Prof. S. R. Lubkin
SAS 4226, 5-1904
Office hours: MW 2-2:45 or by appointment
Class meets Mon and Wed 3-4:15 in Harrelson G100
Text: Mathematical Models in Biology, Leah Edelstein-Keshet. SIAM, 2005. If you find a used copy, you will be fine no matter what the edition, because this book has never been revised. For new copies, your cheapest option is to get the member discount from SIAM. Because NCSU has a student chapter of SIAM, membership is free! Do not monopolize the library copy.
Prerequisites: This course is suitable for grad students and undergrads, depending on your math background. You are expected to have passed multivariate calculus and linear algebra, and you should remember the material well enough to build on it. A course in differential equations is not required; BMA 771 is an introductory differential equations course. You should have, as your second text for BMA 771, a calculus and/or linear algebra book for reference, of your choosing. Keep it easily accessible.
Grades: 8-12 homework sets (60% total) and two exams (midterm 15%, final 25%). Not all homework
problems will be graded, but all should be turned in.
Exams must be an individual effort, but homeworks need not be. I encourage you to work with others on the homeworks, and will pass
out a phone list to facilitate this. If you work with
someone else, put both (all) names on the paper for a common grade. Not
more than 3 to a paper, please. Some of the homeworks are intended to be done "by hand", but unless I
say so specifically, you may use computer assistance, if you include the
details in your writeup (e.g. "using Maple function 'eigenvals' to find
the eigenvalues, we find lambda = 1, 2, and pi").
Important point about working with others: The point is to learn. If one person is doing the work and someone else is copying, then someone is not learning. If you begin every problem by asking your partner how to do it, you are not learning. If you try to solve it alone, and need some assistance along the way, that is learning. By the way, explaining things to others contributes very nicely to your own learning!
Goals: By the end of the course, you should be able to construct, interpret, analyze, understand, discuss, and critique linear and nonlinear ordinary differential and difference equations as models of biological systems, by various methods, and you should know something about the types of behavior that these models exhibit (equilibria, oscillations, bifurcations, etc.).
Another goal and a warning: Although assignments at the beginning will be quite structured, they will get more and more vague; you will have to figure out what is called for. This represents the transition from undergraduate-style to graduate-style work, in preparation for the "real world" and/or research. The vagueness will at first be uncomfortable, but soon it will be exciting, like much in life.
Help: Come to office hours, or send me e-mail. Ask each other. Ask other students.
Logistic map applets: