Using the div-flux theorem (Gauss) to derive divergence in polar coördinates?

[nonequilibrium]

Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?

 

[dolphus]

You can do this. Basically, you just divide the flux, (general vector dot producted with the differential surface element in the coordinate system divided by the differential volume element in the coordinate system. I've written up the entire derivation in spherical coordinates at:

http://copaseticflow.blogspot.com/2012/09/an-intuitive-way-to-spherical-gradient.html