Luento 13, Lineaaristen Dys:ien Maple-käsittelyä

10.10.2000

Esim. 1

> restart:with(LinearAlgebra):A:=Matrix([[-3,1],[1,-3]]);

> esys:=Eigenvectors(A);

> lambda:=esys[1];V:=esys[2];

> v1:=Column(V,1);v2:=Column(V,2);

> X:=C1*exp(lambda[1]*t)*v1+C2*exp(lambda[2]*t)*v2;

Otetaan uusi parametri:

> s=exp(-2*t); # Tämä on vain yhtälö.

> X:=C1*s^2*v1+C2*s*v2;

> XX:=evalm(X);

> parvi:=seq(seq([XX[1],XX[2],s=0..1],C2=-1..1),C1=-1..1);

> plot([parvi]);

Toinen tyyli:

> traje:=(C1,C2)->plot([-C1*s^2+C2*s,C1*s^2+C2*s,s=0..1]):

> with(plots):

> display(traje(1,1));

> display(seq(seq(traje(C1,C2),C2=-2..2),C1=-1..1));

> display(seq(seq(traje(C1,C2),C2=-2..2),C1=-1..1),insequence=true);

>

Exa 1, BdiP ss. 382-384

> restart:with(LinearAlgebra):A:=Matrix([[-1/2,1],[-1,-1/2]]);

> omsys:=Eigenvectors(A):oma:=omsys[1]:omvekt:=omsys[2]:w:=Column(omvekt,1);lambda:=oma[1];

> alpha:=Re(lambda):beta:=Im(lambda):

> u:=map(Re,w);v:=map(Im,w);

> X:=exp(alpha*t)*((a*cos(beta*t)+b*sin(beta*t))*u+b*cos(beta*t)-a*sin(beta*t)*v );

> XX:=evalm(X);

> parvi:=seq(seq([XX[1],XX[2],t=0..10],a=-1..1),b=-1..1):

> plot([parvi[3..4]]);

>