03719nam 22006735 450 991073373290332120200702014226.01-4614-7732-810.1007/978-1-4614-7732-7(CKB)3710000000002543(SSID)ssj0000962735(PQKBManifestationID)11974953(PQKBTitleCode)TC0000962735(PQKBWorkID)10979059(PQKB)11445986(DE-He213)978-1-4614-7732-7(MiAaPQ)EBC3096881(PPN)172419824(EXLCZ)99371000000000254320130709d2013 u| 0engurnn#008mamaatxtccrFirst Steps in Differential Geometry Riemannian, Contact, Symplectic /by Andrew McInerney1st ed. 2013.New York, NY :Springer New York :Imprint: Springer,2013.1 online resource (XIII, 410 p. 54 illus., 25 illus. in color.)Undergraduate Texts in Mathematics,0172-6056Bibliographic Level Mode of Issuance: Monograph1-4614-7731-X Includes bibliographical references (pages 405-406) and index.Basic Objects and Notation -- Linear Algebra Essentials -- Advanced Calculus -- Differential Forms and Tensors -- Riemannian Geometry -- Contact Geometry -- Symplectic Geometry -- References -- Index.Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.Undergraduate Texts in Mathematics,0172-6056Differential geometryGlobal analysis (Mathematics)Manifolds (Mathematics)Complex manifoldsDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Manifolds and Cell Complexes (incl. Diff.Topology)https://scigraph.springernature.com/ontologies/product-market-codes/M28027Differential geometry.Global analysis (Mathematics).Manifolds (Mathematics).Complex manifolds.Differential Geometry.Global Analysis and Analysis on Manifolds.Manifolds and Cell Complexes (incl. Diff.Topology).516.3/6McInerney Andrewauthttp://id.loc.gov/vocabulary/relators/aut524805MiAaPQMiAaPQMiAaPQBOOK9910733732903321First steps in differential geometry820715UNINA