The divergence of a Vector Field is given by
Then in arbitrary orthogonal Curvilinear Coordinates,
, then the field is said to be a Divergenceless Field. For divergence in individual
coordinate systems, see Curvilinear Coordinates.
The divergence of a Tensor is
is the Covariant Derivative and is the Comma Derivative. Expanding the terms gives
See also Curl, Curl Theorem, Gradient, Green's Theorem, Divergence Theorem,
Arfken, G. ``Divergence, .'' §1.7 in
Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 37-42, 1985.
© 1996-9 Eric W. Weisstein