Tensor Analysis and Nonlinear Tensor Functions (Hardcover)

Yuriy I. Dimitrienko

ISBN 10: 140201015X / ISBN 13: 9781402010156

Editore: Kluwer Academic Publishers, New York, NY, 2002

Riguardo questo articolo

Hardcover. This text 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, and so forth. The book suggests a new approach to definition of a tensor in space 3, 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 should 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. Covers the basic fields of tensor calculus. This book suggests a approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor. It presents a theory of tensor invariants and nonlinear anisotropic tensor functions. It is intended for students of mathematical and physical departments of universities. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9781402010156

Dati bibliografici

• Titolo: Tensor Analysis and Nonlinear Tensor Functions (Hardcover)
• Editore: Kluwer Academic Publishers, New York, NY
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 140201015X
• ISBN 13: 9781402010156
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

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.

Contenuti

Preface. Sources of Tensor Calculus. Introduction. 1. Tensor Algebra. 2. Tensors in Linear Spaces. 3. Groups of Transformations. 4. Indifferent Tensors and Invariants. 5. Tensor Functions. 6. Tensor Analysis. 7. Geometry of Curves and Surfaces. 8. Tensors in Riemannian Spaces and Affinely Connected Spaces. 9. Integration of Tensors. 10. Tensors in Continuum Mechanics. 11. Tensor Functions in Continuum Mechanics. References. Subject Index.