Math 293, Homework 9, due Wednesday 10/30/96 in lecture.
See WWW page for homework policies.
(*) problems should not be handed in.

1) Download PPLANE and PPSOLVE from course WWW page.
   Save as M files. 
   Run PPlane with following systems and a number of initial
   conditions for each system. 
   Based on what you see say for which system you would
   describe the point x=y=0 as stable, or unstable and why.
   Turn in one annotated plot for one of the three cases
   (a, b,  c  or d below), you choose which one.
  a) x'=-x, y'= -2y.
  b) x'=y, y'=x.
  c) x'=y, y'=-x.
  d) x'=x+y, y'= y-x.

2) Simulate (Using, say ODE23,
   one of the three chaotic systems described in the E&P
   text (eq 13 or 14 on pgs 390-392,
        eq 15 on pg 393, or
        eq 16 on pg 394)
   and show by one appropriate plot that you have found an
   apparantly chaotic motion. Hand in your code.

*) Read T&F section 13.1 (all). You should be able to
   do essentially all the problems 13.1.1-66 (although
   you may need to use integral tables or a symbolic
   program to do some of the 1D integrals you run into).

   Do enough of these problems, starting with the easiest,
   so that you know what you can do.
   TA HW solution will include a few of these.

3) (a) Hand in  13.1.49.
   (*) Use the method of problems 55 and 56 to
       get a reasonably accurate numeric approximation to
       49 and use it to check your analytic solution (or
       visa versa) pretending that the answer was not at 
       the back of the book.  This  requires that you write 
       a loop in a loop in MATLAB (see sample on loops in 
       course WWW page). TA homework solution will show
       a solution to this.

4) Hand in 13.1.61  (this problem is easy, don't ask for
   help until you have given it 15 min thought.).

-Andy Ruina,   ruina@cornell.edu,   office hrs thursdays 1-5 (TH 102, near stairs)
Math 293 on the net:  http://tam.cornell.edu/faculty/ruina/www_293/home.html