The Many Faces of Stokes’ Theorem

The generalised Stokes theorem has the remarkably compact form

where is a -dimensional manifold with boundary , and is a -form on .

While it may seem alien at first when expressed in full generality, you may recognise some of the many special cases of Stokes’ theorem, especially from vector calculus.

Special cases of Stokes’ theorem

Adjust the parameters below or select a preset to see the associated Stokes theorem.

The metric signature is relevant to the Hodge dual operation (which requires the notion of a metric). Divergence-type theorems arise naturally when is the Hodge dual of a -form