Course Head: Thomas W. Judson
Office: SC 435
Tel: 4954744
Email:judson@math.harvard.edu
Office Hours: 34 pm on Monday, 3:304:30 Thursday or by appointment.
Course Assistants:
Blythe Adler (bmadler@fas.harvard.edu) and
Nick Ma (nma@fas.harvard.edu)
Textbook:
Clifford Taubes.
Modeling Differential Equations in Biology,
PrenticeHall, Upper Saddle River, NJ, 2001.
Course Description:
Considers the construction and analysis of mathematical models that arise in the environmental sciences, biology, the ecological sciences, and in earth and atmospheric sciences. Introduces mathematics that includes multivariable calculus, differential equations in one or more variables, vectors, matrices, and linear and nonlinear dynamical systems. Taught via examples from current literature (both good and bad).
Goals of the Course: To understand how mathematics and other
subjects, in this instance biology, can enrich and enliven each other. After
taking this course one should be able to read and interpret articles in
Biology or related subjects which employ the use of differential equations.
Moreover, one should be able to identify whether the mathematics is merely
"window dressing" or whether it is used in a substantial fashion to gain
insight to an interesting phenomenon.
It is hoped that after taking this course a student will be comfortable
formulating and analyzing elementary differential equations. If such a
student should become a researcher, they should have the ability to employ
mathematical techniques or seek collaboration with a mathematician in order
to model problems of interest.
Grading:
Your course grade will be determined as follows:

Homework 25%

Two Midterms 25% each

Final Project 25%
Midterms:

First midterm Wednesday, October 23, in regular classroom and during
regular class time.

Second midterm Monday, November 25, in regular classroom and during
regular class time.
Makeup exams will be administered only if a documented serious illness or
personal tragedy prevents of person from taking an exam at the scheduled time.
Homework:
Homework problems are an integral part of this course. It is difficult to
understand the material and do well on the exams without working through the
homework problems in a thoughtful manner. Please think about the problems
posed, your strategy, the meaning of the computations you perform, and
the answers you get.
Although discussion of the homework with your peers is
encouraged, copying any part of another person's assignment is at odds with
Harvard's Code of Student Conduct. No late homework will be accepted. The lowest three homework scores will be dropped.
Course Outline:
We will cover all 28 chapters of the textbook in order.
 Chapter 1. Introduction
 Chapter 2. Exponential growth
 Chapter 3. Introduction to Differential Equations
 Chapter 4. Stability in a one component system
 Chapter 5. Systems of First Order Differential Equations
 Chapter 6. Phase plane analysis
 Chapter 7. Introduction to vectors
 Chapter 8. Equilibrium in 2Component, linear systems
 Chapter 9. Stability in nonlinear systems
 Chapter 10. Nonlinear stability again
 Chapter 11. Matrix notation
 Chapter 12. Remarks about Australian Predators
 Chapter 13. Introduction to Advection
 Chapter 14. Diffusion equations
 Chapter 15. Two key properties of the advection and diffusion equations
 Chapter 16. The no trawling zone
 Chapter 17. Separation of variables
 Chapter 18. The diffusion equation and pattern formation
 Chapter 19. Stability criteria
 Chapter 20. Summary of advection/diffusion
 Chapter 21. Traveling waves
 Chapter 22. Traveling wave velocities
 Chapter 23. Periodic solutions
 Chapter 24. Fast and slow
 Chapter 25. Estimating elapsed time
 Chapter 26. Switches
 Chapter 27. Testing for Periodicity
 Chapter 28. Causes of Chaos
