The purpose of the project is to give you an opportunity to pursue an independent study of an interesting mathematical topic in differential equations. If you take this project seriously I expect it will become the most meaningful and memorable part the course for you. If you do not intend to take the project seriously, then turning in weekly homework assignments will be more valuable to you.

Here are some minimum guidelines for a finished project:

1. A beautifully written report of at least ten pages, not including diagrams, that any math251 student can pick up and enjoy.
2. Include diagrams.
3. A 20-30 minute presentation of your topic to the class or to me.

Possible Topics: (Most of these can be found in your text. If you have a great idea that you want to explore, then let me know about it.)

1. Bessel's Equation (always a popular topic for physicists.)
2. Laplace Transform (a nice topic for the pure mathematician, although it has many applications in engineering and physics.)
3. Numerical Techniques (a good topic for those who enjoy computer applications.)
4. The Lorenz Equations (a fascinating way to learn about chaos.)
5. The Poincare-Bendixson Theorem (a nice topic for the pure mathematician with interesting applications to periodic behavior.)
6. The Heat Equation (very interesting from both the pure and applied points of view.)

Important Suggestions:

I suggest that you keep your project narrow and deep rather than broad and superficial. You can learn a lot of good mathematics by learning everything there is to know about one important example. You will also learn more if you challenge yourself to explain the material so clearly and completely that any calculus student can read and appreciate your report. Finally, every time that you get ready to ask me "Am I done yet?" be prepared to hear the answer "Of course not, there are still (blank) days in the semester."