Useful Stuff for the Course

Maple

- 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);