On the change of variables formula for multiple integrals

2016/03/28 by Shibo Liu, Liu, Shibo, Yashan Zhang +1 · 1 citation
Computer Science · Mathematics · #26B15 #26B20 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #math.CA #msc:26B15 #msc:26B20

paper · pdf · doi:10.48550/arxiv.1603.08428

6 pages

openalex publication_date 2016/03/28 · arxiv created 2017/05/15 · arxiv updated 2017/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop an elementary proof of the change of variables 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 Rm, 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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