# Blatt 7
# Aufgabe 7.2
restart;
f := 1-x^2-y^2;
T := mtaylor(f, [x=-1/4, y=-1/4], 2);
plot3d([f,T], x=-1..1, y=-1..1);
restart;
with(VectorCalculus):
SetCoordinates('cartesian'[x,y,z]);
F := VectorField(1/(x^2+y^2+z^2)^(3/2)*<x,y,z>);
divF := Divergence(F);
simplify(divF);
Curl(F);
f := x^2+y^2+z^2;
g := x+2*y+3*z-7;
L := f+lambda*g;
gL := Gradient(L,[x,y,z,lambda]);
solve({gL[1]=0,gL[2]=0,gL[3]=0,gL[4]=0},{x,y,z,lambda});
restart;
f := (x,y) -> x^2+y^4;
int(int(f(x,y),y=-sqrt(1-x^2)..sqrt(1-x^2)),x=-1..1);
int(int(f(r*cos(phi),r*sin(phi))*r,r=0..1),phi=0..2*Pi);