Vectors, Tensors and the Basic Equations of Fluid Mechanics
Автор: Lovelock, David Название: Tensors, Differential Forms, and Variational Principles ISBN: 0486658406 ISBN-13(EAN): 9780486658407 Издательство: Dover Рейтинг: Цена: 2848.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
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 Carath odory'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.
Автор: Hoffmann, Banesh Название: About Vectors ISBN: 0486604896 ISBN-13(EAN): 9780486604893 Издательство: Dover Рейтинг: Цена: 1359.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: From his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors.Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text.Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.
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