Tensors, Differential Forms, and Variational Principles Writen By David Lovelock

PDF BOOK Tensors, Differential Forms, and Variational Principles

By : David Lovelock

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Book Synopsis :

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