Title
Tensors, Differential Forms, And Variational Principles (Dover Books On Mathematics)
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The aim of this book is to present a selfcontained, 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 differentialgeometric concepts.The treatment of the calculus of variations of single and multiple integrals is based ab initio on Carathodory'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 metricsThe 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.
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Frequently Asked Questions
- Q: What is the main focus of the book 'Tensors, Differential Forms, and Variational Principles'? A: The book presents a self-contained account of tensor analysis and the calculus of exterior differential forms, tailored for physicists, engineers, and applied mathematicians.
- Q: Who is the author of this book? A: The author is David Lovelock.
- Q: What topics are covered in the later chapters? A: Later chapters examine the interaction between invariance concepts and the calculus of variations, which is crucial for understanding physical field theories.
- Q: How does this book approach the theory of tensors? A: It develops the theory of tensors and forms through successive abstractions, using simple physical examples to infer generalized principles.
- Q: What is the significance of Noether's theorems in this book? A: Noether's theorems are discussed with simple and direct derivations, emphasizing their impact on variational principles and physical theories.
- Q: Is there an emphasis on practical problems in the book? A: Yes, the book includes various problems ranging from routine exercises to complex challenges, particularly relevant for those using tensor techniques in research.
- Q: What is included in the Appendix of the book? A: The Appendix offers a reformulation of the principal concepts using current global differential geometry terminology, bridging classical tensor analysis and modern theories.
- Q: What is the publication date of the book? A: The book was published on April 1, 1989.
- Q: What is the binding type of this book? A: The book is available in paperback binding.
- Q: How many pages does 'Tensors, Differential Forms, and Variational Principles' have? A: The book consists of 400 pages.