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-xix
  2. Mikhail Itskov
    Pages 123-135
  3. Mikhail Itskov
    Pages 137-171
  4. Mikhail Itskov
    Pages 173-193
  5. Mikhail Itskov
    Pages 195-215
  6. Mikhail Itskov
    Pages 217-290
  7. Back Matter
    Pages 291-300

About this book


This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, 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. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. 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 textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.


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.Department of Continuum MechanicsRWTH Aachen UniversityAachenGermany

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-98805-4
  • Online ISBN 978-3-319-98806-1
  • Series Print ISSN 2192-4732
  • Series Online ISSN 2192-4740
  • Buy this book on publisher's site