On the Change of Variables Formula for Multiple Integrals

On the Change of Variables Formula for Multiple Integrals

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.

Author Details

Shibo Liu

Yashan Zhang

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