Summary: Differential Forms.
Suppose U is an open subset of Rn
Defintion. For each nonnegative integer p we let
be the set of smooth maps
Note that Ap
(U) is a vector space in a natural way. Whenever f is a smooth real valued function on U and
(U) we define f in Ap
(U) by setting f(x) = f(x)(x) for x in U.
Proposition. There is one and only one bilinear map from
W : L(