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＜電子ブック＞
First Steps in Differential Geometry : Riemannian, Contact, Symplectic / by Andrew McInerney
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2013.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2013
本文言語	英語
大きさ	XIII, 410 p. 54 illus., 25 illus. in color : online resource
著者標目	*McInerney, Andrew author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Manifolds and Cell Complexes
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-1-4614-7732-7

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