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Curved Spaces 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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P. M. H. Wilson 作者

Cambridge University Press

译者

2008-1-14 出版日期

196 页数

USD 43.99 价格

Paperback

丛书系列

9780521713900 图书编码

Curved Spaces 在线电子书图书标签: 数学计算机科学数学-微分几何微分几何7 微分几何工程数学几何 Spaces

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Curved Spaces 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Curved Spaces 在线电子书图书描述

This self-contained 2007 textbook presents an exposition of the well-known classical two-dimensional geometries, such as Euclidean, spherical, hyperbolic, and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations, and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalization to abstract surfaces equipped with Riemannian metrics. Themes running throughout include those of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the link to topology provided by the Gauss-Bonnet theorem. Numerous diagrams help bring the key points to life and helpful examples and exercises are included to aid understanding. Throughout the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra.

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