Tensor Analysis and Nonlinear Tensor Functions

✍ Scribed by Yu. I. Dimitrienko (auth.)

• Publisher: Springer Netherlands
• Year: 2002
• Tongue: English
• Leaves: 680
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xviii
Tensor Algebra....Pages 1-64
Tensors in Linear Spaces....Pages 65-128
Groups of Transformations....Pages 129-168
Indifferent Tensors and Invariants....Pages 169-226
Tensor Functions....Pages 227-346
Tensor Analysis....Pages 347-384
Geometry of Curves and Surfaces....Pages 385-436
Tensors in Riemannian Spaces and Affinely Connected Spaces....Pages 437-474
Integration of Tensors....Pages 475-492
Tensors in Continuum Mechanics....Pages 493-554
Tensor Functions in Continuum Mechanics....Pages 555-652
Back Matter....Pages 653-662

✦ Subjects

Linear and Multilinear Algebras, Matrix Theory; Topology; Continuum Mechanics and Mechanics of Materials; Global Analysis and Analysis on Manifolds; Vibration, Dynamical Systems, Control