Advanced calculus and its applications to variational quantum mechanics and relativity theory / Fabio Silva Botelho, Adjunct Professor, Department of Mathematics Federal University of Santa Catarina, Florianopolis SC, Brazil.

Includes bibliographical references and index.

"The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes a detailed and rigorous study on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. In the conclusion of this first part, there is an introduction to Riemannian geometry, which will be used in the subsequent chapters of applications. In the second part, the book develops applications of the previous chapters, specifically on variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry, and in a second step, for a more general context, through fundamentals of differential geometry"-- Provided by publisher.