Mathematical Modeling

Home  >  assignments

Week 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14

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
Sphere
 line drawing for decoration
Fall 2004

URL: assignments/index.html
Last modified: 12/21/2004 Harvard
University FAS Shield
 
Copyright ©The President and Fellows of Harvard College