分析基础（影印版）

样章

作者：

Joseph L. Taylor

定价：

169.00 元

版面字数：

660.00千字

开本：

16开

装帧形式：

精装

页数：

416

最新
印次时间：

2026年03月

ISBN：

978-7-04-065966-5

物料号：

65966-00

出版时间：

2026-03-26

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
- Chapter 1. The Real Numbers
  - 1.1. Sets and Functions
  - 1.2. The Natural Numbers
  - 1.3. Integers and Rational Numbers
  - 1.4. The Real Numbers
  - 1.5. Sup and Inf
- Chapter 2. Sequences
  - 2.1. Limits of Sequences
  - 2.2. Using the Definition of Limit
  - 2.3. Limit Theorems
  - 2.4. Monotone Sequences
  - 2.5. Cauchy Sequences
  - 2.6. lim inf and lim sup
- Chapter 3. Continuous Functions
  - 3.1. Continuity
  - 3.2. Properties of Continuous Functions
  - 3.3. Uniform Continuity
  - 3.4. Uniform Convergence
- Chapter 4. The Derivative
  - 4.1. Limits of Functions
  - 4.2. The Derivative
  - 4.3. The Mean Value Theorem
  - 4.4. L’Hôpital’s Rule
- Chapter 5. The Integral
  - 5.1. Definition of the Integral
  - 5.2. Existence and Properties of the Integral
  - 5.3. The Fundamental Theorems of Calculus
  - 5.4. Logs, Exponentials, Improper Integrals
- Chapter 6. Infinite Series
  - 6.1. Convergence of Infinite Series
  - 6.2. Tests for Convergence
  - 6.3. Absolute and Conditional Convergence
  - 6.4. Power Series
  - 6.5. Taylor’s Formula
- Chapter 7. Convergence in Euclidean Space
  - 7.1. Euclidean Space
  - 7.2. Convergent Sequences of Vectors
  - 7.3. Open and Closed Sets
  - 7.4. Compact Sets
  - 7.5. Connected Sets
- Chapter 8. Functions on Euclidean Space
  - 8.1. Continuous Functions of Several Variables
  - 8.2. Properties of Continuous Functions
  - 8.3. Sequences of Functions
  - 8.4. Linear Functions, Matrices
  - 8.5. Dimension, Rank, Lines, and Planes
- Chapter 9. Differentiation in Several Variables
  - 9.1. Partial Derivatives
  - 9.2. The Differential
  - 9.3. The Chain Rule
  - 9.4. Applications of the Chain Rule
  - 9.5. Taylor’s Formula
  - 9.6. The Inverse Function Theorem
  - 9.7. The Implicit Function Theorem
- Chapter 10. Integration in Several Variables
  - 10.1. Integration over a Rectangle
  - 10.2. Jordan Regions
  - 10.3. The Integral over a Jordan Region
  - 10.4. Iterated Integrals
  - 10.5. The Change of Variables Formula
- Chapter 11. Vector Calculus
  - 11.1. 1-forms and Path Integrals
  - 11.2. Change of Variables
  - 11.3. Differential Forms of Higher Order
  - 11.4. Green’s Theorem
  - 11.5. Surface Integrals and Stokes’s Theorem
  - 11.6. Gauss’s Theorem
  - 11.7. Chains and Cycles
- Appendix. Degrees of Infinity
  - A.1. Cardinality of Sets
  - A.2. Countable Sets
  - A.3. Uncountable Sets
  - A.4. The Axiom of Choice
- Bibliography
- Index