Tensors, Differential Forms and Variational Principles

David Lovelock, Hanno Rund

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English

Dover
01 April 1989

Mathematics & Sciences; Differential calculus & equations; Maths for scientists; Maths for engineers

Series: Dover Books on Mathema 1.4tics

Summary
Details

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

The aim of this book is to present a self-contained, reasonably modern account of tensor analysis and the calculus of exterior differential forms, adapted to the needs of physicists, engineers, and applied mathematicians. In the later, increasingly sophisticated chapters, the interaction between the concept of invariance and the calculus of variations is examined. This interaction is of profound importance to all physical field theories. Beginning with simple physical examples, the theory of tensors and forms is developed by a process of successive abstractions. This enables the reader to infer generalized principles from concrete situations - departing from the traditional approach to tensors and forms in terms of purely differential-geometric concepts.

The treatment of the calculus of variations of single and multiple integrals is based ab initio on Carathéodory's method of equivalent integrals. Subsequent material explores the effects of invariance postulates on variational principles, focusing ultimately on relativistic field theories. Other discussions include: . integral invariants . simple and direct derivations of Noether's theorems . Riemannian spaces with indefinite metrics

The emphasis in this book is on analytical techniques, with abundant problems, ranging from routine manipulative exercises to technically difficult problems encountered by those using tensor techniques in research activities. A special effort has been made to collect many useful results of a technical nature, not generally discussed in the standard literature. The Appendix, newly revised and enlarged for the Dover edition, presents a reformulation of the principal concepts of the main text within the terminology of current global differential geometry, thus bridging the gap between classical tensor analysis and the fundamentals of more recent global theories.

By: David Lovelock, Hanno Rund
Imprint: Dover
Country of Publication: United States
Edition: New edition
Dimensions: Height: 216mm, Width: 140mm, Spine: 20mm
Weight: 475g
ISBN: 9780486658407
ISBN 10: 0486658406
Series: Dover Books on Mathema 1.4tics
Pages: 384
Publication Date: 01 April 1989
Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , A / AS level , Undergraduate
Format: Paperback
Publisher's Status: Unspecified