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Smooth Manifolds / by Rajnikant Sinha
版 | 1st ed. 2014. |
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出版者 | (New Delhi : Springer India : Imprint: Springer) |
出版年 | 2014 |
本文言語 | 英語 |
大きさ | IX, 485 p. 10 illus : online resource |
著者標目 | *Sinha, Rajnikant author SpringerLink (Online service) |
件 名 | LCSH:Geometry, Differential LCSH:Gravitation LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Differential Geometry FREE:Classical and Quantum Gravity FREE:Global Analysis and Analysis on Manifolds |
一般注記 | Chapter 1. Differentiable Manifolds -- Chapter 2. Tangent Spaces -- Chapter 3. Multivariable Differential Calculus -- Chapter 4. Topological Properties of Smooth Manifolds -- Chapter 5. Immersions, Submersions, and Embeddings -- Chapter 6. Sard’s Theorem -- Chapter 7. Whitney Embedding Theorem -- Bibliography This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate studentsof mathematics, the book will also prove useful for researchers. The prerequisites for this text have intentionally been kept to a minimum so that undergraduate students can also benefit from it. It is a cherished conviction that “mathematical proofs are the core of all mathematical joy,” a standpoint this book vividly reflects HTTP:URL=https://doi.org/10.1007/978-81-322-2104-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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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 | 9788132221043 |
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EB00235123 |
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※2017年9月4日以降