图书信息
图书目录
数学分析基本原理（影印版）
暂无简介
作者：
Paul J. Sally, Jr.
定价：
169.00 元
出版时间：
2026-03-27
ISBN：
978-7-04-065967-2
物料号：
65967-00
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
重点项目：
暂无
版面字数：
600.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次印刷时间：
2026-01-05
- 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
