图书信息
图书目录
分析基础（影印版）
暂无简介
作者：
Joseph L. Taylor
定价：
169.00 元
出版时间：
2026-03-26
ISBN：
978-7-04-065966-5
物料号：
65966-00
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：
660.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次印刷时间：
2026年
- 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
