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Tensor algebra and tensor analysis for engineers = with applications to continuum mechanics /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Tensor algebra and tensor analysis for engineers/ by Mikhail Itskov.
其他題名:	with applications to continuum mechanics /
作者:	Itskov, Mikhail.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xxi, 328 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Tensor algebra. -
電子資源:	https://doi.org/10.1007/978-3-031-92357-9
ISBN:	9783031923579

Tensor algebra and tensor analysis for engineers = with applications to continuum mechanics /
Itskov, Mikhail.

Tensor algebra and tensor analysis for engineerswith applications to continuum mechanics /[electronic resource] :by Mikhail Itskov. - Sixth edition. - Cham :Springer Nature Switzerland :2025. - xxi, 328 p. :ill., digital ;24 cm. - Mathematical engineering,2192-4740. - Mathematical engineering..

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.

This is the sixth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, 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 particular, the book discusses such multi-physical topics of solid mechanics as electro- and magnetoelasticity. In addition, advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics are included. This new edition also focuses on numerical aspects of tensor calculus and shows how modern methods of machine learning can be applied to the calculation of tensor functions. Hence, these textbook addresses graduate students as well as scientists working in this field and in particular dealing with interdisciplinary problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

ISBN: 9783031923579

Standard No.: 10.1007/978-3-031-92357-9doiSubjects--Topical Terms:

765822
Tensor algebra.

LC Class. No.: QA200

Dewey Class. No.: 620.00151257

Tensor algebra and tensor analysis for engineers = with applications to continuum mechanics /
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520 $a This is the sixth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, 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 particular, the book discusses such multi-physical topics of solid mechanics as electro- and magnetoelasticity. In addition, advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics are included. This new edition also focuses on numerical aspects of tensor calculus and shows how modern methods of machine learning can be applied to the calculation of tensor functions. Hence, these textbook addresses graduate students as well as scientists working in this field and in particular dealing with interdisciplinary problems. 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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