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.
artykuł
Sacała’s column
Didactics of Mathematics, 2015, Nr 12 (16), s. 85-92
Didactics of Mathematics, 2015, Nr 12 (16)
Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
Stokes’ theorem
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application/pdf
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Two proofs of Stokes’ theorem in new clothes
eng
DOI: 10.15611/dm.2015.12.09
Maciuk, Arkadiusz
2015
Smoluk, Antoni
additivity of integration