微分几何教程
￥ 23.25 8.3折 ￥ 28 九五品
仅1件
作者Wilhelm Klingenberg 著
出版社世界图书出版公司
ISBN9787506200813
出版时间2000-12
版次1
装帧平装
开本16开
纸张胶版纸
页数178页
定价28元
上书时间2024-08-03
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基本信息
书名:微分几何教程
定价：28.00元
作者:Wilhelm Klingenberg 著
出版社：世界图书出版公司
出版日期：2000-12-01
ISBN：9787506200813
字数：
页码：178
版次：1
装帧：平装
开本：16开
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内容提要
Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some elaborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour.
目录
Chapter 0 Calculus in Euclidean Space 0.1 Euclidean Space 0.2 The Topology of Euclidean Space 0.3 Differentiation in Rn 0.4 Tangent Space 0.5 Local Behavior of Differentiable Functions (Injective and Surjective FunctionsChapter 1 Curves 1.1 Definitions 1.2 The Frenet Frame 1.3 The Frenet Equations 1.4 Plane Curves； Local Theory 1.5 Space Curves 1.6 Exercises Chapter 2 Plane Curves: Global Theory 2.1 The Rotation Number 2.2 The Umlaufsatz 2.3 Convex CurvesChapter 3 Surfaces:Local Theory 3.1 Definitions 3.2 The First Fundamental Form 3.3 The Second Fundamental Form 3.4 Curves on Surfaces 3.5 Principal Curvature,Gauss Curvature,and Mean Curvature 3.6 Normal Form for a Surface,Special Coordinates 3.7 Special Surfaces,Developable Surfaces 3.8 The Gauss and Codazzi-Mainardi Equations 3.9 Exercises and Some Further ResultsChapter 4 Intrinsic Geometry of Surfaces:Local Theory 4.1 Vector Fields and Covariant Differentiation 4.2 Parallel Translation 4.3 Geodesics 4.4 Surfaces of Constant Curvature 4.5 Examples and ExercisesChapter 5 Two-dimensional Riemannian GenometryChapter 6 The Global Geometry of SurfacesReferencesIndexIndex of Symbols
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