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内容概要

Kenneth A. Ross (K. A. 罗斯，美国）是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。

书籍目录

Preface

1 Introduction

1 The Set N of Natural Numbers

2 The Set Q of Rational Numbers

3 fhe Set R of Real Numbers

4 The Completeness Axiom

5 The Symbols +∞ and —∞

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 limsup's andliminf's

13 Some Topological Concepts in Metric Spaces

14 Series

15 Alternating 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 L'Hospital's Rule

31 Taylor's Theorem

6 Integration

32 The Riemann Integral

33 Properties of the Riemann Integral

34 Fundamental Theorem of Calculus

35 Riemann—Stieltjes Integrals

36 Improper Integrals

7 Capstone

37 A Discussion of Exponents and Logarithms

38 Continuous Nowhere—Differentiable Functions

Appendix on Set Notation

Selected Hints and Answers

A Guide to the References

References

Symbols Index

Index

作者简介

三十多年来，作为一本从微积分到分析的过渡教程的必备教科书，该书一直畅销于美国及其以外的其他国家的学生当中。事实证明，该书是一本对严格的证明不熟悉的读者非常有益的。简单易懂的书写模式揭开了书面证明的神秘性,同时对微积分的基本理论作了详细的检验。书中给出了充分的证明，精选了许多例子，并且提供了许多从常规到具有挑战性的练习题。第2版延续了第1版简约明晰的风格，增添了一些新的课题，如pi的无理性、Bair

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