資料介紹

相關專題學習資料：

• 數學物理化學/理論科學

中文名: 微分流形與黎曼幾何引論 作者: William M. Boothby 資源格式: DJVU 版本: 英文版.第2版修訂版 出版社: 人民郵電出版社 書號: 9787115165992 發行時間: 2007年 地區: 大陸 語言: 英文 微分流形與黎曼幾何引論  簡介:  微分流形與黎曼幾何引論  內容介紹： 《微分流形與黎曼幾何引論》這是一本非常好的微分流形入門書。全書從一些基本的微積分知識入手，然後一點點深入介紹，主要內容有：流形介紹、多變量函數和映射。 《微分流形與黎曼幾何引論》微分流形和子流形、流形上的向量場、張量和流形上的張量場、流形上的積分法、黎曼流形上的微分法以及曲率。書後有難度適中的習題。 《微分流形與黎曼幾何引論》全書配有很多精美的插圖，本書非常適合初學者閱讀，可作為數學系、物理系、機械系等理工科高年級本科生和研究生的非常實用教材。 微分流形與黎曼幾何引論  目錄:  Ⅰ. Introduction to Manifolds 1.Preliminary Comments on Rn 2.Rn and Euclidean Space 3.Topological Manifolds 4.Further Examples of Manifolds. Cutting and Pasting 5.Abstract Manifolds. Some Examples Ⅱ. Functions of Several Variables and Mappings 1.Differentiability for Functions of Several Variables 2.Differentiability of Mappings and Jacobians 3.The Space of Tangent Vectors at a Point of Rn 4.Another Definition of Ta(Rn) 5.Vector Fields on Open Subsets of Rn 6.The Inverse Function Theorem 7.The Rank of a Mapping Ⅲ. Differentiable Manifolds and Submanifolds 1.The Definition of a Differentiable Manifold 2.Further Examples 3.Differentiable Functions and Mappings 4.Rank of a Mapping, Immersions 5.Submanifolds 6.Lie Groups 7.The Action of a Lie Group on a Manifold. Transformation Groups 8.The Action of a Discrete Group on a Manifold 9.Covering Manifolds Ⅳ. Vector Fields on a Manifold 1.The Tangent Space at a Point of a Manifold 2.Vector Fields 3.One-Parameter and Local One-Parameter Groups Acting on a Manifold 4.The Existence Theorem for Ordinary Differential Equations 5.Some Examples of One-Parameter Groups Acting on a Manifold 6.One-Parameter Subgroups of Lie Groups 7.The Lie Algebra of Vector Fields on a Manifold 8.Frobenius's Theorem 9.Homogeneous Spaces Ⅴ. Tensors and Tensor Fields on Manifolds 1.Tangent Covectors 2.Bilinear Forms. The Riemannian Metric 3.Riemannian Manifolds as Metric Spaces 4.Partitions of Unity 5.Tensor Fields 6.Multiplication of Tensors 7.Orientation of Manifolds and the Volume Element 8.Exterior Differentiation Ⅵ. Integration on Manifolds Ⅶ. Differentiation on Riemannian Manifolds Ⅷ. Curvature 《微分流形與黎曼幾何引論》來源於網絡，僅用於分享知識，學習和交流!請下載完在24小時內刪除。 《微分流形與黎曼幾何引論》禁用於商業用途！如果您喜歡《微分流形與黎曼幾何引論》，請購買正版，謝謝合作！