Luento ti 17.10.00

EHY vakioiden variointikaavalla

> with(linalg):

> A:=matrix([[-2,1],[1,-2]]);g:=t->vector([2*exp(-t),3*exp(t)]);

A := matrix([[-2, 1], [1, -2]])

g := proc (t) options operator, arrow; vector([2*ex...

> psi:=t->matrix([[exp(-3*t),exp(-t)],[-exp(-3*t),exp(-t)]]);

psi := proc (t) options operator, arrow; matrix([[e...

> inverse(psi(s));evalm(% &* g(s));

matrix([[1/2*1/exp(-3*s), -1/2*1/exp(-3*s)], [1/2*1...

vector([exp(-s)/exp(-3*s)-3/2*exp(s)/exp(-3*s), 1+3...

> map(int,%,s);

vector([1/2*exp(s)^2-3/8*exp(s)^4, s+3/4*exp(s)^2])...

> evalm(psi(s)&*%);

vector([exp(-3*s)*(1/2*exp(s)^2-3/8*exp(s)^4)+exp(-...

> map(simplify,%);

vector([1/2*exp(-s)+3/8*exp(s)+exp(-s)*s, -1/2*exp(...

> x:=evalm(psi(s)&*vector([c1,c2])+%);

x := vector([exp(-3*s)*c1+exp(-s)*c2+1/2*exp(-s)+3/...

> map(simplify,%);

vector([exp(-3*s)*c1+exp(-s)*c2+1/2*exp(-s)+3/8*exp...

> vasen:=map(diff,x,s);

vasen := vector([-3*exp(-3*s)*c1-exp(-s)*c2+1/2*exp...

> oikea:=evalm((A&*x)+g(s));

oikea := vector([-3*exp(-3*s)*c1-exp(-s)*c2+1/2*exp...

> evalm(vasen-oikea);

vector([0, 0])

>