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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: materialTypeLabelBookSeries: Mathematical Engineering: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 4th ed. 2015.Description: XVII, 290 p. 20 illus., 13 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319163420.Subject(s): Engineering | Matrix theory | Algebra | Differential geometry | Mechanics | Continuum mechanics | Engineering | Continuum Mechanics and Mechanics of Materials | Differential Geometry | Linear and Multilinear Algebras, Matrix Theory | MechanicsAdditional physical formats: Printed edition:: No titleDDC classification: 620.1 Online 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: This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
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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.

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

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