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Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

  • Textbook
  • © 2015

Overview

Authors:
  1. Mikhail Itskov

    1. RWTH Aachen University, Department of Continuum Mechanics, Kackertstr.9, 52072 Aachen, Germany

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  • Covers many new aspects in the fourth edition
  • Provides a comprehensible exposition of tensor analysis
  • Presents modern developments in the theory of isotropic and anisotropic tensor functions
  • Includes numerous exercises with solutions
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematical Engineering (MATHENGIN)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvii
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  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 37-67

  4. Curves and Surfaces in Three-Dimensional Euclidean Space

    • Mikhail Itskov
    Pages 69-96

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

    • Mikhail Itskov
    Pages 97-119

  6. Fourth-Order Tensors

    • Mikhail Itskov
    Pages 121-133

  7. Analysis of Tensor Functions

    • Mikhail Itskov
    Pages 135-168

  8. Analytic Tensor Functions

    • Mikhail Itskov
    Pages 169-189

  9. Applications to Continuum Mechanics

    • Mikhail Itskov
    Pages 191-212

  10. Solutions

    • Mikhail Itskov
    Pages 213-280

  11. Back Matter

    Pages 281-290
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Keywords

About this book

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.

Authors and Affiliations

  • RWTH Aachen University, Department of Continuum Mechanics, Kackertstr.9, 52072 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/10.1007/978-3-319-16342-0

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Softcover ISBN: 978-3-319-37443-7Published: 06 October 2016

  • eBook ISBN: 978-3-319-16342-0Published: 25 March 2015

  • Series ISSN: 2192-4732

  • Series E-ISSN: 2192-4740

  • Edition Number: 4

  • Number of Pages: XVII, 290

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

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

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