| APPM 3010 Schedule |
| Wk |
Date |
Ch |
Sec |
Topic |
Assignments |
Due |
| 1 |
22 |
1 |
|
Terminology |
|
|
|
| |
24 |
2 |
2,4 |
One-d flows, qualitative analysis |
|
|
|
| |
26 |
|
|
Chaos, the video |
Ch 1 |
§1 #1, 2, 3 §2 #2, 7 §3 #3 §4 #7 §8 #2, 6 |
7-Sep |
| 2 |
29 |
|
|
Discussion Groups—Video |
|
|
|
| |
31 |
|
4,8 |
Linear Stability, Numerics |
|
|
|
| |
Sept-2 |
3 |
1,2 |
Bifurcations: Saddle Node & transcritical |
|
|
|
| 3 |
5 |
|
LABOR DAY |
|
|
|
| |
7 |
|
|
HW Presentations, Bifurcation Theory |
|
Solutions for HW 1 |
|
| |
9 |
3 |
4,5 |
Bead on a Wire |
Ch 3 |
§1 #1, 2, 4; §2 #4, 5; §4 #2, 12; §5 #4; §7 #5 |
21-Sep |
| 4 |
12 |
|
5,6 |
Catastrophe (cusp bifurcations) |
|
|
|
| |
14 |
10 |
1 |
Fixed
Points, and Cobwebs |
|
|
|
| |
16 |
|
2 |
Bifurcations etc. Logistic Map |
|
|
|
| 5 |
19 |
|
2 |
Logistic Map, Part II |
|
|
|
| |
21 |
|
|
HW Presentations and Period 2 |
|
Solutions for 3.7.5 |
|
| |
23 |
|
3 |
Logistic Map: Computer Lab |
Lab |
ECCR 225 12 noon (Lab report is HW 3) |
30-Sep |
| 6 |
26 |
|
4 |
PeriodDoublings |
|
|
|
| |
28 |
|
5 |
Periodic 3 -> Chaos |
|
Project Selection Due |
|
| |
30 |
|
6 |
Lyapunov Exponents |
|
|
|
| 7 |
Oct-3 |
|
7 |
Lyapunov and Chaos |
Ch 10 |
§1 #10,11; §2 #4,6,8; §3 #4,13; §4 #2,6; §6 #5 |
14-Oct |
| |
5 |
|
|
Chaos and Binary Shift |
|
|
|
| |
7 |
|
|
Periodic Windows |
|
|
|
| 8 |
10 |
|
|
Renormalization |
|
|
|
| |
12 |
|
|
Renormalization |
|
|
|
| |
14 |
|
|
Arcadia by Tom Stoppard |
|
Solutions for HW 4 |
|
| 9 |
17 |
5 |
1,2 |
Classification of Linear Systems |
Ch 5 |
§1 #7,10; §2 #3,4,8, E.C. #14 |
Nov-2 |
| |
19 |
6 |
1,2 |
Linear systems, Nullclines |
Ch 6 |
§1 #6,10; §3: #2,6,7, §5: #6 |
Nov-2 |
| |
21 |
|
|
Computer Demos, Phase Plane |
|
|
|
| 10 |
24 |
|
3 |
Linearization about Fixed Points |
|
|
|
| |
26 |
|
5 |
Conservative Systems |
|
|
|
| |
28 |
7 |
1 |
Limit Cycles Def. |
|
|
|
| 11 |
31 |
|
2 |
Gradient Systems and Lyapunov Functions |
|
|
|
| |
Nov-2 |
|
|
HW in class |
|
|
|
| |
4 |
|
3 |
Poincare Bendixson Theorem |
|
|
|
| 12 |
7 |
|
4,5 |
Relaxation Oscillations |
|
|
|
| |
9 |
9 |
1 |
Lorenz Model |
|
|
|
| |
11 |
|
2 |
Lorenz Analysis |
|
Project Proposal Due! |
|
| 13 |
14 |
|
3 |
Lorenz Analysis |
|
|
|
f
| |
16 |
8 |
|
Poincare Maps, Henon Map |
|
|
|
| |
18 |
|
|
Std Map Lab |
|
ECCR 225, the Macintosh Computer Lab. |
Nov 28 |
| 14 |
21 |
|
|
FALL BREAK |
| |
23 |
|
|
FALL BREAK |
| |
25 |
|
|
FALL BREAK |
| 15 |
28 |
|
|
Fractal Dimension |
|
|
|
| |
30 |
|
|
2DMaps, Henon Attractor, Dimension |
|
|
|
| |
Dec-2 |
|
|
Review: What have we learned? |
|
|
|
| 16 |
5 |
|
|
Presentations |
|
Young and Bergenthal |
|
| |
7 |
|
|
Presentations |
|
Beale-Bonafanti and Warren-Stillwell |
|
| |
9 |
|
|
Presentations |
|
Schilling-Firner and Economou-Hass |
|
| |
14 |
|
Final |
Presentations 1:30-4:00PM |
|
Everyone Else |