AM 107 AM 0107/BI 0149
Tuesdays and Thursdays, 2:30 - 3:50 PM
Sciences Library, room 418

Quantitative Models of Biological Systems

(Prerequisites: AM 33-34 or AM 35-36)

Instructor: Russell Jackson
office: 182 George St., room 005
phone: 863-3878
office hours: Wednesdays 3-4
Thursdays 12-1 
and by appointment
Homework Grades

Course description Textbook Computers Syllabus Objectives Schedule

Course Description

Mathematical biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in the biomedical sciences.  Many biological processes can be quantitatively characterized by difference equations and (both ordinary and partial) differential equations.  This course introduces students to a variety of models and develops the analytical tools from Linear Algebra and Dynamical Systems Theory for investigating these models.


Edelstein-Keshet, Leah.  Mathematical Models in Biology. McGraw-Hill, Inc., 1988.

Additional References

Keener, J. and Sneyd, J. Mathematical Physiology. Springer, 1998.

Murray, J.D. Mathematical Biology. 2nd, Corrected Edition, Springer, 1993.

Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications To Physics, Biology, Chemistry and Engineering.  Addison-Wesley, 1994.


A knowledge of computer programming is not neccesary for this class.  However, the computer can often be used to gain valuable insight into modelling problems.  MATLAB is available on the university's network of computers and is natural for use in linear algebra and dynamical systems applications.  To get you started, A MATLAB Primer, written by the late Kermit Sigmon of the University of Florida, is available in PostScipt (.ps) here or in Adobe Acrobat (.pdf) here.  Additionally, John Polking of Rice University has written up several helpful programs (in MATLAB) for visualizing one and two-dimensional ODEs.  These are available through his website here.


I. Discrete Processes in Biology (Difference Equations)
Populations (growth, demography and genetics)

II. Continuous Processes (Ordinary Differential Equations)
More population dynamics (Lotka-Volterra)
Molecular biology (Michaelis-Menten)
Neuroscience (Hodgkin-Huxley/Fitzhugh-Nagumo)
Pathogenesis (HIV/AIDS/drugs)

III. Spatially Distributed Systems (Partial Differential Equations)
More genetics (Fisher's Equation)
Epidemiology (Black Death)

IV. Special Topics (Project Presentations)
Dealer's choice


Learning Objectives and Instructor Expectations

Although the subject matter of this course could easily be made incredibly difficult, I will attempt to present the course material in as simple a manner as possible.  More theoretical aspects, such as proofs, will not generally be presented.  Applications will be emphasized.  Homeworks will be used to reinforce class lectures, not as a method to introduce material not covered in class.  A take-home late-term exam will emphasize basic techniques as applied to simple, fundamental problems.  A final project with both a written paper and an in-class presentation will be your opportunity to demonstrate both your mastery of the materials and your initiative.

Schedule and Homework

Follow the links in the table below to obtain a copy of each homework in PostScript (.ps) or Adobe Acrobat (.pdf) format once it becomes available.  You may also obtain solutions to some of the homework and exam problems here.
Schedule Due Date Homework Copy Additional Items
First day of classes Tuesday, September 5
Homework #1 Thursday, September 14  hw1.html  
Homework #2 Thursday, September 21  hw2.html  
Homework #3 Thursday, September 28 hw3.html am107.m
Homework #4 Thursday, October 5  hw4.html  
Homework #5  Thursday, October 12  hw5.html  
Homework # 6 Thursday, October 19  hw6.html  
Homework # 7 Thursday, October 26 hw7.html  
Thanksgiving Thursday, November 23
Project Presentations
Project Papers
Thursday, November 30
Thursday, December 7
Take-Home Exam Thursday, December 14 final.html
Last day of classes Thursday, December 7


Your course grade will be calculated by weighing your homework, exam, and Final Project in the proportions 35%, 25%, and 40% respectively.  I will assign homeworks most Thursdays, due the following Thursday.  Homework constitutes 35% of your final grade.  There will also be a take-home exam late in the semester which constitutes 25% of your grade.  The final project will account for 40% of your grade: divied up between your written paper, your presentation, and your class participation during others' presentations.

last update: Thursday, November 30, 2000