书籍详情
实分析的基本方法（影印版）
作者：David Bressoud 著
出版社：高等教育出版社
出版时间：2021-03-01
ISBN：9787040556322
定价：¥135.00
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内容简介
本书从Fourier引入三角级数，以及三角级数为19世纪早期的数学家带来的问题开始。书中接着谈到Cauchy为微积分建立一个坚实基础所付出的努力，并细数了他的失败和成功。最后则是Dirichlet对Fourier级数展开有效性的证明，探讨了由于Dirichlet的证明，由Riemann和Weierstrass得出的一些违反直觉的结果。第二版增加了60多个新的习题，重新梳理了无穷级数的无限和、可微性与连续性、收敛性等章节的内容，让读者更容易理解其中的主要观点。 《实分析的基本方法》是一本以实分析发展中的历史事件为基础的入门读本。它可用作教科书，作为传统授课教师的参考资料，或者供那些已经上了课、但仍未理解什么是实分析以及为何要创建它的学生们阅读参考。
作者简介
暂缺《实分析的基本方法（影印版）》作者简介
目录
Preface
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
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
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