7.5 |
Poincare-Bendixon theorem |
|
|
| |
9-Nov |
9.1 |
Relaxation oscillations |
|
|
| 12 |
12-Nov |
9.2 |
Lorenz model |
|
|
| |
14-Nov |
9.1 |
A water-weel model |
|
|
| |
16-Nov |
|
Lorenz system |
|
|
| 13 |
19-Nov |
no classes |
 |
Fall break |
|
| 14 |
26-Nov |
9 |
Lorenz system |
|
|
| |
28-Nov |
9 |
More on Lorenz analysis. |
|
|
| |
30-Nov |
11.1 |
Cantor sets. The horseshoe map. The solenoid. |
|
|
| 15 |
3-Dec |
11 |
More on Cantor sets. |
|
|
| |
5-Dec |
11.3,11.4 |
Fractal dimension. Box dimension. |
|
|
| |
7-Dec |
12 |
The Henon map. A 2D strange attractor. |
|
|
| 16 |
10-Dec |
|
Presentations |
|
|
| |
12-Dec |
|
Presentations |
|
|
| |
14-Dec |
|
Presentations |
|
|
| |
TBA |
TBA |
Final/presentations |
|
|