# Green's theorem

In vector analysis, Green's theorem
is an extension of the **divergence theorem**, which latter
states:

where **V** is a vector and *d***S** an element of a surface.
If **V** has components (*x*, *y*, *z*)
for a volume *v* and a surface *S*, Green's theorem states:

Green's theorem provides a connection between path integrals over a well-connected region in the plane and the area of the region bounded in the plane. It is a form of the fundamental theorem of calculus, and is used today in almost all computer codes that solve partial differential equations.