The divergence of a Vector Field is given by

(1) 
Define

(2) 
Then in arbitrary orthogonal Curvilinear Coordinates,

(3) 
If
, then the field is said to be a Divergenceless Field. For divergence in individual
coordinate systems, see Curvilinear Coordinates.

(4) 
The divergence of a Tensor is

(5) 
where
is the Covariant Derivative and is the Comma Derivative. Expanding the terms gives
See also Curl, Curl Theorem, Gradient, Green's Theorem, Divergence Theorem,
Vector Derivative
References
Arfken, G. ``Divergence, .'' §1.7 in
Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 3742, 1985.
© 19969 Eric W. Weisstein
19990524