| APPM 3010 Schedule (Fall 2012) |
| Wk |
Date |
Ch |
Sec |
Topic |
Assignments |
Due |
| 1 |
27 |
1 |
|
Terminology |
|
|
|
| |
29 |
2 |
2,4 |
One-d flows, qualitative analysis |
|
|
|
| |
31 |
|
|
Chaos, the video |
Ch 2 |
§1 #1, 2, 4 §2 #3, 4 §3 #4 §4 #4 §8 #2, 6 |
12-Sep |
| |
Sept-3 |
|
LABOR DAY |
|
|
|
| 2 |
5 |
|
|
Discussion Groups—Video |
|
|
|
| |
7 |
|
4,8 |
Linear Stability, Numerics |
|
|
|
| 3 |
10 |
3 |
1,2 |
Bifurcations: Saddle Node & transcritical |
|
|
|
| |
12 |
|
|
HW Presentations, Bifurcation Theory |
|
Solutions for Problem2.8.6 |
|
| |
14 |
3 |
4,5 |
Bead on a Wire |
Ch 3 |
§1 #1, 2, 5; §2 #3, 5; §4 #4, 12; §5 #4; §7 #4 |
26-Sep |
| 4 |
17 |
|
5,6 |
Catastrophe (cusp bifurcations) |
|
|
|
| |
19 |
10 |
1 |
Fixed Points, and Cobwebs |
|
|
|
| |
21 |
|
2 |
Bifurcations etc. Logistic Map |
|
|
|
| 5 |
24 |
|
2 |
Logistic Map, Part II |
|
|
|
| |
26 |
|
|
HW Presentations and Period 2 |
|
Solutions for 3.7.4 |
|
| |
28 |
|
3 |
Logistic Lab Logistic Map: Computer Lab |
|
(Project Selection Due) Lab is HW#3 |
3-Oct |
| 6 |
Oct-1 |
|
4 |
PeriodDoublings |
|
|
|
| |
3 |
|
|
Periodic 3 -> Chaos |
|
|
|
| |
5 |
|
5 |
Lyapunov Exponents |
|
|
|
| 7 |
8 |
|
|
Lyapunov and Chaos |
Ch 10 |
§1 #10,11; §2 #4,6,8; §3 #4,13; §4 #2,6; §6 #5 |
17-Oct |
| |
10 |
|
|
Chaos and Binary Shift |
|
|
|
| |
12 |
|
4 |
Universality |
|
|
|
| 8 |
15 |
|
6 |
Renormalization |
|
|
|
| |
17 |
|
|
Arcadia by Tom Stoppard |
|
A class reading of several scenes |
|
| |
19 |
11 |
|
Fractals and Dimension |
|
Solutions for HW 4 |
|
| 9 |
22 |
|
|
Self-Similarity |
|
|
|
| |
24 |
5 |
|
Classification of Linear Systems |
Ch 5 |
§1 #7,10; §2 #4,8,10 E.C. #14 |
Nov-7 |
| |
26 |
6 |
1,2 |
Linear systems, Nullclines |
Ch 6 |
§1 #6,11; §3: #2,6,7, §5: #5 |
Nov-7 |
| 10 |
29 |
|
|
Computer Demos, Phase Plane |
|
|
|
|
31 |
|
3 |
Linearization about Fixed Points |
|
|
|
| |
Nov-2 |
|
5 |
Conservative Systems |
|
Project Proposal Due! |
|
| 11 |
5 |
7 |
1 |
Limit Cycles Def. |
|
|
|
|
|
|
|
HW in class |
|
|
|
| |
|
|
2 |
Gradient Systems and Lyapunov Functions |
|
|
|
| 12 |
12 |
|
3 |
Poincare Bendixson Theorem |
|
|
|
| |
14 |
9 |
1 |
Lorenz Model-the Water wheel |
|
|
|
| |
16 |
|
2 |
Lorenz Analysis |
|
|
|
| 13 |
19 |
|
|
FALL BREAK |
| |
21 |
|
|
FALL BREAK |
| |
23 |
|
|
FALL BREAK |
| 14 |
26 |
|
|
Lorenz Analysis-Lyapunov |
|
|
|
f
| |
28 |
|
|
Poincare & Stoboscopic Maps, Std Map |
|
|
|
| |
30 |
|
|
Fixed Points and Stability |
|
|
|
| 15 |
Dec-3 |
|
|
Std Map Lab |
|
ECCR 225, the Macintosh Computer Lab. |
Dec 7 |
| |
5 |
12 |
2 |
Henon Attractor, Dimension |
|
|
|
| |
7 |
12 |
1 |
Baker's Transformation, Horseshoe |
|
|
|
| 16 |
10 |
|
|
Symbolic Dynamics |
|
|
|
| |
12 |
|
|
Presentations |
|
Ethan Oehring & Eric James |
|
| |
14 |
|
|
Presentations |
|
Randell Callahan & Mackenzie Green |
Written Proposals Due |
| |
18 |
|
Final |
Presentations 7:30-10:00PM |
|
Everyone Else |
|