《分析基础》是2008年世界图书出版公司出版的图书，作者是(美国)丁罗斯(Ross.K.A)。《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，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：(美国)丁罗斯(Ross.K.A)

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