实分析演讲集(英文)
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作者(澳)芬纳·拉尔森 著
出版社哈尔滨工业大学出版社
ISBN9787560391199
出版时间2020-11
装帧平装
开本16开
定价38元
货号1202302397
上书时间2024-11-25
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目录
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
More exercises
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
More exercises
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
More exercises
Chapter 4 Open,closed,and compact sets
4.1 Open and closed sets
4.2 Compact sets
More exercises
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
More exercises
Chapter 6 Differentiation
6.1 Differentiable functions
6.2 The mean value theorem
More exercises
Chapter 7 Integration
7.1 The Riemann integral
7.2 The fundamental theorem of calculus
7.3 The natural logarithm and the exponential function
More exercises
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
More exercises
Chapter 9 Metric spaces
9.1 Examples of metric spaces
9.2 Convergence and completeness in metric spaces
More exercises
Chapter 10 The contraction principle
10.1 The contraction principle
10.2 Picards theorem
More exercises
Index
编辑手记
内容摘要
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。
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