# Tensor Algebra and Tensor Analysis for Engineers

## With Applications to Continuum Mechanics

Textbook

Part of the Mathematical Engineering book series (MATHENGIN)

1. Front Matter
Pages i-xv
2. Mikhail Itskov
Pages 1-34
3. Mikhail Itskov
Pages 35-62
4. Mikhail Itskov
Pages 63-83
5. Mikhail Itskov
Pages 85-106
6. Mikhail Itskov
Pages 107-119
7. Mikhail Itskov
Pages 121-153
8. Mikhail Itskov
Pages 155-175
9. Mikhail Itskov
Pages 177-195
10. Mikhail Itskov
Pages 197-260
11. Back Matter
Pages 261-269

### Introduction

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area.

This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

### 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

#### Authors and affiliations

1. 1.Lehr- und FG KontinuumsmechanikRWTH AachenAachenGermany

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 ansiotropic 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
• Series Abbreviated Title Mathematical Engineering
• DOI https://doi.org/10.1007/978-3-642-30879-6
• Copyright Information Springer-Verlag Berlin Heidelberg 2013
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering Engineering (R0)
• Hardcover ISBN 978-3-642-30878-9
• Softcover ISBN 978-3-642-44818-8
• eBook ISBN 978-3-642-30879-6
• Series ISSN 2192-4732
• Series E-ISSN 2192-4740
• Edition Number 3
• Number of Pages XVI, 272
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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