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## Didactics of Mathematics

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

### Two proofs of Stokes’ theorem in new clothes

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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.
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85-92
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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.
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