Tensor algebra and tensor analysis for engineers: with applications to continuum mechanics

Mikhail Itskov (auth.)9783540939078, 9783540939061, 3540939067

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 the book is to bridge this gap by means of the consequent and fundamental exposition. The book is addressed primarily to engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling an autonomous study. The last chapters of the book deal with modern developments in the theory of isotropic an anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

In the last decades, the absolute notation for tensors has become widely accepted and is now a current state of the art for publications in solid and structural mechanics. This is opposed to a majority of books on tensor calculus referring to index notation. The latter one complicates the understanding of the matter especially for readers with initial knowledge. Thus, this book aims at being a modern textbook on tensor calculus for engineers in line with the contemporary way of scientific publications.

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Table of contents :
Front Matter….Pages 1-10
Vectors and Tensors in a Finite-Dimensional Space….Pages 1-33
Vector and Tensor Analysis in Euclidean Space….Pages 35-58
Curves and Surfaces in Three-Dimensional Euclidean Space….Pages 59-79
Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors….Pages 81-101
Fourth-Order Tensors….Pages 103-114
Analysis of Tensor Functions….Pages 115-144
Analytic Tensor Functions….Pages 145-164
Applications to Continuum Mechanics….Pages 165-183
Back Matter….Pages 1-62