03387nam 2200661Ia 450 991026060850332120200520144314.097802623156160262315610(CKB)2670000000417710(EBL)3339642(SSID)ssj0000950126(PQKBManifestationID)11577442(PQKBTitleCode)TC0000950126(PQKBWorkID)11004720(PQKB)11644416(MiAaPQ)EBC3339642(CaBNVSL)mat06574626(IDAMS)0b00006481de8858(IEEE)6574626(ScCtBLL)2ff79234-6be6-4b0b-b08d-87174a4da953(OCoLC)854583698(EXLCZ)99267000000041771020130125d2013 uy 0engur|n|---|||||txtccrFunctional differential geometry /Gerald Jay Sussman and Jack Wisdom with Will Farr1st ed.Cambridge, MA MIT Pressc20131 online resource (249 p.)Description based upon print version of record.9780262315609 0262315602 9780262019347 0262019345 Includes bibliographical references and index.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; IndexPhysics 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.Geometry, DifferentialFunctional differential equationsMathematical physicsGeometry, Differential.Functional differential equations.Mathematical physics.516.3/6Sussman Gerald Jay475718Wisdom Jack731763Farr Will872701MiAaPQMiAaPQMiAaPQBOOK9910260608503321Functional differential geometry1948239UNINA