Operations On Vector Fields

We compute the curl and divergence of a vector field and compute the gradient of a function using Maple. These commands are also in the linalg package.

with(linalg):
f := vector( [ x^2-2*y*z, y^3+3*x*z, z^2 + x*y ] );    f is the vector field
v := vector( [x,y,z] );                  x,y,z the independent variables
curl(f, v);                              curl of the vector field f
diverge(f, v);                           divergence of the vector field f
p := x^2 + y^3*z^2 ;                     a function of x,y,z
grad(p, v);                              gradient of p

Once can also plot two and three dimensional vector fields using commands in the plots package. To plot the two dimensional vector field over the range -2<x,y<2, use

with(plots): with(linalg):
f := vector( [y, sin(x) + y/10] );
fieldplot( f, x=-2..2, y=-2..2 );