Editing Vector field (section)

===Divergence===
{{Main|Divergence}}
The [[divergence]] of a vector field on Euclidean space is a function (or scalar field).  In three-dimensions, the divergence is defined by
<math display="block">\operatorname{div} \mathbf{F} = \nabla \cdot \mathbf{F} = \frac{\partial F_1}{\partial x} + \frac{\partial F_2}{\partial y} + \frac{\partial F_3}{\partial z},</math>

with the obvious generalization to arbitrary dimensions.  The divergence at a point represents the degree to which a small volume around the point is a [[sources and sinks|source or a sink]] for the vector flow, a result which is made precise by the [[divergence theorem]].

The divergence can also be defined on a [[Riemannian manifold]], that is, a manifold with a [[Riemannian metric]] that measures the length of vectors.