Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

  • Mikhail Itskov

Part of the Mathematical Engineering book series (MATHENGIN)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Mikhail Itskov
    Pages 107-119
  3. Mikhail Itskov
    Pages 121-153
  4. Mikhail Itskov
    Pages 155-175
  5. Mikhail Itskov
    Pages 177-195
  6. Mikhail Itskov
    Pages 197-260
  7. Back Matter
    Pages 261-269

About this book

Introduction

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area.

This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

Keywords

Christoffel Symbols Coordinate Transformation Covariant and Contravariant Derivatives Derivative of the Stretch and Rotation Tensor Generalized Rivlin’s Identities Polar Decomposition of the Deformation Gradient Spectral Decomposition of Second-order Tensors Tensor Algebra Tensor-valued Functions Tensors in Finite-dimensional Space

Authors and affiliations

  • Mikhail Itskov
    • 1
  1. 1.Lehr- und FG KontinuumsmechanikRWTH AachenAachenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-30879-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-30878-9
  • Online ISBN 978-3-642-30879-6
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • About this book