f[x_,y_,z_]:=x^2 y z; F[x_,y_,z_]:={-y,x,z^2 x};
grad[U_]:={D[U[x,y,z],x],D[U[x,y,z],y],D[U[x,y,z],z]};
curl[F_]:={D[F[x,y,z][[3]],y]-D[F[x,y,z][[2]],z],
           D[F[x,y,z][[1]],z]-D[F[x,y,z][[1]],x],
           D[F[x,y,z][[2]],x]-D[F[x,y,z][[3]],y]};
div[F_]:=D[F[x,y,z][[1]],x]
        +D[F[x,y,z][[2]],y]
        +D[F[x,y,z][[3]],z];
