分析基础:微积分理论
分析基础:微积分理论
图书信息
出版社: 世界图书出版公司; 第1版 (2008年10月1日)
外文书名: Elementary Analysis: The Theory Of Calculus
平装: 351页
正文语种: 英语
开本: 16
ISBN: 9787506292665
条形码: 9787506292665
尺寸: 22.2 x 14.8 x 2.2 cm
重量: 440 g
作者简介
作者:(美国)丁罗斯 (Ross.K.A)
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。
目录
Preface
1 Introduction
1 The Set 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 lira sup''s and lim inf''s
13 * Some Topological Concepts in Metric Spaces
14 Series
15 Alternating Series and Integral Tests
16 * Decimal Expansions of Peal 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
Differentiation
28 Basic Properties of the Derivative
29 The Mean Value Theorem
30 * UHospital''s Rule
31 Taylor''s Theorem
5 Integration
32 The Riemann Integral
33 Properties of the Riemann Integral
34 Fundamental Theorem of Calculus
35 * Riemann-Stieltjes Integrals
36 * Improper Integrals
37 * A Discussion of Exponents and Logarithms
Appendix on Set Notation
Selected Hints and Answers
References
8ymhola Index
Index