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Abstract

We will introduce the algebra \(\Omega ^{*}(U)\) of differential forms on an open subset \(U\subset \mathbb {R}^{n}\), although the formalism to define it on a submanifold of \(\mathbb {R}^{n}\) is the same.

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Notes

  1. 1.

    The tensor product \(V^{\otimes _{p}}\) is defined in Appendix C.

  2. 2.

    For more details on the De Rham theory, see Ref. [45].

  3. 3.

    The proofs can be read in [29].

  4. 4.

    Figures 3, 4, 5, 6, 7, 8, 9 and 10 were kindly provided by Jos Leys. See Ref. [47] (iv).

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Correspondence to Celso Melchiades Doria .

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Doria, C.M. (2021). Differential Forms, Stokes Theorem. In: Differentiability in Banach Spaces, Differential Forms and Applications . Springer, Cham. https://doi.org/10.1007/978-3-030-77834-7_6

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