Useful Stuff for the Course

• Maple V can be downloaded from Public at Public/Licensed Software/ Key Server Controlled/Limited Support/Maple V
• A basic introduction to Maple (in PDF format - you'll need Adobe Acrobat Reader to view it) can be downloaded
• Once you've installed Maple, start it up and try it out. Here are a few matrix commands to try:
  >A := array([[0.3,0.7],[0.9,0.1]]);
  > evalm(A &* A);
  > evalm(A^2);
  > evalm(A^10);
  > with(linalg);
  > inverse(A);
  > evalm(A &* inverse(A));
  > ?matrix;
  > ?linalg;
  > P := array([[0.95,0.03,0.02],[0.1,0.5,0.4],[0.03,0.07,0.9]]);
  (To find the fixed point probability vector for P, do the following:)
  > solve({0.95*w1+0.1*w2+0.03*w3=w1,0.03*w1+0.5*w2+0.07*w3=w2,
  w1+w2+w3=1},{w1,w2,w3});
  To investigate the logistic map, try the following commands:
  plot(3.4*x*(1-x),x=0..1);
  plot({x,3.4*x*(1-x)},x=0..1);
  The fsolve command finds real-valued solutions to equations:
  fsolve(x=3.4*x*(1-x),x,0..1);
  f := x -> 3.4*x*(1-x);
  fsolve(x=f(f(x)),x,0..1);