----------------------------------------------
 --- Tutorial proposal form                 ---
 --- for students working with Jim Mahoney  ---
 ----------------------------------------------

 $Id$


 Basic guidelines :

    A typical tutorial is 3 credits : one class per week
    and 8 hours or so of work.  Tutorials are usually for juniors
    or seniors working on advanced or interdisplinary work related
    to computers for which no corresponding course exists.
   
    Group tutorials are also possible; ask around and come talk to me.

    The best way to submit this form is to 
      1) edit this file to include your answers,
      2) email it to mahoney@marlboro.edu, and 
      3) discuss it with me in person.

    Please do come talk to me about your specific situation in any case.


 Your name :            Jesse Welch____________________________________
 

 Tutorial title :       Scientific Computing____________________________


 Desired credits :      Three___________________________________________


 Tutorial description: (appropriate for the registrar's permanent record)

  A study of nonlinear differential equations leading to chaos specifically,
  a study of the differential equation which governs the behavior of the
  nonlinear damped driven pendulum.  Including a study parameter space 
  of chaotic solutions, and methods for determining whether chaos is present in 
  solutions.  Also error control verses computational time.

 What exactly do you want to study?  
 Be as explicit as you can, including a schedule if possible.

  I plan to be working with mathematica to build a differential
  equation solver which will create graphical output in a way useful to 
  observe the chaos and periodicity of solutions to my equation.  I want to map 
  out the parameter space in a way that plots out chaotic verses periodic solutions 
  in the parameter space.  To do that I will need to make the computer program able
  to determine whether solutions are chaotic or not, most likely through the calculation of 
  Lyapunov exponents.  I also want to map out poincare sections of chaotic solutions 
  and make an animation showing the evolution of the poincare sections with the evolution 
  of parameters.  There are many other smaller things that will end up being incorporated 
  into the final project.

 How does this relate to your plan and/or other course work?

  This relates very directly to my plan, as 40% of my plan is going to be
  a paper on this topic and include all the things I mentioned above.  For
  a final project, I plan to culminate everything I've done into a single 
  mathematica package to be called upon later.  This will give the whole 
  project a nice tidy wrapped up feeling to it, as well as the original 
  idea of having a package with functions waiting to be called.  This 
  final package will in the end be included as an appendix to the paper I 
  write, and the package will be used very extensivly when I give a lecture
  on this subject, which will be 10% of my plan.  The functionality of this
  package will make the lecture go much smoother, as the output will be very
  easy to attain.

 What resources have you identified?
 (e.g. books, articles, websites, experience, ...) 

  I have several books on the subject on nonlinear ODE's and chaos in general.
  I also have a paper from the American Journal of Physics which works with 
  this problem specifically.  Through the combination of these things, as well
  as all the references and footnotes included in these books and paper have given
  me a nice place to launch from.  I also hoped you might have a suggestion or two 
  on a nice text or paper.

 What will be the gradeable products, and on what schedule?
 (e.g. projects, programs, papers, tests, ...)

  The most directly gradable part of this will be the final package itself.
  Though, there will obviously be weekly, and many times daily progress that
  I can record and work on with you.  I am also meeting with Travis once a 
  week on this topic, but more specifically on the paper I'm writing, but there
  will be a lot of what we work on included in the paper itself.  So I guess I
  don't know if thats something worth including here or not.