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Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

  • Textbook
  • Aug 2025
  • Latest edition

Overview

Authors:
  1. Mikhail Itskov

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

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  • Well-received textbook in its sixth revised edition
  • Provides a comprehensible exposition of tensor analysis
  • Presents modern developments in the theory of isotropic and anisotropic tensor functions

Part of the book series: Mathematical Engineering (MATHENGIN)

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About this book

This is the sixth 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. In particular, the book discusses such multi-physical topics of solid mechanics as electro- and magnetoelasticity. In addition, advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics are included. This new edition also focuses on numerical aspects of tensor calculus and shows how modern methods of machine learning can be applied to the calculation of tensor functions. Hence, these textbook addresses graduate students as well as scientists working in this field and in particular dealing with interdisciplinary problems. 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
  • matrix theory

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

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2025

  • Hardcover ISBN: 978-3-031-92356-2Due: 27 August 2025

  • Softcover ISBN: 978-3-031-92359-3Due: 27 August 2026

  • eBook ISBN: 978-3-031-92357-9Due: 27 August 2025

  • Series ISSN: 2192-4732

  • Series E-ISSN: 2192-4740

  • Edition Number: 6

  • Number of Pages: V, 335

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