| | | 多維實分析 第2卷 | 該商品所屬分類:研究生 -> 理學 | 【市場價】 | 243-352元 | 【優惠價】 | 152-220元 | 【作者】 | (荷)杜斯特馬特 | 【所屬類別】 | 圖書 教材 研究生/本科/專科教材 理學圖書 自然科學 數學 數學分析 | 【出版社】 | 世界圖書出版公司 | 【ISBN】 | 9787510005183 | 【折扣說明】 | 一次購物滿999元台幣免運費+贈品 一次購物滿2000元台幣95折+免運費+贈品 一次購物滿3000元台幣92折+免運費+贈品 一次購物滿4000元台幣88折+免運費+贈品
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開本:24開 紙張:膠版紙 包裝:平裝 是否套裝:否 國際標準書號ISBN:9787510005183 作者:(荷)杜斯特馬特 出版社:世界圖書出版公司 出版時間:2009年08月 
"目錄 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 TheoremVolume 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 2.10Commuting 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
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