Students and teachers of mathematical specialties

Simplified justification of the most important changes of variable in multiple integral

S. S. Pukhov

Lomonosov Moscow State University

Abstract: The paper gives rigorous proofs of the transition in the integral to polar and spherical (including generalized) coordinates, significantly simplified compared to those available in the literature.

Keywords: change of variables in an integral, transition to polar coordinates, transition to spherical coordinates, general linear change in an m-fold integral, transformation formulas for the Jordan measure and multiple integral, the method of elementary Gaussian transformations.

UDC: 517.38