分析方法(修订版)(英文版)
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浙江嘉兴
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作者RobertS.Strichartz（R.S.斯特里查兹，美国）
出版社世界图书出版公司
ISBN9787519248659
出版时间2018-11
装帧其他
开本16开
定价139元
货号30317045
上书时间2024-10-29
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目录
Preface
1 Preliminaries
1.1 The Logic cf Quantifiers
1.1.1 Rules of Quantifiers
1.1.2 Examples
1.1.3 Exercises
1.2 Infinite Sets
1.2.1 Countable Sets
1.2.2 Uncountable Sets
1.2.3 Exexcises
1.3 Proofs
1.3.1 How to Discover Proofs
1.3.2 How to Understand Proofs
1.4 The Rational Number System
1.5 The Axiom of Choice*
2 Construction of the Real Number System
2.1 Cauchy Sequences
2.1.1 Motivation
2.1.2 The Definition
2.1.3 Exercises
2.2 The Reals as an Ordered Field
2.2.1 Defining Arithmetic
2.2.2 The Field Axioms
2.2.3 Order
2.2.4 Exercises
2.3 Limits and Completeness
2.3.1 Proof of Completeness
2.3.2 Square Roots
2.3.3 Exercises
2.4 Other Versions and Visions
2.4.1 Infinite Decimal Expansions
2.4.2 Dedekind Cuts*
2.4.3 Non-Standard Analysis*
2.4.4 Constructive Analysis*
2.4.5 Exercises
2.5 Summary
3 Topology of the Real Line
3.1 The Theory of Limits
3.1.1 Limits, Sups, and Infs
3.1.2 Limit Points
3.1.3 Exercises
3.2 Open Sets and Closed Sets
3.2.1 Open Sets
3.2.2 Closed Sets
3.2.3 Exercises
3.3 Compact Sets
3.3.1 Exercises
3.4 Summary
4 Continuous Functions
4.1 Concepts of Continuity
内容摘要
数学主要讲述思想方法的学科，深入理解数学比掌握一大堆的定理、定义、问题和技术显得更为重要
。本书介绍分析方法，结合详尽、广泛的阐述，便于读者深入理解分析内涵和基本方法。
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