Changes

Well, consider some specific point, <math>(x_0,y_0,z_0)=\vec{p}</math>.  If we surround <math>\vec{p}</math> with a sphere, call it ''S'', then obviously  

Well, consider some specific point, <math>(x_0,y_0,z_0)=\vec{p}</math>.  If we surround <math>\vec{p}</math> with a sphere, call it ''S'', then obviously  

<math>\oiint_S \vec{F} dS </math>

<math>

\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \vec{F} dS </math>

will contain some contribution from whatever "flow" is coming out of, or going into, <math>\vec{p}</math>.  It will, of course, also contains contributions from the various other points in its interior, but, if we let the radius ''r'' of the sphere ''S'' go to 0, then this integral will ONLY measure the flow at <math>\vec{p}</math>.  Hence we define the '''divergence''' of a vector field <math>\vec{F}</math> as

will contain some contribution from whatever "flow" is coming out of, or going into, <math>\vec{p}</math>.  It will, of course, also contains contributions from the various other points in its interior, but, if we let the radius ''r'' of the sphere ''S'' go to 0, then this integral will ONLY measure the flow at <math>\vec{p}</math>.  Hence we define the '''divergence''' of a vector field <math>\vec{F}</math> as

<math>\div \vec{F} = \lim_{r\to 0} \oiint_S \vec{F} dS </math>

<math>\operatorname{div}\ \vec{F} = \lim_{r\to 0} \left( \frac{1}{\frac{4}{3}\pi r^3} \iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \vec{F}\cdot\vec{n}_S  dS \right)</math>

 

where <math>\vec{n}_S</math> is the outward pointing surface normal of unit length to ''S''.

==Computation==

==Computation==