Curl of a Vector Field

Both Stokes' Theorem and Gauss' Theorem are three-dimensional generalizations of Green's Theorem. To state these theorems we need the notions of curl and divergence in three dimensions. The curl of a vector field in the plane is a scalar field, while the curl of a vector field in space is another vector field. However, the divergence in both cases is scalar.

This can be remembered by writing the curl as a "determinant"

The divergence of F is the real valued function