**Prof. S. R. Lubkin**

SAS 4226, 5-1904

lubkin@eos.ncsu.edu, http://www4.ncsu.edu/~lubkin/

**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.

- Please staple all homeworks.
- Every graph must be labeled.
Always label all axes. Arrowheads have a very specific meaning indicating
the direction of motion or of a vector or time. Arrows do not belong on
axes or curves unless they are intended to indicate time
or motion or vectors.
- If you are asked to
make an argument, or "show that..." then you need to use enough
words to make that argument. Mathematical symbols without context make no
sense. Look at your textbook: it is mostly words with symbols used within
the sentences. That is how your homework should be
written.
- If you do calculations in Maple (for instance)
and hand in the Maple session, the printout should be
edited for clarity and conciseness just as you would edit your
handwritten notes (only giving me your best work). It is easy to make
graphs in Maple, but you should only show those graphs
which illustrate your point. Delete graphs which
do not contribute to your discussion. The same holds for any computer
tool, e.g. Excel. Clean it up, but show what you did. Show what you did,
but clean it up.

**Links**

Logistic map applets:

http://www.enm.bris.ac.uk/staff/hinke/courses/Chaos/applets/iteration/Iteration.html