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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.


Given a vector field F(x, y, z) = Pi + Qj + Rk in space. The curl of F is the new vector field


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


The divergence of F is the real valued function


Last Update: 2006-11-22