Title:

Two proofs of Stokes’ theorem in new clothes

Group publication title:

Didactics of Mathematics

Creator:

Maciuk, Arkadiusz ; Smoluk, Antoni

Subject and Keywords:

Stokes’ theorem ; Sacała’s column ; additivity of integration

Description:

Didactics of Mathematics, 2015, Nr 12 (16), s. 85-92

Abstrakt:

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.

Publisher:

Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu

Place of publication:

Wrocław

Date:

2015

Resource Type:

artykuł

Format:

application/pdf

Resource Identifier:

doi:10.15611/dm.2015.12.09

Language:

eng

Relation:

Didactics of Mathematics, 2015, Nr 12 (16)

Rights:

Pewne prawa zastrzeżone na rzecz Autorów i Wydawcy

Access Rights:

Dla wszystkich zgodnie z licencją

License:

CC BY-NC-ND

Location:

Uniwersytet Ekonomiczny we Wrocławiu