MA332 lecture notes, Fall 1998
Week 5, Thursday

Reading: F&B Chapter 5.6: Adaptive Techniques, 5.7: Systems,
and start Chapter 6.

How many already know Gaussian elimination?


   Schedule for immediate future:

   This week: systems of IVPs
   Next week: Chapter 6, direct methods for systems of equations
   Following week: Iterative methods and eigenvalue/vector problems

   Homework: out Friday, due next Thursday.

1) Exam review.

2) Systems of IVPs: total no-brainer

3) Maple hints

   a) hangups?

   b) suggestions for making things better?

   c) index errors (fencepost errors)

      Using indices that agree with the book's can make life easier,
      but sometimes it obscures what's going on.  The better your
      feeling for how the method works, the more likely you can debug
      it.  Try making up your own notation.

   d) Use and print intermediate variables/values to help debug.

   e) out of memory errors:  usually means that you have an undefined
      variable that's getting carried through a calculation symbolically

      Undefined array elements are treated as symbols.

      Check one iteration before doing many.

      Print intermediate values and see if there are any stray symbols.
      
   f) learning new features:

      Read the book

      Read the online help

      Type in and try out the examples provided.

      If you want to know how something works, try it!

   g) If I help you debug a program, you should be learning how to
      debug, not learning what the bug was.  Pay attention to the
      process.

   h) Avoid magical thinking.  Maple is deterministic.  If you don't
      understand a result, simplify the problem.

   i) Don't count on error messages to tell you when you do something
      wrong.  They produce many false negatives.

   j) When you get a result, especially an unexpected one, you never
      know whether it is correct (and weird) or incorrect.  It is
      a disconcerting feeling.  Get used to it.