If you wish, you may form a small group to do a project on material related to this course for 20% of your grade. This is an opportunity to choose a subject which interests you and to study it in more depth (and perhaps to get to know other students with similar interests). You are urged to work in groups of two or three (groups of one or four are permitted). The subject must relate in some fashion to ordinary, partial or finite difference equations. You should expect to produce a report of four to eight typed pages, depending on the number of people in your group. You are expected to use resources other than the course text. Typed copy is always preferable to handwritten work, and computer generated pictures often make the project more interesting. A video was once submitted as part of the work and enjoyed by all (it received an A!). This is your chance to do something that interests you.

Interesting applications of ordinary differential equations can be found in almost any book with modeling in the title, as well as in many engineering texts, most physics books, and some biology books. There are many books with chaos in the title which describe the basic experiments on long-term behavior of finite difference equations. We also have some hand-outs, which you can request once you have decided what you are interested in. Here are some of the topics which have been used by previous students:

Mathematical model of the glucose regulatory system
Hilbert's 16th problem
Warfare strategies
Epidemiological models for AIDS
Economic games
Kepler's laws of planetary motion
Modeling of the HIV virus
Euler's method for numerically solving ODEs
The arms race
Period doubling in the parabola
Electrical circuits
Predator-prey model in ecology
And much, much more!
 

Good places to start are in the applied parts of your text, and any book on chaos which actually writes down the equations. I highly recommend:

Hoppenstadt and Peskin, Mathematics in Medicine and the Life Sciences. Springer-Verlag.

Hirsch and Smale, Differential Equations, Dynamical Systems and Linear Algebra. Academic Press (for Kepler's Laws)

Braun, Coleman and Drew, Differential Equation Models. Springer-Verlag.

Projects which have received good grades in previous semesters may be examined during office hours. Also, I have some relevant books which you may borrow for short periods of time. One good way to get to know
Professor Uhlenbeck is to come in during office hours and look through the books and old projects.

An evaluation form which should be included with your project is attached. It reminds you of the deadlines and gives you some idea of what is expected of the project. Each group should hand in their page each time they submit topic, title and references, and final project. It is understood that a project cannot be outstanding in all categories; the list tells you what we are looking for.

You need to clear your topic with Professor Uhlenbeck according to the published schedule. Topic, group members and at least one reference are due about four weeks into the course. An outline will be due about eight weeks into the course. And the completed project is due about one week before the last class day. Projects turned in late will be graded WHEN and if the professor gets around to it.
 

February 24                Submit topic, list of group members, and at least one reference on the topic for your project
March 24
 Submit title, outline (or description), and list of references for project
April 28                     Project due
 

Your work must be your own. You must acknowledge your sources. You may not copy from books, conversations, and most particularly the Web without giving proper credit. This is a serious offense, and university students should consult with a faculty member if they have any doubts about what is proper to quote or copy, and how you are expected to reference ALL material in scholarly fashion.

You must use a source outside your textbook for reference material, but you are not expected to write a senior thesis! Have fun. Most students who have done a project for M427K have found it a lot of fun and a good way to interact with other students.

The project evaluation form is available so students have some idea on what criteria their project will be graded. You need to hand in the same (or a reworked) copy of this form all three times you submit material for your project.