Variable conversion in surface integral

[nigels]

Hello helpful fellas, I'm reading an ecological model that involves setting up boundaries conditions. As part of a longer derivation, there is this flux equation (seen in attachment). Since I haven't formally studied vector calculus, please educate me in how it works and preferably with derivations showing the equality.

Thanks.

 

[HallsofIvy]

That is the "Gauss's theorem" in three dimensions. Wikipedia has an article on that and variations at http://en.wikipedia.org/wiki/Divergence_theorem.

 

[nigels]

Thanks!