Editing Green's theorem (section)

{{Short description|Theorem in calculus relating line and double integrals}}
{{About|the theorem in the plane relating double integrals and line integrals|Green's theorems relating volume integrals involving the Laplacian to surface integrals|Green's identities}}
{{Distinguish|text=[[Green's law]] for waves approaching a shoreline}}
{{Calculus |Vector}}

In vector calculus, '''Green's theorem''' relates a [[line integral]] around a [[Curve#Definition|simple closed curve]] {{mvar|C}} to a [[double integral]] over the [[Plane (geometry)|plane]] region {{mvar|D}} (surface in <math>\R^2</math>) bounded by {{mvar|C}}. It is the two-dimensional special case of [[Kelvin–Stokes theorem|Stokes' theorem]] (surface in <math>\R^3</math>). In one dimension, it is equivalent to the fundamental theorem of calculus. In three dimensions, it is [[Divergence theorem#Multiple dimensions|equivalent to the divergence theorem]].