多维实分析第2卷

版次：1
页数：
字数：
印刷时间：2009年08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：9787510005183
作者:（荷）杜斯特马特著出版社:世界图书出版公司出版时间:2009年08月

目　　录

Volume Ⅱ
Preface
Acknowledgments
Introduction
6 Integration
6.1 Rectangles
6.2 Riemann integrability
6.3 Jordan measurability
6.4 Successive integration
6.5 Examples of successive integration
6.6 Change of Variables Theorem: formulation and examples
6.7 Partitions of unity
6.8 Approximation of Riemann integrable functions
6.9 Proof of Change of Variables Theorem

Volume Ⅱ Preface Acknowledgments Introduction 6 Integration 6.1 Rectangles 6.2 Riemann integrability 6.3 Jordan measurability 6.4 Successive integration 6.5 Examples of successive integration 6.6 Change of Variables Theorem: formulation and examples 6.7 Partitions of unity 6.8 Approximation of Riemann integrable functions 6.9 Proof of Change of Variables Theorem 6.10 Absolute Riemann integrability 6.11 Application of integration: Fourier transformation 6.12 Dominated convergence 6.13 Appendix: two other proofs of Change of Variables Theorem 　7 Integration over Submanifolds 7.1 Densities and integration with respect to density 7.2 Absolute Riemann integrability with respect to density 7.3 Euclidean d-dimensional density 7.4 Examples of Euclidean densities 7.5 Open sets at one side of their boundary 7.6 Integration of a total derivative 7.7 Generalizations of the preceding theorem 7.8 Gauss' Divergence Theorem 7.9 Applications of Gauss' Divergence Theorem 8 Oriented Integration 8.1 Line integrals and properties of vector fields 8.2 Antidifl'erentiation 8.3 Green's and Cauchy's Integral Theorems 8.4 Stokes' Integral Theorem 8.5 Applications of Stokes' Integral Theorem 8.6 Apotheosis: differential forms and Stokes' Theorem 8.7 Properties of differential forms 8.8 Applications of differential forms 8.9 Homotopy Lemma 8.10 Poincard's Lemma 8.11 Degree of mapping 　Exercises Exercises for Chapter 6 Exercises for Chapter 7 Exercises for Chapter 8 　Notation 　Index Volume Ⅰ Preface Acknowledgments Introduction 　1 Continuity 1.1 Inner product and norm 1.2 Open and closed sets 1.3 Limits and continuous mappings 1.4 Composition of mappings 1.5 Homeomorphisms 1.6 Completeness 1.7 Contractions 1.8 Compactness and uniform continuity 1.9 Connectedness 　2 Differentiation 2.1 Linear mappings 2.2 Differentiahle mappings 2.3 Directional and partial derivatives 2.4 Chain rule 2.5 Mean Value Theorem 2.6 Gradient 2.7 Higher-order derivatives 2.8 Taylor's formula 2.9 Critical points 2.10　Commuting limit operations 　3 Inverse Function and Implicit Function Theorems 3.1 Diffeomorphisms 3.2 Inverse Function Theorems 3.3 Applications of Inverse Function Theorems 3.4 Implicitly defined mappings 3.5 Implicit Function Theorem 3.6 Applications of the Implicit Function Theorem 3.7 Implicit and Inverse Function Theorems on C 　4 Manifolds 4.1 Introductory remarks 4.2 Manifolds 4.3 Immersion Theorem 4.4 Examples of immersions 4.5 Submersion Theorem 4.6 Examples of submersions 4.7 Equivalent definitions of manifold 4.8 Morse's Lemma 　5 Tangent Spaces 5.1 Definition of tangent space 5.2 Tangent mapping 5.3 Examples of tangent spaces 5.4 Method of Lagrange multipliers 5.5 Applications of the method of multipliers 5.6 Closer investigation of critical points 5.7 Gaussian curvature of surface 5.8 Curvature and torsion of curve in R3 5.9 One-parameter groups and infinitesimal generators 5.10 Linear Lie groups and their Lie algebras 5.11 Transversality 　Exercises Review Exercises Exercises for Chapter 1 Exercises lot Chapter 2 Exercises for Chapter 3 Exercises for Chapter 4 Exercises for Chapter 5 　Notation 　Index

显示全部信息

多维实分析第2卷下载

发布书评

多维实分析 第2卷

发布书评

相关图书推荐

多维实分析第2卷