'''Green's Theorem''' relates enables easy calculation of the [[circulation]] of a two-dimensional function, as well as the area inside any closed curve. This theorem expresses the line integral of two functions over a closed curve to in terms of the double integral of the partial derivatives of those same functions:
::<math>\oint_{C} (P\, \mathrm{d}x + Q\, \mathrm{d}y) = \iint_{R} \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right)\, \mathrm{d}x{d}y.</math>
Simply stated, Green's Theorem converts a line integral over a closed curve (which may be difficult to computea loop) into a double integral (which may be that is often easier to solve). This theorem is an extension of calculus to the context of integrals in planar regions.
Green's Theorem is a popular topic in advanced calculus courses, but is not as useful in physics and engineering as its three-dimensional counterpart, the [[Divergence Theorem]].