数学分析原理 本书特色

《数学分析原理(英文)》是数学分析方面的经典著作，主要介绍了数列的收敛性、点集拓扑、黎曼积分、超越函数、傅里叶级数等内容。它也可以作为实数分析，泛函分析，谐波分析等课程的课外读物。对于需要学习微积分的非数学专业的学生，这本书是一个好的选择。

数学分析原理 内容简介

《数学分析原理(英文)》由哈尔滨工业大学出版社出版。

数学分析原理 目录

Preface
1 Sets and Proofs
1．1 Sets， Elements， and Subsets
1．2 Operations on Sets
1．3 Language of Logic
1．4 Techniques of Proof
1．5 Relations
1．6 Functions
1．7 Axioms of Set Theory
Exercises

2 Numbers
2．1 SystemN
2．2 Systems Z and Q
2．3 Least Upper Bound Property and Q
2．4 System R
2．5 Least Upper Bound Property and R
2．6 Systems R， C， and *R
2．7 Cardinality
Exercises

3 Convergence
3．1 Convergence ofNumerical Sequences
3．2 Cauchy Criterion for Convergence
3．3 Ordered Field Structure and Convergence
3．4 Subsequences
3．5 NumericalSeries
3．6 Some Series of Particular Interest
3．7 AbsoluteConvergence
3．8 Number e
Exercises

4 Point Set Topology
4．1 MetricSpaces
4．2 Open and Closed Sets
4．3 Completeness
4．4 Separability
4．5 TotaIBoundedness
4．6 Compactness
4．7 Perfectness
4．8 Connectedness
4．9* Structure of Open and Closed Sets
Exercises

5 Continuity
5．1 Definition and Examples
5．2 Continuity and Limits
5．3 Continuity and Compactness
5．4 Continuity and Connectedness
5．5 Continuity and Oscillation
5．6 Continuity of Rk-valued Functions
Exercises

6 Space C(E， E')
6．1 UniformContinuity
6．2 UniformConvergence
6．3 Completeness of C(E， E)
6．4 Bernstein and Weierstrass Theorems
6．5* Stone and Weierstrass Theorems
6．6* Ascoli-Arzela Theorem
Exercises

7 Differentiation
7．1 Derivative
7．2 Differentiation and Continuity
7．3 Rules of Differentiation
7．4 Mean-ValueTheorems
7．5 Taylor'sTheorem
7．6* DifferentialEquations
7．7* Banach Spaces and the Space C1 (a，b)
7．8 A View to Differentiation in Rk
Exercises

8 Bounded Variation
8．1 Monotone Functions
8．2 CantorFunction
8．3 Functions ofBoundedVariation
8．4 Space BV(a， b)
8．5 Continuous Functions of Bounded Variation
……

自然科学 数学 数学理论

在线阅读