分析基础
Douban
K.A.罗斯 (Kenneth A.Ross)
Overview
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
contents
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
