||AM 0107/BI 0149
Tuesdays and Thursdays, 2:30 - 3:50 PM
Sciences Library, room 418
Quantitative Models of Biological
(Prerequisites: AM 33-34 or AM 35-36)
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
Edelstein-Keshet, Leah. Mathematical
Models in Biology. McGraw-Hill,
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.
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
Populations (growth, demography and genetics)
II. Continuous Processes (Ordinary Differential
More population dynamics (Lotka-Volterra)
Molecular biology (Michaelis-Menten)
III. Spatially Distributed Systems (Partial
More genetics (Fisher's Equation)
Epidemiology (Black Death)
IV. Special Topics (Project Presentations)
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.
|First day of classes
||Tuesday, September 5
||Thursday, September 14
||Thursday, September 21
||Thursday, September 28
||Thursday, October 5
||Thursday, October 12
|Homework # 6
||Thursday, October 19
|Homework # 7
||Thursday, October 26
||Thursday, November 23
|Thursday, November 30
Thursday, December 7
||Thursday, December 14
|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