Tensor Algebra and Tensor Analysis for Engineers - Mikhail Itskov

Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

(Autor)

Buch | Softcover
XVI, 272 Seiten
2014 | 3rd ed. 2013
Springer Berlin (Verlag)
978-3-642-44818-8 (ISBN)
74,99 inkl. MwSt
This book provides a comprehensive exposition of tensor analysis. It presents modern developments in the theory of isotropic and anisotropic tensor functions and includes numerous exercises with solutions.

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.

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.

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.

Erscheint lt. Verlag 20.9.2014
Reihe/Serie Mathematical Engineering
Zusatzinfo XVI, 272 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 444 g
Themenwelt Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Technik Maschinenbau
Schlagworte Christoffel Symbols • Coordinate Transformation • Covariant and Contravariant Derivatives • Derivative of the Stretch and Rotation Tensor • Generalized Rivlin's Identities • Generalized Rivlin’s Identities • matrix theory • Polar Decomposition of the Deformation Gradient • Spectral Decomposition of Second-order Tensors • Tensor Algebra • Tensors in Finite-dimensional Space • Tensor-valued Functions
ISBN-10 3-642-44818-6 / 3642448186
ISBN-13 978-3-642-44818-8 / 9783642448188
Zustand Neuware
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