Mathematical Modeling
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| Week | Date | Topic | Homework and Reading (due at the beginning of class) |
|---|---|---|---|
| 1 | Monday 9/20/04 |
Course Orientation.
Notes |
|
| Wednesday 9/22/04 |
Chapter 1. Introduction.
Notes |
||
| Friday 9/24/04 |
Chapter 2. Exponential Growth.
Notes |
Read " HIV-1 Dynamics in Vivo: Virion Clearance Rate, Infected Cell Life-Span, and Viral Generation Time," pp. 15-22. | |
| 2 | Monday 9/27/04 |
Chapter 3. Introduction to Differential
Equations.
Notes |
Chapter 2. Exercises 1, 2, 4 (a, b,
c, d), 5; pp. 43-44.
Solutions |
| Wednesday 9/29/04 |
Chapter 4. Stability in a One-Component System.
Notes |
Read "Biologists Sort the Lessons of Fisheries Collapse," pp. 53-55; "New Study Provides some Good News for Fisheries," pp. 55-57; "Population Dynamics of Exploited Fish Stocks at Low Population Levels," pp. 57-62. | |
| Friday 10/01/04 |
Chapter 4. Stability in a One-Component System.
Notes |
Chapter 3. Exercises 1, 2, 3, 4;
pp. 62-63.
Solutions Read "Left Snails and Right Minds," pp. 23-31. |
|
| 3 | Monday 10/04/04 |
Chapter 5. Systems of First-Order
Differential Equations.
Notes |
Chapter 4. Exercises 1, 2, 4, 6; pp. 71-72.
Solutions Read "Wolves, Moose, and Tree Rings on Isle Royale," pp. 96-102. |
| Wednesday 10/06/04 |
Chapter 6. Phase Plane Analysis.
Notes |
||
| Friday 10/08/04 |
Chapter 6. Phase Plane Analysis.
dfield and pplane Notes |
Chapter 5. Exercises 1; p. 86. Chapter 6. Exercises 1, 2, 3, 4 (a, c) 5; pp. 102-103. Solutions |
|
| 4 | Monday 10/11/04 |
Columbus Day No Class |
|
| Wednesday 10/13/04 |
Chapter 7. Definition of Vectors.
Notes |
||
| Friday 10/15/04 |
Chapter 8. Equilibrium in Two-Component, Linear Systems.
Notes |
Chapter 7. Part 1: Exercise 1;
Part 2: Exercises 1, 2, 3, 4, 5, 6; pp. 125-126.
Solutions Read "Better Protection for the Ozone Layer," pp. 131-138. |
|
| 5 | Monday 10/18/04 |
Chapter 9. Stability in Nonlinear Systems.
Notes |
Read "Hopes for the Future: Restoration Ecology and
Conservation,"
pp. 153-166. |
| Wednesday 10/20/04 |
Chapter 9. Stability in Nonlinear Systems.
Notes |
||
| Friday 10/22/04 |
Chapter 10. Nonlinear Stability Revisited.
Notes |
Chapter 8. Exercises 1, 2, 3, 4, 5, 7; pp. 138-139.
Chapter 9. Exercises 1, 2, 4, 5; pp. 145-146. Solutions |
|
| 6 | Monday 10/25/04 |
Chapter 11. Matrix Notation.
Notes |
|
| Wednesday 10/27/04 |
Chapter 12. Remarks about Australian Predators.
Notes |
Chapter 10. Exercises 1, 3, 4; p. 172.
Chapter 11. Exercises 1, 2, 3, 4; p. 177. Solutions Read "The Case of the Missing Meat Eaters," pp. 181-184. |
|
| Friday 10/29/04 |
Chapter 13. Introduction to Advection.
Notes |
Read "Malaria: Focus on Mosquito Genes," pp. 198-202. | |
| 7 | Monday 11/01/04 |
Chapter 13. Introduction to Advection.
Notes |
Read "Past Temperatures Directly from the Greenland Ice Sheet," pp. 238-245. |
| Monday 11/01/04 |
Midterm I Review Session.
7:30-9:00 PM in Science Center E. |
||
| Wednesday 11/03/04 |
Chapter 14. Diffusion Equations.
Notes |
||
| Wednesday 11/03/04 |
Midterm I - Chapters 1-12.
7:30-9:30 PM in Science Center D. |
||
| Friday 11/05/04 |
Chapter 15. Two Key Properties of the Advection and Diffusion Equations.
Notes |
Chapter 13. Exercises 1, 3, 5, 6, 7, 8; pp. 213-215.
Solutions |
|
| 8 | Monday 11/08/04 |
Chapter 16. The No-Trawling Zone.
Notes |
Chapter 14. Exercises 1, 3, 5, 6, 8, 10 (a, c, e), 12 (a, c, e);
pp. 224-225.
Solutions Read "Fishing for Answers: Deep Trawls Leave Destruction in Their Wake---But for How Long?" pp. 255-257. |
| Wednesday 11/10/04 |
Chapter 17. Separation of Variables.
Notes |
Chapter 15. Exercises 1 (a, c), 2 (a, c); p. 245.
Solutions |
|
| Friday 11/12/04 |
Chapter 17. Separation of Variables.
Notes Solving the Reaction-Diffusion Equation using separation of variables. |
Chapter 16. Exercises 1, 3 (a, c), 4
(a, c, e); p. 258.
Solutions |
|
| 9 | Monday 11/15/04 |
Chapter 18. The Diffusion Equation and Pattern Formation.
Notes |
Read "Dynamics of Stripe Formation," pp. 280-282; "A Reaction-Diffusion Wave on the Skin of the Marine Angelfish," pp. 282-286; "Letters to Nature," pp. 286-288. |
| Wednesday 11/17/04 |
Chapter 18. The Diffusion Equation and
Pattern Formation.
Notes |
||
| Friday 11/19/04 |
Chapter 19. Stability Criterion.
Notes |
Chapter 17. Exercises 1 (a, c, e, f), 2, 3; pp. 264-265.
Solutions Read "Direct and Continuous Assessment by Cells of Their Position in a Morphogen Gradient," pp. 296-300; "Activin Signalling and Response to a Morphogen Gradient," pp. 300-309. |
|
| 10 | Monday 11/22/04 |
Chapter 19. Stability Criterion.
Notes |
Chapter 18. Exercises 1, 2, 3, 5 (a,
c); pp. 309-310.
Solutions |
| Wednesday 11/24/04 |
Chapter 20. Summary of Advection/Diffusion.
Notes |
Chapter 19. Exercises 1, 2, 3, 4, 9 (a,
c);
pp. 316-317.
Solutions |
|
| Friday 11/26/04 |
Thanksgiving Recess No Class |
||
| 11 | Monday 11/29/04 |
Chapter 21. Traveling Waves.
Notes |
Read "Hantavirus Outbreak Yields to PCR," pp. 358-363; "US Braces for Hantavirus Outbreak," pp. 363-364. |
| Wednesday 12/01/04 |
Chapter 21. Traveling Waves.
Notes |
Chapter 20. Exercises 1, 2; pp. 349-350. Solutions |
|
| Friday 12/03/04 |
Chapter 22. Traveling Wave Velocities.
Notes |
Preliminary Project Proposal Due
Project Description |
|
| 12 | Monday 12/06/04 |
Chapter 23. Periodic Solutions.
Notes |
Chapter 21. Exercises 1, 2 (for Exercise 1 (a, c)), 3; p. 364.
Solutions Read "Snowshoe Hare Populations: Squeezed from Below and Above," pp. 382-385; "Impact of Food and Predation on the Snowshoe Hare Cycle," pp. 385-391. |
| Wednesday 12/08/04 |
Chapter 24. Fast and Slow.
Notes |
Chapter 22. Exercises 1, 2, 3, 4; p. 374. Solutions Read "Disparate Rates of Molecular Evolution in Cospeciating Hosts and Parasites," pp. 401-410. | |
| Friday 12/10/04 |
Chapter 24. Fast and Slow.
Notes |
Chapter 23. Exercises 1 (a, c, e), 2 (a, c); pp. 391-392.
Solutions |
|
| Sunday 12/12/04 |
Midterm II Review Session.
7:30-9:00 PM in Science Center E. |
||
| 13 | Monday 12/13/04 |
Chapter 25. Estimating Elapsed Time.
Notes |
Chapter 24. Exercises 1 (a, c), 2 (a, c); pp. 410-411.
Solutions Read "Thresholds in Development," pp. 421-428. |
| Wednesday 12/15/04 |
Chapter 26. Switches.
Notes |
||
| Wednesday 12/15/04 |
Midterm II - Chapters 13-25.
7:30-9:30 PM in Science Center D. |
||
| Friday 12/17/04 |
Chapter 27. Testing for Periodicity.
Notes |
Chapter 25. Exercises 1, 2, 5, 6; pp. 414-415.
Chapter 26. Exercises 1 (a, c), 2 (a, c), 3; pp. 428-429. Solutions |
|
| 14 | Monday 12/20/04 |
Chapter 28. Causes of Chaos.
Notes | Chapter 27. Exercises 1, 2; p. 450.
Solutions |
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