@Article{JMS-50-268, author = {Liu , Shibo and Zhang , Yashan}, title = {On the Change of Variables Formula for Multiple Integrals}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n3.17.04}, url = {http://global-sci.org/intro/article_detail/jms/10620.html} }