数学分析基本原理（影印版）

样章

作者：

Paul J. Sally, Jr.

定价：

169.00 元

版面字数：

600.00千字

开本：

16开

装帧形式：

精装

页数：

384

最新
印次时间：

2026年3月

ISBN：

978-7-04-065967-2

物料号：

65967-00

出版时间：

2026年3月

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

目录
- 前辅文
- Preface
- Acknowledgments
- Chapter 1. The Construction of Real and Complex Numbers
  - 1.1. The Least Upper Bound Property and the Real Numbers
  - 1.2. Consequences of the Least Upper Bound Property
  - 1.3. Rational Approximation
  - 1.4. Intervals
  - 1.5. The Construction of the Real Numbers
  - 1.6. Convergence in R
  - 1.7. Automorphisms of Fields
  - 1.8. Complex Numbers
  - 1.9. Convergence in C
  - 1.10. Independent Projects
- Chapter 2. Metric and Euclidean Spaces
  - 2.1. Introduction
  - 2.2. Definition and Basic Properties of Metric Spaces
  - 2.3. Topology of Metric Spaces
  - 2.4. Limits and Continuous Functions
  - 2.5. Absolute Continuity and Bounded Variation in R
  - 2.6. Compactness, Completeness, and Connectedness
  - 2.7. Independent Projects
- Chapter 3. Complete Metric Spaces
  - 3.1. The Contraction Mapping Theorem and Its Applications to Differential and Integral Equations
  - 3.2. The Baire Category Theorem and the Uniform Boundedness Principle
  - 3.3. Stone-Weierstrass Theorem
  - 3.4. The p-adic Completion of Q
  - 3.5. Independent Projects
- Chapter 4. Normed Linear Spaces
  - 4.1. Definitions and Basic Properties
  - 4.2. Bounded Linear Operators
  - 4.3. Fundamental Theorems about Linear Operators
  - 4.4. Extending Linear Functionals
  - 4.5. Generalized Limits and the Dual of l∞(F)
  - 4.6. Adjoint Operators and Isometries of Normed Linear Spaces
  - 4.7. Concrete Facts about Isometries of Normed Linear Spaces
  - 4.8. Locally Compact Groups
  - 4.9. Hilbert Spaces
  - 4.10. Convergence and Selfadjoint Operators
  - 4.11. Independent Projects
- Chapter 5. Differentiation
  - 5.1. Review of Differentiation in One Variable
  - 5.2. Differential Calculus in Rn
  - 5.3. The Derivative as a Matrix of Partial Derivatives
  - 5.4. The Mean Value Theorem
  - 5.5. Higher-Order Partial Derivatives and Taylor’s Theorem
  - 5.6. Hypersurfaces and Tangent Hyperplanes in Rn
  - 5.7. Max-Min Problems
  - 5.8. Lagrange Multipliers
  - 5.9. The Implicit and Inverse Function Theorems
  - 5.10. Independent Projects
- Chapter 6. Integration
  - 6.1. Measures
  - 6.2. Lebesgue Measure
  - 6.3. Measurable Functions
  - 6.4. The Integral
  - 6.5. Lp Spaces
  - 6.6. Fubini’s Theorem
  - 6.7. Change of Variables in Integration
  - 6.8. Independent Projects
- Chapter 7. Fourier Analysis on Locally Compact Abelian Groups
  - 7.1. Fourier Analysis on the Circle
  - 7.2. Fourier Analysis on Locally Compact Abelian Groups
  - 7.3. The Determination of ^G
  - 7.4. The Fourier Transform on (R, +)
  - 7.5. Fourier Inversion on (R, +)
  - 7.6. Fourier Analysis on p-adic Fields
  - 7.7. Independent Projects
- Appendix A. Sets, Functions, and Other Basic Ideas
  - A.1. Sets and Elements
  - A.2. Equality, Inclusion, and Notation
  - A.3. The Algebra of Sets
  - A.4. Cartesian Products, Counting, and Power Sets
  - A.5. Some Sets of Numbers
  - A.6. Equivalence Relations and the Construction of Q
  - A.7. Functions
  - A.8. Countability and Other Basic Ideas
  - A.9. The Axiom of Choice
  - A.10. Independent Projects
- Appendix B. Linear Algebra
  - B.1. Fundamentals of Linear Algebra
  - B.2. Linear Transformations
  - B.3. Linear Transformations and Matrices
  - B.4. Determinants
  - B.5. Geometric Linear Algebra
  - B.6. Independent Projects
- Bibliography
- Index of Terminology
- Index of Notation Definitions