Overview:

• The project is in two parts, the preliminary part due Tuesday, April 2 and the final part due at noon on Thursday May 9th.
  
• The preliminary part is worth 50 points and the final part 100 points.  But the whole project will be normalized to 40% of the final grade.
• You are required to talk to me in person about your project before turning in the preliminary part.  You will likely discover that I want to simplify everything.
  
• The preliminary part should be between 5 and 10 pages of genuine content .
• The final part should be longer but I will regard it as a bad thing if there is more than 25 pages of text and numbers.  That is, you might have a number of figures but I think that good technical writing will allow you to do the main part of the job in well under 25 pages.

What to include in the preliminary part:

• Start with a relatively detailed description of the problem you propose to address.  This will typically mean a description of an equation, first of all by explaining the source of the equation and then by explaining the particular form of the problem you are interested in.  For instance, in some cases the goal is to understand the effect of a parameter on the solutions.  In some cases you are doing a pure boundary problem, in other cases an initial and boundary value problem.  You don't have to do a PDE but it should involve a continuum model.  That is, to specify an exact solution must require infinitely many numbers.  Pure ODE problems are not allowed.  Inverse problems, delay differential equations, and differential algebraic equations are interesting non-PDE classes and are encouraged;  you may discover that your scientific/engineering situation requires such mathematical frameworks.
• Please try to do a really simple case of your problem in the preliminary part.
• Then propose what numerical approach you intend to follow for the remainder of the project.  This is the most important thing in the preliminary part!  For instance, spend a page on describing existing literature.  Spend a page on a search for existing software.  A first place to look is in the Matlab documentation.  For instance, linear algebra routines of varius types, ODE routines, splines, Fourier transforms, etc. can all be done well without leaving the world of Matlab.  After that you may want to look at Matlab toolboxes, but you are in charge of getting access to these.  Some of these toolboxes are too general and too complete--I encourage you not to just run one of them on you problem though that may be possible in some cases.  For further existing codes, see Netlib at  netlib.bell-labs.com/netlib .

What to include in the final part:

• Everything else.  I hope that your emphasis will be on understanding and evaluating numerical quality.  That is, some of your project must be used to explain the mathematical model in which you are interested, but mostly you want to compare numerical approaches and/or evaluate the quality of  the numerical approach(es).  For instance, examine in  detail a simple case where you can get an analytical solution or analytical approximation.  More realistically, a comparison of the result of certain calculations for different parameter values and different methods may make up the bulk of your project.  
• If it is at all possible, do a local truncation error calculation and a stability analysis if they are appropriate.
• Include a bibliography that shows you have looked into existing ways of solving your kind of problem and also shows where your problem comes from.