实分析的基本方法（影印版）

样章

作者：

David Bressoud

定价：

135.00元

ISBN：

978-7-04-055632-2

版面字数：

550.000千字

开本：

16开

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

出版时间：

2021-03-09

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：

数论

暂无

前辅文
1 Crisis in Mathematics: Fourier’s Series
- 1.1 Background to the Problem
- 1.2 Difficulties with the Solution
2 Infinite Summations
- 2.1 The Archimedean Understanding
- 2.2 Geometric Series
- 2.3 Calculating π
- 2.4 Logarithms and the Harmonic Series
- 2.5 Taylor Series
- 2.6 Emerging Doubts
3 Differentiability and Continuity
- 3.1 Differentiability
- 3.2 Cauchy and the Mean Value Theorems
- 3.3 Continuity
- 3.4 Consequences of Continuity
- 3.5 Consequences of the Mean Value Theorem
4 The Convergence of Infinite Series
- 4.1 The Basic Tests of Convergence
- 4.2 Comparison Tests
- 4.3 The Convergence of Power Series
- 4.4 The Convergence of Fourier Series
5 Understanding Infinite Series
- 5.1 Groupings and Rearrangements
- 5.2 Cauchy and Continuity
- 5.3 Differentiation and Integration
- 5.4 Verifying Uniform Convergence
6 Return to Fourier Series
- 6.1 Dirichlet’s Theorem
- 6.2 The Cauchy Integral
- 6.3 The Riemann Integral
- 6.4 Continuity without Differentiability
7 Epilogue
A Explorations of the Infinite
- A.1 Wallis on π
- A.2 Bernoulli’s Numbers
- A.3 Sums of Negative Powers
- A.4 The Size of n!
B Bibliography
C Hints to Selected Exercises
Index