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 grounds for 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.§§