Tensor Algebra and Tensor Analysis for Engineers
With Applications to Continuum Mechanics
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Beschreibung
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.
There is a gap between engineering courses in tensor algebra, and the treatment of linear transformations within classical linear algebra. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as absolutely necessary. The many exercises provided include solutions, enabling autonomous study. The last chapters address modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore interest PhD-students and scientists working in this area.
In recent decades, the absolute notation for tensors has become widely accepted and is now 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. This is a modern textbook on tensor calculus for engineers in line with contemporary scientific publications.
Compact and illustrated introduction for readers of different levels Numerous exercises with solutions Applications to continuum mechanics Tensor algebra in absolute notation Treatment of tensors on the basis of linear algebra Includes supplementary material: sn.pub/extras
Autor*in
Mikhail Itskov
Themen in »Tensor Algebra and Tensor Analysis for Engineers«
Algebra Anisotropic Tensor Functions Derivates of Tensor Functions Isotropic Tensor Functions Kinematics of Continua Tensor Analysis Tensor Calculus Transformation calculus linear algebra mechanics matrix theory
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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)
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