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  1. 1 Didactics of Mathematics

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  1. 1 Maciuk A.

  2. 1 Smoluk A.

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  1. 1 2015

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Two proofs of Stokes’ theorem in new clothes

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Maciuk A., Smoluk A.
Didactics of Mathematics
|
2015
|
issue 12(16)
85-92
EN
The paper presents two proofs of Stokes’ theorem that are intuitively simple and clear. A manifold, on which a differential form is defined, is reduced to a three-dimensional cube, as extending to other dimensions is straightforward. The first proof reduces the integral over a manifold to the integral over a boundary, while the second proof extends the integral over a boundary to the integral over a manifold. A new idea consists in the definition of Sacała’s line that inspired the authors to taking a different look at the proof of Stokes’ theorem.
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