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

✍ Scribed by Professor Dr.-Ing. Mikhail Itskov (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 243
• Category: Library

✦ Synopsis

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 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 and 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.

 

✦ Table of Contents

Front Matter....Pages I-XI
Vectors and Tensors in a Finite-Dimensional Space....Pages 1-31
Vector and Tensor Analysis in Euclidean Space....Pages 33-55
Curves and Surfaces in Three-Dimensional Euclidean Space....Pages 57-77
Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors....Pages 79-98
Fourth-Order Tensors....Pages 99-110
Analysis of Tensor Functions....Pages 111-139
Analytic Tensor Functions....Pages 141-160
Applications to Continuum Mechanics....Pages 161-178
Back Matter....Pages 179-239

✦ Subjects

Numerical and Computational Methods in Engineering;Continuum Mechanics and Mechanics of Materials;Mathematical Methods in Physics;Linear and Multilinear Algebras, Matrix Theory;Mechanics