| Date |
Topic |
Assignment |
Due Date |
| 1/24-1/25 | |||
| Th |
1 Overview Lab #1 Introduction to Mathematica |
Read Chapter 1 | |
| F |
2.1-2 Flows on the line | 2.1.2, 2.1.3, 2.2.3, 2.2.4 |
Wed 1/30 |
| 1/28-2/1 |
|||
| M | 2.3 Population growth |
2.3.2, 2.3.4, 2.4.4, 2.4.7 | Fri 2/1 |
| W |
2.5 Existence and uniqueness |
2.5.1, 2.5.4, 2.5.6 | Wed 2/6 |
| Th |
Lab #2 Euler's Method | ||
| F |
Picard iteration 2.6 Impossibility of oscillations |
2.7.3, 2.7.4, 2.7.6 , 2.7.7 | Wed 2/6 |
| 2/4-2/8 |
|||
| M |
2.7 Potentials 3.1 Saddle-node bifurcation |
3.1.2, 3.1.4, 3.1.5 | Fri 2/8 |
| W |
3.2 Transcritical bifurcation Example from lecture |
3.2.3, 3.2.5, 3.2.6 | Wed 2/13 |
| Th |
Lab #3 Bifurcation diagrams | ||
| F |
Finish 3.2 | ||
| 2/11-2/15 |
|||
| M |
3.3 Laser threshold | 3.3.1, 3.3.2 | Mon 2/18 |
| W |
3.4 Pitchfork bifurcation Example from lecture |
3.4.4, 3.4.5, 3.4.6, 3.4.11, 3.4.16 | Fri 2/22 |
| Th |
No class | ||
| F |
No class | ||
| 2/18-2/22 |
|||
| M |
3.5 Overdamped bead on a rotating hoop | 3.5.7, 3.5.8 | Wed 2/27 |
| W |
Dimensional analysis | ||
| Th |
Lab #4 Another bifurcation diagram | ||
| F |
Singular limit | ||
| 2/25-3/1 |
|||
| M |
3.6 Imperfect Bifurcations | 3.6.2, 3.6.3, 3.6.4 | Fri 3/1 |
| W |
3.7 Insect Outbreak | 3.7.6 | Fri 3/8 |
| Th |
Lab#5 Tricritical bifurcation Original article |
||
| F |
Biochemical switch (3.7.5) | ||
| 3/4-3/8 |
|||
| M | Review | ||
| W |
Exam 1 | ||
| Th |
Lab #6 Biochemical switch | ||
| F |
4.1 Flows on the circle |
4.1.3, 4.1.7, 4.1.8 | Fri 3/15 |
| 3/11-3/15 |
|||
| M |
4.3 Nonuniform oscillator | 4.3.3, 4.3.6, 4.3.9 | Mon 3/25 |
| W |
4.5 Fireflies | 4.5.1 | Mon 3/25 |
| Th |
Lab #7 Overdamped pendulum | ||
| F |
5.1 Linear systems | 5.1.10, 5.1.11 | Fri 3/29 |
| 3/16-3/24 |
Spring break | ||
| 3/25-3/29 | |||
| M |
5.2 Classification (eigenvalue analysis) | 5.2.1, 5.2.2, 5.2.3, 5.2.5, 5.2.7, 5.2.9 | Mon 4/1 |
| W |
2nd order systems: existence and uniqueness | ||
| Th |
Lab #8 Eigenvalues and stability of dynamical systems | ||
| F |
Forced systems and resonance | Resonance example | |
| 4/1-4/5 |
|||
| M |
5.3 Love affairs | 5.3.3, 5.3.4 | Fri 4/5 |
| W |
6.1-2 Phase portraits | 6.1.2, 6.1.3, 6.1.6, 6.2.2 | Mon 4/8 |
| Th |
Lab #9 Nonlinear systems | ||
| F |
6.3 Fixed points and linearization | 6.3.2, 6.3.3, 6.3.6, 6.3.11 | Fri 4/12 |
| 4/8-4/12 |
|||
| M |
6.4 Rabbits vs sheep |
6.4.6 |
Mon 4/15 |
| W |
6.5 Conservative systems | 6.5.19 | Wed 4/17 |
| Th |
Lab #10 Conservative systems | ||
| F |
6.6 Reversible systems | 6.6.3 | Wed 4/17 |
| 4/15-4/19 |
|||
| M |
7.1 Limit cycles | 7.1.5, 7.1.8 Project proposal due today |
Fri 4/19 |
| W |
7.2 Liapunov functions | 7.2.6, 7.2.10, 7.2.13 | Wed 4/24 |
| Th |
Lab #11 Scroll circuit | ||
| F |
7.3 Poincare-Bendixson theorem Review |
7.3.1 |
Fri 4/26 |
| 4/22-4/26 |
|||
| M |
Exam 2 | ||
| W |
7.5 Relaxation oscillators | 7.5.5 | Mon 4/29 |
| Th |
Lab #12 Limit cycles | ||
| F |
8.1 Bifurcations revisited | 8.1.1-4,8.1.6, 8.1.13 | Wed 5/1 |
| 4/29-5/3 |
|||
| M |
8.2 Hopf bifurcations |
8.2.2, 8.2.3, 8.2.5 Hopf example |
Fri 5/3 |
| W |
8.3 Oscillating chemical reactions 9.0 Lorenz equations |
8.3.1 Project outline due today Chemical oscillator example |
Mon 5/6 |
| Th |
Lab #13 Lorenz equations | ||
| F |
9.1 Chaotic water wheel | 9.1.3 | Wed 5/8 |
| 5/6-5/8 |
|||
| M |
9.2 Properties of Lorenz eqs |
9.2.2 Estimating Liapunov exponents |
Wed 5/8 |
| W |
9.3,5 Chaos on a strange attractor Exam 3: take home exam, due 4pm Wed May 15 Project due 4pm Tuesday May 14 |
Watch Strogatz's demos of chaos (go to website, then open Quicktime video at bottom) |