Discrete analogue of Green's theorem Following formula concerning finite differences is in a way a discrete analogue of the fundamental theorem of calculus:
$$\sum_{n=a}^b \Delta f(n) = f(b+1) - f(a) $$
We can think about the Green's theorem as a two-dimensional generalization of fundamental theorem of calculus, so I'm interested is there a discrete analogue of Green's theorem?

It's entirely about summation: in a partition of a plane region $R$, we have the following for any function $G$ defined on the edges of the partition:
$$\sum_{\partial R} G=\sum_{R} \Delta G$$
($\Delta G$ is defined on the faces of the partition).
