Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics / Edition 5

by Mikhail Itskov

Overview

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.

Product Details

ISBN-13:	9783319988054
Publisher:	Springer International Publishing
Publication date:	09/16/2018
Series:	Mathematical Engineering
Edition description:	5th ed. 2019
Pages:	300
Product dimensions:	6.10(w) x 9.25(h) x (d)

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.

Table of Contents

Vectors and Tensors in a Finite-Dimensional Space.- Vector and Tensor Analysis in Euclidean Space.- Curves and Surfaces in Three-Dimensional Euclidean Space.- Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors.- Fourth-Order Tensors.- Analysis of Tensor Functions.- Analytic Tensor Functions.- Applications to Continuum Mechanics.

Editorial Reviews

From the reviews:

"Most books on continuum mechanics begin with a more or less lengthy introduction into this mere mathematical topic. … With the present introduction to tensors, Itskov has filled this gap. … It is written in a clear and modern style … . contains a lot of interesting representations, which will be appreciated by researchers in the field. … All in all, the book can be clearly recommended both for students and researchers in the field of continuum mechanics." (Technische Mechanik, Vol. 28 (3), 2008)

From the Publisher