Year: 2017
Author: Shibo Liu, Yashan Zhang
Journal of Mathematical Study, Vol. 50 (2017), Iss. 3 : pp. 268–276
Abstract
We develop an elementary proof of the change of variables formula in multiple integrals. Our proof is based on an induction argument. Assuming the formula for $(m-1)$-integrals, we define the integral over hypersurface in $\mathbb{R}^m$, establish the divergent theorem and then use the divergent theorem to prove the formula for $m$-integrals. In addition to its simplicity, an advantage of our approach is that it yields the Brouwer Fixed Point Theorem as a corollary.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v50n3.17.04
Journal of Mathematical Study, Vol. 50 (2017), Iss. 3 : pp. 268–276
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Change of variables surface integral divergent theorem Cauchy-Binet formula.
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