# Exterior derivative

On a differentiable manifold, the **exterior derivative** extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described in its current form by Élie Cartan in 1899. It allows for a natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus.

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If a differential *k*-form is thought of as measuring the flux through an infinitesimal *k*-parallelotope at each point of the manifold, then its exterior derivative can be thought of as measuring the net flux through the boundary of a (*k* + 1)-parallelotope at each point.