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2015 | 12(16) | 85-92
Article title

Two proofs of Stokes’ theorem in new clothes

Content
Title variants
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.
Year
Issue
Pages
85-92
Physical description
Contributors
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.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-493915bf-a327-417e-a7cc-1da2278ed6c4
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