Changes

:<math>\operatorname{div}\,\mathbf{F} = \lim_{V \rightarrow 0} \frac{ \oint_\mathbf{S} \mathbf{F} \cdot d\mathbf{a} }{V}</math>

:<math>\operatorname{div}\,\mathbf{F} = \lim_{V \rightarrow 0} \frac{ \oint_\mathbf{S} \mathbf{F} \cdot d\mathbf{a} }{V}</math>

Where the integral is over the boundary surface <math>\mathbf{S}=\partial V</math> surrounding the volume element V, which is taken to be zero in the limit.

Where the integral is over the boundary surface <math>\mathbf{S}=\partial V</math> surrounding the volume element V, which is taken to be zero in the limit.<ref>[http://mathworld.wolfram.com/Divergence.html Divergence] from Wolfram Mathworld</ref>

==Cartesian coordinates==

==Cartesian coordinates==

Intuitively, the divergence measures the degree to which the vector field is diverging from a given point.  If you were to measure the divergence of the vector field of wind speed in the vicinity of a meteorological high pressure area, it would be positive, because the net motion of air is outward.  If measured near a low pressure area, the divergence would be negative.

Intuitively, the divergence measures the degree to which the vector field is diverging from a given point.  If you were to measure the divergence of the vector field of wind speed in the vicinity of a meteorological high pressure area, it would be positive, because the net motion of air is outward.  If measured near a low pressure area, the divergence would be negative.

==References==

==References==

*[http://mathworld.wolfram.com/Divergence.html Divergence] from Wolfram Mathworld

 

*[[Curl]]

*[[Laplacian]]

[[Category:Calculus]]

[[Category:Calculus]]

[[Category:Physics]]

[[Category:Physics]]