张量几何第2版

版次：1
页数：
字数：
印刷时间：2009年06月01日
开本：24开
纸张：胶版纸
包装：平装
是否套装：否
国际标准书号ISBN：9787510004797
作者:（英）多德森　著出版社:世界图书出版公司出版时间:2009年06月

目　　录

Introduction
0. Fundamental Not(at)ions
　1. Sets
　2. Functions
　3. Physical Background
I. Real Vector Spaces
　1. Spaces
　　Subspace geometry, components
　2. Maps
　　Linearity, singularity, matrices
　3. Operators
　　Projections, eigenvMues, determinant, trace
II. Affine Spaces
　1. Spaces

Introduction 0. Fundamental Not(at)ions 　1. Sets 　2. Functions 　3. Physical Background I. Real Vector Spaces 　1. Spaces 　　Subspace geometry, components 　2. Maps 　　Linearity, singularity, matrices 　3. Operators 　　Projections, eigenvMues, determinant, trace II. Affine Spaces 　1. Spaces 　　Tangent vectors, parallelism, coordinates 　2. Combinations of Points 　　Midpoints, convexity 　3. Maps 　　Linear parts, translations, components III. Dual Spaces 　1. Contours, Co- and Contravariance, Dual Basis IV. Metric Vector Spaces 　1. Metrics 　　Basic geometry and examples, Lorentz geometry 　2. Maps 　　Isometries, orthogonal projections and complements, adjoints 　3. Coordinates 　　Orthonormal bases 　4. Diagonalising Symmetric Operators 　　Principal directions, isotropy V. Tensors and Multilinear Forms 　1. Multilinear Forms 　　Tensor Products, Degree, Contraction, Raising Indices Vii Topological Vector Spaces 　1. Continuity 　　Metrics: topologies, homeomorphisms 　2. Limits 　　Convergence and continuity 　3. The Usual Topology 　　Continuity in finite dimensions 　4. Compactness and Completeness 　　Intermediate Value Theorem, convergence, extrema VII. Differentiation and Manifolds 　1. Differentiation 　　Derivative as local linear approxiamation 　2. Manifolds 　　Charts, maps, diffeomorphisms 　3. Bundles and Fields 　　Tangent and tensor bundles, metric tensors 　4. Components 　　Hairy Ball Theorem, transformation formulae, raising indic 　5. Curves 　　Parametrisation, length, integration 　6. Vector Fields and Flows 　　First order ordinary differential equations 　7. Lie Brackets 　　Commuting vector fields and flows VIII. Connections and Covariant Differentiation 　1. Curves and Tangent Vectors 　　Representing a vector by a curve 　2. Rolling Without Turning 　　Differentiation along curves in embedded manifolds 　3. Differentiating Sections 　　Connections horizontal vectors, Christoffel symbols 　4. Parallel Transport 　　Integrating a connection IX. Geodesics X. Curvature XI. Special Relativity XII. General Relativity Bibliography Index of Notations Index

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