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);
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