Tensor Analysis and Nonlinear Tensor Functions

  • Yu. I. Dimitrienko

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Yu. I. Dimitrienko
    Pages 1-64
  3. Yu. I. Dimitrienko
    Pages 65-128
  4. Yu. I. Dimitrienko
    Pages 129-168
  5. Yu. I. Dimitrienko
    Pages 169-226
  6. Yu. I. Dimitrienko
    Pages 227-346
  7. Yu. I. Dimitrienko
    Pages 347-384
  8. Yu. I. Dimitrienko
    Pages 385-436
  9. Yu. I. Dimitrienko
    Pages 475-492
  10. Yu. I. Dimitrienko
    Pages 493-554
  11. Yu. I. Dimitrienko
    Pages 555-652
  12. Back Matter
    Pages 653-662

About this book

Introduction

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.

Keywords

Connected space algebra calculus continuum mechanics mechanical engineering mechanics solids

Authors and affiliations

  • Yu. I. Dimitrienko
    • 1
  1. 1.Bauman Moscow State Technical UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-3221-5
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6169-0
  • Online ISBN 978-94-017-3221-5
  • About this book
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