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Tensor Calculus for Engineers and Physicists

  • Emil de Souza Sánchez Filho

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Emil de Souza Sánchez Filho
    Pages 1-71
  3. Emil de Souza Sánchez Filho
    Pages 73-135
  4. Emil de Souza Sánchez Filho
    Pages 137-153
  5. Emil de Souza Sánchez Filho
    Pages 155-226
  6. Emil de Souza Sánchez Filho
    Pages 227-293
  7. Emil de Souza Sánchez Filho
    Pages 295-335
  8. Back Matter
    Pages 337-345

About this book

Introduction

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.


Keywords

Tensor calculus textbook Calculus for engineers Differential Geometry Continuum Mechanics Theory of Elasticity Solid Mechanics Manifolds Vectorial Space Theory of Shell

Authors and affiliations

  • Emil de Souza Sánchez Filho
    • 1
  1. 1.Fluminense Federal UniversityRio de JaneiroBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-31520-1
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-31519-5
  • Online ISBN 978-3-319-31520-1
  • Buy this book on publisher's site