Functional differential geometry / / Gerald Jay Sussman and Jack Wisdom with Will Farr

• Autore: Sussman Gerald Jay
• Pubblicazione: Cambridge, Massachusetts : , : MIT Press, , [2013]; [Piscataqay, New Jersey] : , : IEEE Xplore, , [2013]
• Descrizione fisica: 1 online resource (249 p.)
• Disciplina: 516.3/6
• Soggetto topico: Geometry, Differential; Functional differential equations; Mathematical physics
• Altri autori: WisdomJack FarrWill
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Contents; Preface; Prologue; 1 Introduction; 2 Manifolds; 3 Vector Fields and One-Form Fields; 4 Basis Fields; 5 Integration; 6 Over a Map; 7 Directional Derivatives; 8 Curvature; 9 Metrics; 10 Hodge Star and Electrodynamics; 11 Special Relativity; A Scheme; B Our Notation; C Tensors; References; Index
• Sommario/riassunto: Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misřables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
• Titolo autorizzato: Functional differential geometry
• ISBN: 0-262-31561-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910260608503321
• Lo trovi qui: Univ. Federico II