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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Tensor Analysis and Nonlinear Tensor Functions
Authors: Yu. I. Dimitrienko
DOI: https://doi.org/10.1007/978-94-017-3221-5
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 2002
Hardcover ISBN: 978-1-4020-1015-6Published: 30 November 2002
Softcover ISBN: 978-90-481-6169-0Published: 01 December 2010
eBook ISBN: 978-94-017-3221-5Published: 29 June 2013
Edition Number: 1
Number of Pages: XVIII, 662
Topics: Linear and Multilinear Algebras, Matrix Theory, Topology, Solid Mechanics, Global Analysis and Analysis on Manifolds, Vibration, Dynamical Systems, Control