Skip to main content
SpringerLink
Log in
Book cover

Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

  • Textbook
  • © 2019

Overview

Authors:
  1. Mikhail Itskov

    1. Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Covers many new aspects in the fifth edition, such as electro- and magnetoelasticity
  • Provides a comprehensible exposition of tensor analysis
  • Presents modern developments in the theory of isotropic and anisotropic tensor functions
  • Includes numerous exercises with solutions

Part of the book series: Mathematical Engineering (MATHENGIN)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Vectors and Tensors in a Finite-Dimensional Space

    • Mikhail Itskov
    Pages 1-36

  3. Vector and Tensor Analysis in Euclidean Space

    • Mikhail Itskov
    Pages 37-72

  4. Curves and Surfaces in Three-Dimensional Euclidean Space

    • Mikhail Itskov
    Pages 73-97

  5. Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors

    • Mikhail Itskov
    Pages 99-121

  6. Fourth-Order Tensors

    • Mikhail Itskov
    Pages 123-135

  7. Analysis of Tensor Functions

    • Mikhail Itskov
    Pages 137-171

  8. Analytic Tensor Functions

    • Mikhail Itskov
    Pages 173-193

  9. Applications to Continuum Mechanics

    • Mikhail Itskov
    Pages 195-215

  10. Solutions

    • Mikhail Itskov
    Pages 217-290

  11. Back Matter

    Pages 291-300
    Download chapter PDF
Back to top

Keywords

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.

Authors and Affiliations

  • Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

    Mikhail Itskov

About the author

Prof. Itskov studied Automobile Engineering at the Moscow State Automobile and Road Technical University, Russia. In 1990 he received his doctoral degree in mechanics, and in 2002 he obtained his habilitation degree in mechanics from the University of Bayreuth, Germany. Since 2004 he has been full professor for continuum mechanics at the RWTH  Aachen University, Germany. His research interests comprise tensor analysis, non-linear continuum mechanics, in particular the application to anisotropic materials, as well as the mechanics of elastomers and soft tissues in a broad sense.

Bibliographic Information

  • Book Title: Tensor Algebra and Tensor Analysis for Engineers

  • Book Subtitle: With Applications to Continuum Mechanics

  • Authors: Mikhail Itskov

  • Series Title: Mathematical Engineering

  • DOI: https://doi.org/10.1007/978-3-319-98806-1

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-319-98805-4Published: 27 September 2018

  • Softcover ISBN: 978-3-030-07536-1Published: 26 December 2018

  • eBook ISBN: 978-3-319-98806-1Published: 15 September 2018

  • Series ISSN: 2192-4732

  • Series E-ISSN: 2192-4740

  • Edition Number: 5

  • Number of Pages: XIX, 300

  • Number of Illustrations: 7 b/w illustrations, 13 illustrations in colour

  • Topics: Solid Mechanics, Differential Geometry, Linear and Multilinear Algebras, Matrix Theory, Classical Mechanics

Publish with us

Policies and ethics

Back to top

Search

Navigation