Now that we are getting good at doing applications, time to look ahead to your class project. Pick a topic or two to discuss that you think would make for a good project -- you aren't locked into it yet -- just some you would think would make good project. You can discuss those from the text or find others on the internet. Discuss why you find the problem interesting and how you might proceed to solve it. If you have had linear algebra, you may want to look ahead to later chapters where we cover matrices -- a good project could mix our class with linear algebra. (You may also consider topics from the text -- for example, the "group projects" at the end of the chapters).

Questions to answer are --

What is the model (differential equation(s)) for the application?

What are the variables (input and output) and parameters (values that are constant in a given problem, but could be changed -- for example, the growth constant in population growth) in the problem?

What are appropriate methods of solution?

Looking ahead -- the project should have these parts --

>> An introduction that states the problem and gives some background into it

>> An analysis of the problem -- basically a "by hand" solution and the theory behind it.

>> An application of some tool like Matlab or Mathematica (or your own program) to solving the problem (either symbolically or numerically)

>> A generalization of the problem via some parameterization, which may then be applied for solution in your tool of choice from the previous step. (For example, see the demonstrations using the Mathematica "Manipulate" command to change parameter values and view their effects.)

>> Conclusion

>> References