实分析常以基础集合论、函数概念的定义等开始，专门研究数列、数列极限、微分、积分和函数序列，以及实函数的连续性、光滑性及其他相关性质。为了避免人们对实数先入为主的概念，本书把实数看作是一个完整有序域的元素。全书共十章，介绍了集合和函数，实数，开、闭和紧集，连续性，函数序列与函数系列，度量空间和收缩原理等内容，最后几章还对实分析的应用做了论述。为了学习者能进一步理解实分析的相关理论，作者还给出了多个不同难度的练习供读者参考。

Pretace
To the student
Chapter 1.Numbers，sets，and functions
1.1.The natural numbers，integers，and rational numbers
1.2.Sets
1.3.FLlnctions
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Chapter 2.The real numbers
2.1.The complete ordered field of real numbers
2.2.Consequences of completeness
2.3.Countable and uncountable sets
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Chapter 3.Sequences
3.1.Convergent sequences
3.2.New 1imits from old
3.3.Monotone sequences
3.4.Series
3.5.Subsequences and Cauchy sequences
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Chapter 4.Open，closed，and compact sets
4.1.0 pen and closed sets
4.2.Compact sets
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Chapter 5.Continuity
5.1.Limits of functions
5.2.Continuous functions
5.3.Continuous functions on compact sets and intervals
5.4.Monotone functions
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Chapter 6.Differentiation
6.1.Differentiable functions
6.2.The mean value theorem
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Chapter 7.Integration
7.1.The Riemann integral
7.2.The fundamental theorem of calculus
7.3.The natural logarithm and the exponential function
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Chapter 8.Sequences and series of functions
8.1.Pointwise and uniform convergence
8.2.Power series
8.3.Taylor series
8.4.The trigonometric functions
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Chapter 9.Metric spaces
9.1.Examples of metric spaces
9.2.Convergence and completeness in metric spaces
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Chapter 10.The contraction principle
10.1.The contraction principle
10.2.Picard’s theorem
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Index
编辑手记