Two proofs of Stokes’ theorem in new clothes

• Authors: Maciuk Arkadiusz , Smoluk Antoni
• Languages of publication: EN

Abstracts

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.

Keywords

EN

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

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Didactics of Mathematics
• Year: 2015
• Issue: 12(16)
• Pages: 85-92

Contributors

author

Maciuk Arkadiusz

author

Smoluk Antoni

References

• Cartan H. (1967). Formes différentielles. Hermann. Paris.
• Fichtenholz G.M. (1949). A Course in Differential and Integral Calculus [in Russian]. Vol. 3.
• Katz V.J. (1979). The history of Stokes’ theorem. Mathematics Magazine 52 (3). Pp.146-156.
• Markvorsen S. (2008). The classical version of Stokes’ theorem revisited. International Journal of Mathematical Education in Science and Technology 39(7). Pp. 879-888.
• Petrello R.C. (1998). Stokes’ theorem (California State University, Northridge). Available from http://scholarworks.csun.edu.
• Rudin W. (1976). Principles of Mathematical Analysis. New York. McGraw–Hill.