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Author
Maciuk Arkadiusz (Wrocław University of Economics, Poland), Smoluk Antoni (Wrocław University of Economics, Poland)
Title
Two Proofs of Stokes' Theorem in new Clothes
Source
Didactics of Mathematics, 2015, nr 12 (16), s. 85-92, rys., bibliogr. 6 poz.
Keyword
Matematyka
Mathematics
Note
summ.
Abstract
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.(original abstract)
Accessibility
The Main Library of the Cracow University of Economics
The Library of Warsaw School of Economics
The Library of University of Economics in Katowice
The Main Library of the Wroclaw University of Economics
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Bibliography
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  1. Cartan H. (1967). Formes différentielles. Hermann. Paris.
  2. Fichtenholz G.M. (1949). A Course in Differential and Integral Calculus [in Russian]. Vol. 3.
  3. Katz V.J. (1979). The history of Stokes' theorem. Mathematics Magazine 52 (3). Pp.146-156.
  4. Markvorsen S. (2008). The classical version of Stokes' theorem revisited. International Journal of Mathematical Education in Science and Technology 39(7). Pp. 879-888.
  5. Petrello R.C. (1998). Stokes' theorem (California State University, Northridge). Available from http://scholarworks.csun.edu.
  6. Rudin W. (1976). Principles of Mathematical Analysis. New York. McGraw-Hill.
Cited by
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ISSN
1733-7941
Language
eng
URI / DOI
http://dx.doi.org/10.15611/dm.2015.12.09
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