书籍详情
分析基础
作者：（美）丁罗斯 著
出版社：世界图书出版公司
出版时间：2008-10-01
ISBN：9787506292665
定价：¥59.00
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内容简介
《分析基础：微积分理论》旨在为对严格的证明不熟悉的读者，提供一本学习标准积分教程的后继教程。对于学习高等分析教程，复变量、微分方程、傅里叶分析、数值分析、多变量微积分以及统计的人来说读《分析基础：微积分理论》是很有必要的。同样也可以作为将来中学老师的参考教科书。有关实线的概念《分析基础：微积分理论》研究不多，许多抽象概念，如矩阵空间和有序系，在《分析基础：微积分理论》中都避免讨论；最小上界的性质在《分析基础：微积分理论》中拿来即用，实线的有序性贯穿于书的始终；数字序列的透彻讲解作为学习标准微积分的基础；选修部分可以让学生学习矩阵空间和Riemann-Stieltjes积分。
作者简介
暂缺《分析基础》作者简介
目录
Preface
1 Introduction
1 TheSet N of Natural Numbers
2 The Set Q of Rational Numbers
3 The Set R of Real Numbers
4 The Completeness Axiom
5 The Symbols +oo and -oo
6 * A Development of R
2 Sequences
7 Limits of Sequences
8 A Discussion.about Proofs
9 Limit Theorems for Sequences
10 Monotone Sequences and Cauchy Sequences
11 Subsequences
12 lim sap's and lim inf's
13 * Some Topological Concepts in Metric spaces
14 Series
15 Aternatin4g Series and Integral Tests
16 * Decimal Expansions of Real Numbers
3 Continuity
17 Continuous Functions
18 Properties of Continuous Functions
19 Uniform Continuity
20 Limits of Functions
21 * More on Metric Spaces: Continuity
22 * More on Metric Spaces: Connectedness
4 Sequences and Series of Functions
23 Power Series
24 Uniform Convergence
25 More on Uniform Convergence
26 Differentiation and Integration of Power series
27 * weierstrass's Approximation Theorem
5 Differentiation
28 Basic Properties of the Derivative
29 The Mean Value Theorem
30 * UHospital's Rule
31 Taylor s Theorem
6 Integration
32 The Riemann Integral
33 Properties of the Riemann Integral
34 Fundamental Theorem of Calctflus
35 * Riemann-Stieltjes Integrals
36 * Improper Integrals
37 * A Discussion of Exponents and Logarithms
Appendix on Set Notation
Selected Hints and Answers
References
Symbols Index
Index
1 Introduction
1 TheSet N of Natural Numbers
2 The Set Q of Rational Numbers
3 The Set R of Real Numbers
4 The Completeness Axiom
5 The Symbols +oo and -oo
6 * A Development of R
2 Sequences
7 Limits of Sequences
8 A Discussion.about Proofs
9 Limit Theorems for Sequences
10 Monotone Sequences and Cauchy Sequences
11 Subsequences
12 lim sap's and lim inf's
13 * Some Topological Concepts in Metric spaces
14 Series
15 Aternatin4g Series and Integral Tests
16 * Decimal Expansions of Real Numbers
3 Continuity
17 Continuous Functions
18 Properties of Continuous Functions
19 Uniform Continuity
20 Limits of Functions
21 * More on Metric Spaces: Continuity
22 * More on Metric Spaces: Connectedness
4 Sequences and Series of Functions
23 Power Series
24 Uniform Convergence
25 More on Uniform Convergence
26 Differentiation and Integration of Power series
27 * weierstrass's Approximation Theorem
5 Differentiation
28 Basic Properties of the Derivative
29 The Mean Value Theorem
30 * UHospital's Rule
31 Taylor s Theorem
6 Integration
32 The Riemann Integral
33 Properties of the Riemann Integral
34 Fundamental Theorem of Calctflus
35 * Riemann-Stieltjes Integrals
36 * Improper Integrals
37 * A Discussion of Exponents and Logarithms
Appendix on Set Notation
Selected Hints and Answers
References
Symbols Index
Index
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