j math study vol 50 no 3 pp 268 276 doi 10 4208 jms v50n3 17 04 september2017 onthechangeofvariablesformulafor multipleintegrals 1 2 shiboliu andyashanzhang 1 department of mathematics xiamen university ...
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...J math study vol no pp doi jms vn september onthechangeofvariablesformulafor multipleintegrals shiboliu andyashanzhang department of mathematics xiamen university p r china macau receivedjanuary accepted revised may abstract wedevelopanelementaryproofofthechangeofvariablesformulainmulti ple integrals our proof is based on an induction argument assuming the formula for m we dene integral over hypersurface in rm establish diver genttheoremandthenusethedivergenttheoremtoprovetheformulaform addition to its simplicity advantage approachis that it yields brouwer fixed point theorem as a corollary amssubjectclassications b keywords changeofvariables surfaceintegral divergenttheorem cauchy binetformula introduction thechangeofvariables multiple fundamental mul tivariable calculus can be stated follows let d and bounded open domains with piece wise c boundaries suchthat disac diffeomorphism if f then z df y dy x dx where det jacobian determinant at usual proofs this one nds advanced textbooks v...