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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-xvii
  2. Mikhail Itskov
    Pages 121-133
  3. Mikhail Itskov
    Pages 135-168
  4. Mikhail Itskov
    Pages 169-189
  5. Mikhail Itskov
    Pages 191-212
  6. Mikhail Itskov
    Pages 213-280
  7. Back Matter
    Pages 281-290

About this book

Introduction

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

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.RWTH Aachen University, Department of Continuum Mechanics, Kackertstr.952072 AachenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-16342-0
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-16341-3
  • Online ISBN 978-3-319-16342-0
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site
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