Tensor Analysis and Nonlinear Tensor Functions

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Springer Science & Business Media, Jun 29, 2013 - Mathematics - 662 pages
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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.

 

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Contents

TENSOR ALGEBRA
1
TENSORS IN LINEAR SPACES
65
GROUPS OF TRANSFORMATIONS
129
INDIFFERENT TENSORS AND INVARI
169
TENSOR FUNCTIONS
227
TENSOR ANALYSIS
347
GEOMETRY OF CURVES AND SUR
385
TENSORS IN RIEMANNIAN SPACES
437
INTEGRATION OF TENSORS
475
TENSORS IN CONTINUUM MECHAN
493
TENSOR FUNCTIONS IN CONTINUUM
555
References
653
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