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＜電子ブック＞
Tensor Analysis and Nonlinear Tensor Functions / by Yuriy I. Dimitrienko

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XVIII, 662 p : online resource
著者標目	*Dimitrienko, Yuriy I author SpringerLink (Online service)
件　名	LCSH:Algebras, Linear LCSH:Topology LCSH:Mechanics, Applied LCSH:Solids LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Multibody systems LCSH:Vibration FREE:Linear Algebra FREE:Topology FREE:Solid Mechanics FREE:Global Analysis and Analysis on Manifolds FREE:Multibody Systems and Mechanical Vibrations
一般注記	1. Tensor Algebra -- 2. Tensors in Linear Spaces -- 3. Groups of Transformations -- 4. Indifferent Tensors and Invariants -- 5. Tensor Functions -- 6. Tensor Analysis -- 7. Geometry of Curves and Surfaces -- 8. Tensors in Riemannian Spaces and Affinely Connected Spaces -- 9. Integration of Tensors -- 10. Tensors in Continuum Mechanics -- 11. Tensor Functions in Continuum Mechanics -- References Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science HTTP:URL=https://doi.org/10.1007/978-94-017-3221-5

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