| Week |
Date |
Sections |
Topics covered |
tentative homework |
Due |
| 1 |
25-Aug |
1 |
Terminology |
|
|
| |
27-Aug |
2.2,2.4 |
One-dimensional flows, fixed points, stability |
2.1.4, 2.2.1, 2.2.6, 2.2.8, 2.2.9, 2.2.12, 2.4.2, 2.4.9 (optional) |
3-Sept |
| |
29-Aug |
|
Discussion groups |
Group projects |
12-Sept |
| 2 |
1-Sep |
No class |
Labor Day |
|
|
| |
3-Sep |
2.4,2.8 |
Linear stability. Numerics |
|
|
| |
5-Sep |
2.8 |
Chaos: the movie |
|
|
| 3 |
8-Sep |
3.1,3.2 |
Bifurcations (saddle node and transcritical) |
3.1.1,3.1,3.,3.2.3,3.2.4 |
19-Sept |
| |
10-Sep |
3.6 |
Catastrophe (cusp bifurcations) |
|
|
| |
12-Sep |
3.3,3.4 |
Bifurcations (transcritical, pitchfork) |
3.4.4,3.4.6,(optional 3.4.14) |
22-Sept |
| 4 |
15-Sep |
3.5,3.6 |
Bead on a wire |
|
|
| |
17-Sep |
3.8 |
Insect outbreak |
|
|
| |
19-Sep |
10.1 |
Fixed points and cobwebs |
3.6.3, 10.1.9,10.1.11 |
29-Sept |
| 5 |
22-Sep |
10.2 |
More on bifurcations. Logistic map |
|
|
|
24-Sep |
|
HW presentations |
|
|
|
26-Sep |
10.3 |
Logistic map - computer lab |
10.3.5, 10.3.10 |
6-Oct |
| 6 |
29-Sept |
10.4 |
Period doubling |
|
|
| |
1-Oct |
10.5 |
Period 3. Chaos |
10.5.1, 10.5.2, 10.5.7 |
10-Oct |
| |
3-Oct |
10.6 |
Lyapunov exponents |
|
|
| 7 |
6-Oct |
10.7 |
Chaos and binary shift |
|
|
| |
8-Oct |
3.5 |
Periodic windows |
|
|
| |
10-Oct |
3.6 |
Renormalization |
|
|
| 8 |
13-Oct |
3.7 |
More on renormalization |
|
|
| |
15-Oct |
3.8 |
Midterm I (in class) |
Exam,Solutions |
Oct-22 |
| |
17-Oct |
5.1,5.2 |
Classification of linear systems |
|
|
| 9 |
20-Oct |
5.3 |
More on classification |
5.2.11, 5.3.3, 5.3.4, 5.3.5, 5.3.6 |
Oct-24 |
|
22-Oct |
|
Love affairs |
|
|
| |
24-Oct |
5.2 |
More on linear systems |
5.1.9, 5.1.10 (a)&(e), 5.2.8, 5.2.13 |
Oct-31 |
| 10 |
27-Oct |
6.1 |
Linear / nonlinear systems. The phase plane. |
|
|
| |
29-Oct |
6.1,6.2 |
Nonlinear systems. Nullclines. |
|
|
| |
31-Oct |
6.3,6.5 |
Linearization about fixed points. Conservative systems |
6.3.10, 6.3.14, 6.5.1, 6.5.2 |
7-Nov |
| 11 |
3-Nov |
7.1,7.2 |
Limit cycles. Gradient systems and Lyapunov functions |
7.2.9(a & c), 7.2.12 |
14-Nov |
| |
5-Nov |
7.4,7.5 |
Poincare-Bendixon theorem |
|
|
| |
7-Nov |
9.1 |
Relaxation oscillations |
|
|
| 12 |
10-Nov |
9.2 |
Lorenz model |
|
|
| |
12-Nov |
9.1 |
A water-weel model |
|
|
| |
14-Nov |
|
Lorenz system |
9.2.1 |
|
| 13 |
17-Nov |
9 |
Lorenz system |
|
|
| |
19-Nov |
9 |
Midterm II (in class) |
Exam |
|
| |
21-Nov |
11.1 |
Cantor sets. The horseshoe map. The solenoid. |
Movie night |
|
| 14 |
24-Nov |
No classes |
 |
Go vegan! |
|
| 15 |
1-Dec |
11 |
More on Cantor sets. |
|
|
| |
3-Dec |
11.3,11.4 |
Fractal dimension. Box dimension. |
11.2.5,11.3.2,11.3.4, 11.3.7,11.3.9,11.4.1,11.4.2 |
|
| |
5-Dec |
12 |
The Henon map. A 2D strange attractor. |
|
|
| 16 |
8-Dec |
|
Presentations |
|
|
| |
10-Dec |
|
Presentations |
|
|
| |
12-Dec |
|
Presentations |
|
|
| |
TBA |
TBA |
Final/presentations |
|
|