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First Steps in Differential Geometry : Riemannian, Contact, Symplectic / by Andrew McInerney
(Undergraduate Texts in Mathematics. ISSN:21975604)
版 | 1st ed. 2013. |
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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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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781461477327 |
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EB00227685 |
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※2017年9月4日以降