Tensor Calculus for Engineers and Physicists

This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the groundsfor the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.

Presents concepts in a straightforward way, while maintaining a great level of rigor Provides 56 solved exercises and a select set of unsolved problems with answers Presents a didactic and concise text suited to undergraduate and graduate students Enriches understanding of tensor calculus applied to all technical sciences and engineering disciplines, providing the reader with complete illustrations that supplement the presented concepts

Autorentext

Prof. Dr. Emil de Souza Sanchez Filho received his degree in civil engineering in 1976, his M. Sc. in 1998, and his D. Sc. in 1992 from COPPE-Federal University of Rio de Janeiro. In 1993-1994 he became visiting Researcher at Technische Universitat Braunschweig, Germany. In the periods 2003-2005 and 2013-2014 he worked as a postdoctoral fellow at PUC-Rio, where he is today Guest Professor (2004-2015). Currently, the author is full professor at Fluminense Federal University, Brazil. He worked in the construction industry and has large experience in Structural Engineering. He has published more than 220 papers (articles in peer reviewed journals and conference articles), chapters in 9 books, and acted as editor of 3 books and as author of 3 books: Solid Mechanics Elements, Tensors, and Tensor Calculus."

Inhalt

Chapter 1 Fundamental Concepts.- Chapter 2 Covariant, Absolute and Contravariant Differentiation.- Chapter 3 Integral Theorems.- Chapter 4 Differential Operators.- Chapter 5 Riemann Spaces.- Chapter 6 Parallelisms of Vectors.