没有合适的资源?快使用搜索试试~ 我知道了~
首页Elementary Real Analysis
Elementary Real Analysis
5星 · 超过95%的资源 需积分: 12 37 下载量 114 浏览量
更新于2023-03-03
评论 3
收藏 5.3MB PDF 举报
实分析基础,2001年版本,752页,如果看Rudin的Real and Complex Analysis和Royden的Real Analysis比较有困难,请阅读此书,此书比较基本,适合初学实分析和自学实分析的人群!
资源详情
资源评论
资源推荐
ELEMENTARY
REAL ANALYSIS
—————————————
thomson·bruckner
2
—————————————
Brian S. Thomson
Judith B. Bruckner
Andrew M. Bruckner
www.classicalrealanalysis.com
This PDF file is for the text Elementary Real Analysis originally pub-
lished by Prentice Hall (Pearson) in 2001. The authors retain the copyright
and all commercial uses. [2007]
Library of Congress Cataloging-in-Publication Data
Thomson, Brian S.
Elementary real analysis/ Brian S. Thomson,
Judith B. Bruckner, Andrew M. Bruckner.
p. cm.
Includes index.
ISBN: 0-13-019075-6
1. Mathematical analysis. I. Bruckner, Judith B.
II. Bruckner, Andrew M. III. Title
QA300. T45 2001 00-041679
515–dc21 CIP
Acquisitions Editor: George Lobell
Editor in Chief: Sally Yagan
Production Editor: Lynn Savino Wendel
Assistant Vice President Production and Manufacturing: David W. Riccardi
Executive Managing Editor: Kathleen Schiaparelli
Senior Managing Editor: Linda Mihatov Behrens
Manufacturing Buyer: Alan Fischer
Manufacturing Manager: Trudy Pisciotti
Director of Marketing: John Tweeddale
Marketing Manager: Angela Battle
Marketing Assistant: Vince Jansen
Art Director: Jayne Conte
Editorial Assistant: Gale Epps
Cover Designer: Kiwi Design
c
Original copyright 2001 by Prentice-Hall, Inc. The authors now retain all rights
under copyright.
All rights reserved. No part of this book may be
reproduced, in any form or by any means, without
permission in writing from the authors.
Originally printed in the United States of America
10987654321
ISBN: 0-13-019075-6
CONTENTS
PREFACE xii
1 PROPERTIES OF THE REAL NUMBERS 1
1.1 Introduction 1
1.2 The Real Number System 2
1.3 Algebraic Structure 5
1.4 Order Structure 8
1.5 Bounds 9
1.6 Sups and Infs 10
1.7 The Archimedean Property 13
1.8 Inductive Property of IN 15
1.9 The Rational Numbers Are Dense 16
1.10 The Metric Structure of R 18
1.11 Challenging Problems for Chapter 1 21
2 SEQUENCES 23
2.1 Introduction 23
2.2 Sequences 25
2.2.1 Sequence Examples 26
2.3 Countable Sets 29
2.4 Convergence 32
2.5 Divergence 37
2.6 Boundedness Properties of Limits 39
2.7 Algebra of Limits 41
2.8 Order Properties of Limits 47
2.9 Monotone Convergence Criterion 52
2.10 Examples of Limits 56
2.11 Subsequences 61
2.12 Cauchy Convergence Criterion 65
iii
iv
2.13 Upper and Lower Limits 68
2.14 Challenging Problems for Chapter 2 74
3 INFINITE SUMS 77
3.1 Introduction 77
3.2 Finite Sums 78
3.3 Infinite Unordered sums 84
3.3.1 Cauchy Criterion 86
3.4 Ordered Sums: Series 90
3.4.1 Properties 91
3.4.2 Special Series 92
3.5 Criteria for Convergence 98
3.5.1 Boundedness Criterion 99
3.5.2 Cauchy Criterion 99
3.5.3 Absolute Convergence 100
3.6 Tests for Convergence 104
3.6.1 Trivial Test 104
3.6.2 Direct Comparison Tests 105
3.6.3 Limit Comparison Tests 107
3.6.4 Ratio Comparison Test 108
3.6.5 d’Alembert’s Ratio Test 109
3.6.6 Cauchy’s Root Test 111
3.6.7 Cauchy’s Condensation Test 112
3.6.8 Integral Test 114
3.6.9 Kummer’s Tests 115
3.6.10 Raabe’s Ratio Test 118
3.6.11 Gauss’s Ratio Test 118
3.6.12 Alternating Series Test 121
3.6.13 Dirichlet’s Test 122
3.6.14 Abel’s Test 123
3.7 Rearrangements 129
3.7.1 Unconditional Convergence 130
3.7.2 Conditional Convergence 131
3.7.3 Comparison of
∞
i=1
a
i
and
i∈IN
a
i
133
3.8 Products of Series 135
3.8.1 Products of Absolutely Convergent Series 138
3.8.2 Products of Nonabsolutely Convergent Series 139
3.9 Summability Methods 141
3.9.1 Ces`aro’s Method 142
3.9.2 Abel’s Method 144
3.10 More on Infinite Sums 148
v
3.11 Infinite Products 150
3.12 Challenging Problems for Chapter 3 154
4 SETS OF REAL NUMBERS 158
4.1 Introduction 158
4.2 Points 159
4.2.1 Interior Points 159
4.2.2 Isolated Points 161
4.2.3 Points of Accumulation 161
4.2.4 Boundary Points 162
4.3 Sets 165
4.3.1 Closed Sets 166
4.3.2 Open Sets 167
4.4 Elementary Topology 173
4.5 Compactness Arguments 176
4.5.1 Bolzano-Weierstrass Property 178
4.5.2 Cantor’s Intersection Property 179
4.5.3 Cousin’s Property 181
4.5.4 Heine-Borel Property 182
4.5.5 Compact Sets 186
4.6 Countable Sets 189
4.7 Challenging Problems for Chapter 4 190
5 CONTINUOUS FUNCTIONS 193
5.1 Introduction to Limits 193
5.1.1 Limits (ε-δ Definition) 193
5.1.2 Limits (Sequential Definition) 197
5.1.3 Limits (Mapping Definition) 200
5.1.4 One-Sided Limits 201
5.1.5 Infinite Limits 203
5.2 Properties of Limits 204
5.2.1 Uniqueness of Limits 205
5.2.2 Boundedness of Limits 205
5.2.3 Algebra of Limits 207
5.2.4 Order Properties 210
5.2.5 Composition of Functions 213
5.2.6 Examples 215
5.3 Limits Superior and Inferior 222
5.4 Continuity 223
5.4.1 How to Define Continuity 223
5.4.2 Continuity at a Point 227
剩余751页未读,继续阅读
micropuss6
- 粉丝: 0
- 资源: 1
上传资源 快速赚钱
- 我的内容管理 收起
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
会员权益专享
最新资源
- RTL8188FU-Linux-v5.7.4.2-36687.20200602.tar(20765).gz
- c++校园超市商品信息管理系统课程设计说明书(含源代码) (2).pdf
- 建筑供配电系统相关课件.pptx
- 企业管理规章制度及管理模式.doc
- vb打开摄像头.doc
- 云计算-可信计算中认证协议改进方案.pdf
- [详细完整版]单片机编程4.ppt
- c语言常用算法.pdf
- c++经典程序代码大全.pdf
- 单片机数字时钟资料.doc
- 11项目管理前沿1.0.pptx
- 基于ssm的“魅力”繁峙宣传网站的设计与实现论文.doc
- 智慧交通综合解决方案.pptx
- 建筑防潮设计-PowerPointPresentati.pptx
- SPC统计过程控制程序.pptx
- SPC统计方法基础知识.pptx
资源上传下载、课程学习等过程中有任何疑问或建议,欢迎提出宝贵意见哦~我们会及时处理!
点击此处反馈
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功
评论1