| Professor: | Dr. Douglas Anderson |
| Ivers 234D | |
| 299-4453 | |
| andersod@cord.edu |
Office Hours: TTh 1:00-4:00, MWF by discovery.
This course will be of interest to those wishing to study modern mathematics in the form of discrete dynamical systems and recursion equations using the computer algebra systems Dynamica and Mathematica. Any mathematics student that enjoyed reading Chaos: Making a New Science by James Gleick or Does God Play Dice? The New Mathematics of Chaos by Ian Stewart will enjoy this course. 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, ISBN: 1584882875. This is a first-edition book from Chapman & Hall/CRC, so there are a few misprints; see the errata page.
Mathematica: To download Mathematica 5.2 from the campus network, go to the download Mathematica page for a free Concordia student version.
Dynamica: To download Dynamica, go to the download Dynamica website. Save it in Program Files > Wolfram Research > Mathematica > 5.1 > 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 |
| Sep 1 | 1.1, 1.2 Linear Difference Eqns | Mathematica for Chapter 1 |
| 3 | Mathematica Lab | Sunday 6pm-8pm, Ivers 222 |
| 4 | 1.3, 1.4A Intro to Stability | (67) 1.1, 1.2 |
| 6 | 1.4.1 More Stability | |
| 8 | 1.4.1 Attractors | (67) 1.4: 1,2,4,5 |
| 11 | Memorial Auditorium | Fall Symposium |
| 13 | 1.5 Nonhyperbolic Case | Handout |
| 15 | 1.6 Bifurcations | Handout |
| 18 | 1.6 Bifurcation Diagrams | |
| 20 | Feigenbaum Number | (68) 1.5: 1,3,4,5; 1.6 |
| 22 | 1.7.4A Lyapunov Numbers | (69) 1.9: 1,2,3 [Hint: p in (-2,0)] |
| 25 | 1.7.4B Conjugacy | |
| 27 | 1.8.1 Cantor Set | (70) 1.12, 1.13 |
| 29 | 1.8.2 Topologically Transitive Functions | |
| Oct 2 | 1.8.2 Chaotic Tent Map | |
| 4 | Baker Map | Handout |
| 6 | 1.8.2 Code Space | |
| 9 | 1.9 Global Attractivity | (71) 1.15: 1,2,3,5 |
| 11 | 1.9 Dissipative Maps | |
| 13 | 1.11 Exercises 1.18:5&6 | (72) 1.18: (1) thru (4), abcd |
| 16 | Exercise 1.18 | continue 1~4:abcd |
| 18 | 1-dimension finale | (73) 1.18.8 |
| 20 | Fall Break | No Class |
| 23 | Fall Break | No Class |
| 25 | 2.2 Linear Theory | |
| 27 | No Class | Nebraska Workshop |
| 30 | 2.2.3 Second-order Equations | |
| Nov 1 | Phase Planes | Handout |
| 3 | 2.3 Equilibria | Mathematica for Chapter 2 |
| 6 | 2.5 Linearization | (192) 2.3, 2.4 |
| 8 | 2.6 Discrete Predator Prey | |
| 10 | No Class | |
| 13 | 2.7 Period Doubling | Handout: 1,2,4(a),5 |
| 15 | 2.11 Manifolds | |
| 17 | 2.11 Homoclinic Orbits | |
| 20 | Two-Species Dynamics | Handout 1-5 |
| 22 | Basins of Attraction | Cournot Duopoly |
| 24 | Thanksgiving Break | No Class |
| 27 | 2.12 Henon's Map | |
| 29 | Cremona Map | Handout 1-5 |
| Dec 1 | 2.13 Invariant Functions | |
| 4 | 2.14 Lyapunov Functions | (196) 2.15: 1-3 |
| 6 | 2.15 Lyness Map | |
| 8 | 2.16 Invariant Intervals | (197) 2.16: 1-3 |
| 11 | Chaos in 3D | Lorenz Model for Atmospheric Dynamics |
| 2.17 Dynamica Session | ||
| Chaotic Population Dynamics | Juvenile-Adult Model | |
| Fractals | Mathematica for Chapter 6 | |