Tensor Algebra and Tensor Analysis for Engineers [electronic resource] : With Applications to Continuum Mechanics / by Mikhail Itskov.

By: Itskov, Mikhail [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextLanguage: English Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: xiii, 247 pages with 13 illus online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540939078Subject(s): Engineering | Matrix theory | Mathematical physics | Mechanics | Materials | Engineering | Mechanics | Linear and Multilinear Algebras, Matrix Theory | Mathematical Methods in Physics | Continuum Mechanics and Mechanics of Materials | Computational IntelligenceAdditional physical formats: Printed edition:: No titleOnline resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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. This second edition is completed by a number of additional examples and exercises. The text and formulae are thoroughly revised and improved where necessary.
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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.

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. This second edition is completed by a number of additional examples and exercises. The text and formulae are thoroughly revised and improved where necessary.

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