实分析的基本方法（影印版）
作者： David Bressoud
出版时间：2021-03
出版社：高等教育出版社
- 高等教育出版社
- 9787040556322
- 1版
- 369851
- 46253884-4
- 精装
- 16开
- 2021-03
- 550
- 344
- 理学
- 数学
- 数学类
- 研究生及以上
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
