Surface to surface changes of variables and applications

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on August 25, 2008)Vita.Thesis (M.S.) University of Missouri-Columbia 2008.The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration process is affected by a surface to surface change of variables. We provide precise answers to these and other related issues, and discuss a number of applications, such as the invariance of Lebesgue and Sobolev spaces on surfaces..Includes bibliographical reference