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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
版次：
1
最新版次
印刷时间：
2026-01-05
ISBN：
978-7-04-065967-2
物料号：
65967-00
出版时间：
2026-03-27
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
  • 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

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