Two proofs of Stokes’ theorem in new clothes - Maciuk, Arkadiusz; Smoluk, Antoni (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2015)
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.
Didactics of Mathematics, 2015, Nr 12 (16), s. 85-92
Keywords: Stokes’ theorem; Sacała’s column; additivity of integration