For example, the differential[?] of a smooth function on a manifold (a 0form) is a 1form.
Differential forms of degree k are integrated over k dimensional chains. If <math>k=0</math>, this is just evaluation of functions at points. Other values of <math>k=1, 2, 3, ...</math> correspond to line integrals, surface integrals, volume integrals etc.
The set of all kforms on a manifold is a vector space. Furthermore, there are two other operations: wedge product and exterior derivative.
The fundamental relationship between the exterior derivative and integration is given by the general Stokes' theorem, which also provides the duality between de Rham cohomology and the homology of chains.
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