作者：KennethA.Ross著
页数：432
出版社：世界图书出版公司
出版日期：2016
ISBN：9787519205331
电子书格式：pdf/epub/txt
内容简介
三十多年来，作为一本从微积分到分析的过渡教程的第一教科书，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。
作者简介
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。
本书特色
三十多年来，作为一本从微积分到分析的过渡教程的第一教科书，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
目录
Preface1 Introduction1 The Set N of Natural Numbers2 The Set Q of Rational Numbers3 fhe Set R of Real Numbers4 The Completeness Axiom5 The Symbols +∞ and -∞6 A Development of R
2 Sequences7 Limits of Sequences8 A Discussion about Proofs9 Limit Theorems for Sequences10 Monotone Sequences and Cauchy Sequences11 Subsequences12 limsup’s andliminf’s13 Some Topological Concepts in Metric Spaces14 Series15 Alternating Series and Integral Tests16 Decimal Expansions of Real Numbers3 Continuity17 Continuous Functions18 Properties of Continuous Functions19 Uniform Continuity20 Limits of Functions21 More on Metric Spaces：Continuity22 More on Metric Spaces：Connectedness4 Sequences and Series of Functions23 Power Series24 Uniform Convergence25 More on Uniform Convergence26 Differentiation and Integration of Power Series27 Weierstrass’s Approximation Theorem5 Differentiation28 Basic Properties of the Derivative29 The Mean Value Theorem30 L’Hospital’s Rule31 Taylor’s Theorem6 Integration32 The Riemann Integral33 Properties of the Riemann Integral34 Fundamental Theorem of Calculus35 Riemann-Stieltjes Integrals36 Improper Integrals7 Capstone37 A Discussion of Exponents and Logarithms38 Continuous Nowhere—Differentiable FunctionsAppendix on Set NotationSelected Hints and AnswersA Guide to the ReferencesReferencesSymbols IndexIndex
2 Sequences7 Limits of Sequences8 A Discussion about Proofs9 Limit Theorems for Sequences10 Monotone Sequences and Cauchy Sequences11 Subsequences12 limsup’s andliminf’s13 Some Topological Concepts in Metric Spaces14 Series15 Alternating Series and Integral Tests16 Decimal Expansions of Real Numbers3 Continuity17 Continuous Functions18 Properties of Continuous Functions19 Uniform Continuity20 Limits of Functions21 More on Metric Spaces：Continuity22 More on Metric Spaces：Connectedness4 Sequences and Series of Functions23 Power Series24 Uniform Convergence25 More on Uniform Convergence26 Differentiation and Integration of Power Series27 Weierstrass’s Approximation Theorem5 Differentiation28 Basic Properties of the Derivative29 The Mean Value Theorem30 L’Hospital’s Rule31 Taylor’s Theorem6 Integration32 The Riemann Integral33 Properties of the Riemann Integral34 Fundamental Theorem of Calculus35 Riemann-Stieltjes Integrals36 Improper Integrals7 Capstone37 A Discussion of Exponents and Logarithms38 Continuous Nowhere—Differentiable FunctionsAppendix on Set NotationSelected Hints and AnswersA Guide to the ReferencesReferencesSymbols IndexIndex
