Differential Geometry of Curves and Surfaces / by Kristopher Tapp
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2016 |
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| 書誌ID | OB01018253 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Introduction -- Curves -- Additional topics in curves -- Surfaces -- The curvature of a surface -- Geodesics -- The Gauss–Bonnet theorem -- Appendix A: The topology of subsets of Rn -- Recommended excursions -- Index. License restrictions may limit access Summary: This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it. |
| 著者標目 | *Tapp, Kristopher SpringerLink (Online service) |
| 統一書名標目 | Undergraduate Texts in Mathematics, |
| 件 名 | LCSH:Mathematics LCSH:Differential geometry FREE:Mathematics FREE:Differential Geometry |
| 分 類 | LCC:QA641-670 DC23:516.36 |
| 巻冊次 | ISBN:9783319397993 RefWorks出力（各巻） print ; ISBN:9783319397986 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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※2020年8月16日以降