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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