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Stokes' theorem
In
vector calculus
, and more generally
differential geometry
,
Stokes' theorem
(also called
the generalized Stokes' theorem
) is a statement about the
integration
of
differential forms
on
manifolds
, which both simplifies and generalizes several
theorems
from
vector calculus
. Stokes' theorem says that the integral of a differential form ω over the
boundary
of some
orientable
manifold Ω is equal to the integral of its
exterior derivative
dω over the whole of Ω, i.e.,
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