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[美] 亚伯拉罕(Abraham P.) 著
出版社: 世界图书出版公司 ISBN:9787510070181 版次:2 商品编码:11483421 包装:平装 外文名称:Manifollds, Tensor Analysis, and Applications 2nd ed 开本:24开 出版时间:2014-03-01 用纸:胶版纸 页数:654 正文语种:英文
Background Notation
CHAPTER 1 Topology
1.1 Topological Spaces
1.2 Metric Spaces
1.3 Continuity
1.4 Subspaces. Products. and Quotients
1.5 Compactness
1.6 Connectedness
1.7 Baire Spaces
CHAPTER 2 Banach Spaces and Differential Calculus
2.1 Banach Spaces
2.2 Linear and Multilinear Mappings
2.3 The Derivativc
2.4 Propcrties of che Dcrivarive
2.5 The Inverse and Implicit Function Theorems
CHAPTER 3 Manifolds and Vector Bundles
3.1 Manifolds
3.2 Submanifolds. Products. and Mappings
3.3 The Tangcnt Bundle
3.4 Veaor Bundles
3.5 Submersions. Immersions and Transversality
CHAPTER 4 Vector Fields and Dynamical Systems
4.1 Vector Fields and Flows
4.2 Vector Fields as Differemial Operators
4.3 An Imroduction to Dynamical Systems
4.4 Frobenius' Theorcm and Foliations
CHAPTER 5 Tensors
5.1 Tensors in Linear Spaces
5.2 Tensor Bundles and Tensor Fields
5.3 The Lie Derivative: Algebraic Approach
5.4 The Lie Derivative: Dynamic Approach
5.5 Partitions of Unity
CHAPTER 6 Differential Forms
6.1 Exterior Algebra
6.2 Determinants. Volumes. and the Hodge Star Operator
6.3 Differential Forms
6.4 The Exterior Derivative. tnterior Produa. and Lie Derivative
6.5 Orientation. Volume Elements, and the Codifferential
CHAPTER 7 Integration on Manifolds
7.1 The Definition of (he Integral
7.2 Stokes' Theorem
7.3 The Classical Theorems of Green. Gauss, and Stokes
7.4 Induced Flows on Function Spaces and Ergodicity
7.5 Introduction to Hodge-deRham Theory and Topological Applicarions of
Differential Forms
CHAPTER 8 Applications
8.1 Hamiltonian Mechanics
8.2 Fluid Mechanics
8.3 Electromagnctism
8.3 The Lie-Poisson Bracket in Continuum Mechanics and Plasma Physics
8.4 Constraints and Control
References
Index
Supplementary Chapters-Available from the authors as they are produced
S-1 Lie Groups
S-2 Introduction to Differential Topology
S-3 Topics in Riemannian Geometry
流形、张量分析和应用(第2版) [Manifollds, Tensor Analysis, and Applications 2nd ed] 电子书 下载 mobi epub pdf txt
流形、张量分析和应用(第2版) [Manifollds, Tensor Analysis, and Applications 2nd ed]-so88
流形、张量分析和应用(第2版) [Manifollds, Tensor Analysis, and Applications 2nd ed] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[美] 亚伯拉罕(Abraham P.) 著
出版社: 世界图书出版公司 ISBN:9787510070181 版次:2 商品编码:11483421 包装:平装 外文名称:Manifollds, Tensor Analysis, and Applications 2nd ed 开本:24开 出版时间:2014-03-01 用纸:胶版纸 页数:654 正文语种:英文
内容简介
The purpose of this book is to provide core material in nonlinear analysis for mathematicians. physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism. plasma dynamics and control theory are given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development.内页插图
目录
PrefaceBackground Notation
CHAPTER 1 Topology
1.1 Topological Spaces
1.2 Metric Spaces
1.3 Continuity
1.4 Subspaces. Products. and Quotients
1.5 Compactness
1.6 Connectedness
1.7 Baire Spaces
CHAPTER 2 Banach Spaces and Differential Calculus
2.1 Banach Spaces
2.2 Linear and Multilinear Mappings
2.3 The Derivativc
2.4 Propcrties of che Dcrivarive
2.5 The Inverse and Implicit Function Theorems
CHAPTER 3 Manifolds and Vector Bundles
3.1 Manifolds
3.2 Submanifolds. Products. and Mappings
3.3 The Tangcnt Bundle
3.4 Veaor Bundles
3.5 Submersions. Immersions and Transversality
CHAPTER 4 Vector Fields and Dynamical Systems
4.1 Vector Fields and Flows
4.2 Vector Fields as Differemial Operators
4.3 An Imroduction to Dynamical Systems
4.4 Frobenius' Theorcm and Foliations
CHAPTER 5 Tensors
5.1 Tensors in Linear Spaces
5.2 Tensor Bundles and Tensor Fields
5.3 The Lie Derivative: Algebraic Approach
5.4 The Lie Derivative: Dynamic Approach
5.5 Partitions of Unity
CHAPTER 6 Differential Forms
6.1 Exterior Algebra
6.2 Determinants. Volumes. and the Hodge Star Operator
6.3 Differential Forms
6.4 The Exterior Derivative. tnterior Produa. and Lie Derivative
6.5 Orientation. Volume Elements, and the Codifferential
CHAPTER 7 Integration on Manifolds
7.1 The Definition of (he Integral
7.2 Stokes' Theorem
7.3 The Classical Theorems of Green. Gauss, and Stokes
7.4 Induced Flows on Function Spaces and Ergodicity
7.5 Introduction to Hodge-deRham Theory and Topological Applicarions of
Differential Forms
CHAPTER 8 Applications
8.1 Hamiltonian Mechanics
8.2 Fluid Mechanics
8.3 Electromagnctism
8.3 The Lie-Poisson Bracket in Continuum Mechanics and Plasma Physics
8.4 Constraints and Control
References
Index
Supplementary Chapters-Available from the authors as they are produced
S-1 Lie Groups
S-2 Introduction to Differential Topology
S-3 Topics in Riemannian Geometry
前言/序言
流形、张量分析和应用(第2版) [Manifollds, Tensor Analysis, and Applications 2nd ed] 电子书 下载 mobi epub pdf txt
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