分析基础(微积分理论第2版)(英文版)

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。罗斯所著的《分析基础（微积分理论第2版）（英 文版）》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。

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