Can Green's Theorem be extended to three dimensions?

[robert spicuzza]

If you start with the two dimensional green's theorem, and you want to extend this three dimensions.

F=<P,Q>
Closed line integral = Surface Integral of the partials (dP/dx + dQ/dy) da
seems to leads the divergence theorem,
When the space is extended to three dimensions.

On the other hand:
Closed line integral = Surface Integral of the partials (dQ/dx - dP/dy) da
seems to lead to Stokes theorem when the space is extended to three dimensions.

Would it be correct to view these two vector calculus theorems this way.
Start with the two dimensional Green's theorem and go either way to get the Divergence
or Stokes theorem.

 

[fresh_42]

Stokes, Green, and Gauß are all generalizations of the fundamental theorem of calculus. Gauß is a special case of Stokes as is Green.