| Professor: | Dr. Douglas Anderson |
| Ivers 234E | |
| 299-4453 (office), 236-7254 (home) | |
| andersod@cord.edu |
Office Hours: TTh 1:00-3:30, MWF by discovery.
This course will be of interest to those wishing to study modern mathematics using the computer algebra systems Dynamica and Mathematica. Topics will include Discrete Dynamical Systems, Difference Equations, Stability Analysis, Phase Portraits, Bifurcation, and Chaos. This is a course that will count as one of the required 300 or above courses for a math major or minor. Prerequisites: Calculus II, Linear Algebra.
Text: Discrete Dynamical Systems and Difference Equations with Mathematica, by Mustafa R.S. Kulenovic and Orlando Merino. This is a just-published book from Chapman & Hall/CRC, so there are a few misprints; see the errata page.
Dynamica: To download Dynamica, go to the download Dynamica website. Save it in Program Files > Wolfram > Mathematica > 4.1 > AddOns > ExtraPackages. Once it is in ExtraPackages, unzip it and put the file Dynamica.m directly in the ExtraPackages folder, outside of the Dynamica subfolder.
| Date | Section | Exercises |
| Aug 30 | 1.1, 1.2 Linear Difference Eqns | Mathematica for Chapter 1 |
| Sep 2 | 1.3, 1.4A Intro to Stability | (67) 1.1, 1.2 |
| 4 | 1.4.1 More Stability | |
| 6 | 1.4.1 Attractors | (67) 1.4: 1,2,4,5 |
| 9 | 1.5 Nonhyperbolic Case | (68) 1.5: 1,3,4,5 |
| 11 | 1.6 Bifurcations | |
| 13 | 1.7 Dynamica | |
| 16 | 1.7.4A Lyapunov Numbers | (69) 1.9: 1,2,3 [Hint: p in (-2,0)] |
| 18 | 1.7.4B Conjugacy | |
| 20 | 1.8.1 Cantor Set | (70) 1.12, 1.13 |
| 23 | 1.8.2 Topologically Transitive Functions | |
| 25 | 1.8.2 Chaotic Tent Map | |
| 27 | Baker Map | Handout |
| 30 | 1.8.2 Code Space | |
| Oct 2 | 1.9 Global Attractivity | (71) 1.15: 1,2,3,5 |
| 4 | 1.9 Dissipative Maps | (72) 1.18: (1) thru (4), abcd |
| 7 | No Class | Work on problems |
| 9 | 1.11 Exercises 5&6 | |
| 11 | 2.2 Linear Theory | |
| 14 | 2.2.3 Second-order Equations | |
| 16 | Phase Planes | Handout |
| 18 | Mid-Sem Recess | No Class |
| 21 | Mid-Sem Recess | No Class |
| 23 | 2.3 Equilibria | Mathematica for Chapter 2 |
| 25 | 2.5 Linearization | (192) 2.3, 2.4 |
| 28 | 2.6 Discrete Predator Prey | |
| 30 | 2.7 Period Doubling | Computer Lab |
| Nov 1 | 2.11 Manifolds | Handout: 1,2,4(a),5 |
| 4 | 2.12 Henon's Map | |
| 6 | 2.13 Invariant Functions | (197) 2.16 |
| 8 | 2.14 Lyapunov Functions | |
| 11 | 2.15 Lyness Map | |
| 13 | 2.17 Dynamica Session | |
| 15 | Review 1-D Dynamics | (73) 1.18.8 |
| 18 | 2.16 Invariant Intervals | Discuss 2.11 |
| 20 | 2.18 Area-Preserving Maps | (193) 2.7:1,2,5a,6,7 |
| 22 | 2.11 Homoclinic Orbits | |
| 25 | Two-Species Dynamics | (179) Problem 12: 1-4 |
| 27 | ||
| 29 | Thanksgiving | No Class |
| Dec 2 | Feigenbaum Number | Analyze your favorite unimodal map |
| 4 | Chaotic Population Dynamics | Juvenile-Adult Model |
| 6 | Chaos in 3D | Lorenz Model for Atmospheric Dynamics |
| 9 | Fractals | Mathematica for Chapter 6 |
| 11 | Pictures 1, 2 | movie poster |
