分析（第1卷） [Analysis 1] 下载 mobi epub pdf 电子书 2025

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内容简介

　　The present book strives for clarity and transparency. Right from the begin-ning， it requires from the reader a willingness to deal with abstract concepts， as well as a considerable measure of self-initiative. For these e&，rts， the reader will be richly rewarded in his or her mathematical thinking abilities， and will possess the foundation needed for a deeper penetration into mathematics and its applications.
　　This book is the first volume of a three volume introduction to analysis. It de- veloped from. courses that the authors have taught over the last twenty six years at the Universities of Bochum， Kiel， Zurich， Basel and Kassel. Since we hope that this book will be used also for self-study and supplementary reading， we have included far more material than can be covered in a three semester sequence. This allows us to provide a wide overview of the subject and to present the many beautiful and important applications of the theory. We also demonstrate that mathematics possesses， not only elegance and inner beauty， but also provides efficient methods for the solution of concrete problems.

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目录

Preface
Chapter Ⅰ Foundations
1 Fundamentals of Logic
2 Sets
Elementary Facts
The Power Set
Complement, Intersection and Union
Products
Families of Sets
3 Functions，
Simple Examples
Composition of Functions
Commutative Diagrams
Injections, Surjections and Bijections
Inverse Functions
Set Valued Functions
4 Relations and Operations
Equivalence Relations
Order Relations
Operations
5 The Natural Numbers
The Peano Axioms
The Arithmetic of Natural Numbers
The Division Algorithm
The Induction Principle
Recursive Definitions
6 Countability
Permutations
Equinumerous Sets
Countable Sets
Infinite Products
7 Groups and Homomorphisms
Groups
Subgroups
Cosets
Homomorphisms
Isomorphisms
8 R.ings, Fields and Polynomials
Rings
The Binomial Theorem
The Multinomial Theorem
Fields
Ordered Fields
Formal Power Series
Polynomials
Polynomial Functions
Division of Polynomiajs
Linear Factors
Polynomials in Several Indeterminates
9 The Rational Numbers
The Integers
The Rational Numbers
Rational Zeros of Polynomials
Square Roots
10 The Real Numbers
Order Completeness
Dedekind's Construction of the Real Numbers
The Natural Order on R
The Extended Number Line
A Characterization of Supremum and Infimum
The Archimedean Property
The Density of the Rational Numbers in R
nth Roots
The Density of the Irrational Numbers in R
Intervals
Chapter Ⅱ Convergence
Chapter Ⅲ Continuous Functions
Chapter Ⅳ Differentiation in One Variable
Chapter Ⅴ Sequences of Functions
Appendix Introduction to Mathematical Logic
Bibliography
Index

前言/序言

　　Logical thinking， the analysis of complex relationships， the recognition of under- lying simple structures which are common to a multitude of problems - these are the skills which are needed to do mathematics， and their development is the main goal of mathematics education.
　　Of course， these skills cannot be learned 'in a vacuum'. Only a continuous struggle with concrete problems and a striving for deep understanding leads to success. A good measure of abstraction is needed to allow one to concentrate on the essential， without being distracted by appearances and irrelevancies.
　　The present book strives for clarity and transparency. Right from the begin-ning， it requires from the reader a willingness to deal with abstract concepts， as well as a considerable measure of self-initiative. For these e&，rts， the reader will be richly rewarded in his or her mathematical thinking abilities， and will possess the foundation needed for a deeper penetration into mathematics and its applications.
　　This book is the first volume of a three volume introduction to analysis. It de- veloped from. courses that the authors have taught over the last twenty six years at the Universities of Bochum， Kiel， Zurich， Basel and Kassel. Since we hope that this book will be used also for self-study and supplementary reading， we have included far more material than can be covered in a three semester sequence. This allows us to provide a wide overview of the subject and to present the many beautiful and important applications of the theory. We also demonstrate that mathematics possesses， not only elegance and inner beauty， but also provides efficient methods for the solution of concrete problems.
　　Analysis itself begins in Chapter II. In the first chapter we discuss qLute thor- oughly the construction of number systems and present the fundamentals of linear algebra. This chapter is particularly suited for self-study and provides practice in the logical deduction of theorems from simple hypotheses. Here， the key is to focus on the essential in a given situation， and to avoid making unjustified assumptions.An experienced instructor can easily choose suitable material from this chapter to make up a course， or can use this foundational material as its need arises in the study of later sections.
　　……

分析（第1卷） [Analysis 1] 下载 mobi epub pdf txt 电子书 格式

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l^2里面既然是实数数列，其定义便是从N到R的函数，怎么可以是有限呢？否则这函数就不是well-defined的了。

评分☆☆☆☆☆

这本书覆盖了从入门机械制图工程师/技师所必需知道的关于产业的知识。书中还覆盖了所必需的进阶知识。 《实分析教程(第2版)(英文影印版)》是一部备受专家好评的教科书，书中用现代的方式清晰论述了实分析的概念与理论，定理证明简明易懂，可读性强。在第一版的基础上做了全面修订，有200道例题，练习题由原来的1200道增加到1300习题。本书的写法像一部文学读物，这在数学教科书很少见，因此阅读本书会是一种享受。

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满意满意满意满意满意满意满意满意满意满意

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书中有些证明需要构造算子或代数结构，但由于书中没有给出wff的相关逻辑规则，实际上，这些算子和代数结构不应该要求读者去构造。因为这本书并没有告诉读者如何去检验自己的构造是否合理。

评分☆☆☆☆☆

注意Hilbert space一定是Banach space，而Hilbert space 和 Banach space都是特殊的topological vector space。的确，所以老一点的书都直接定义Hilbert space是l^2，因为那时都假设有一个可数的orthonormal basis。看谢惠民吧，那个什么多维骑还是放一边。不过答案只有提示，很多答案可以在薛春华中找我看一本数学书大概三百页厚，半个月看不完啊，一天也就看两三页，看得时间也不多，就两三个钟，还消化不良，有时候想赶快看越快看越学得少与不懂。你们都是怎么看书的，来跟大家分享下吧!

评分☆☆☆☆☆

这本书覆盖了从入门机械制图工程师/技师所必需知道的关于产业的知识。书中还覆盖了所必需的进阶知识。 《实分析教程(第2版)(英文影印版)》是一部备受专家好评的教科书，书中用现代的方式清晰论述了实分析的概念与理论，定理证明简明易懂，可读性强。在第一版的基础上做了全面修订，有200道例题，练习题由原来的1200道增加到1300习题。本书的写法像一部文学读物，这在数学教科书很少见，因此阅读本书会是一种享受。

评分☆☆☆☆☆

注意Hilbert space一定是Banach space，而Hilbert space 和 Banach space都是特殊的topological vector space。的确，所以老一点的书都直接定义Hilbert space是l^2，因为那时都假设有一个可数的orthonormal basis。看谢惠民吧，那个什么多维骑还是放一边。不过答案只有提示，很多答案可以在薛春华中找我看一本数学书大概三百页厚，半个月看不完啊，一天也就看两三页，看得时间也不多，就两三个钟，还消化不良，有时候想赶快看越快看越学得少与不懂。你们都是怎么看书的，来跟大家分享下吧!

评分☆☆☆☆☆

作者的典型风格,因为他们承认在他们的前言,是定义数学对象和概念在最一般的方式。他们,然后通过这些定义的后果。考虑一个特定的例子,这种方法,社区的定义提出了三世的连续性。1,一个函数(定义度量空间之间)是连续在x如果每个社区V f(x)存在一个这样的社区你x f(U)包含在诉随后,证明这是相当于两个传统的ε三角洲定义和连续性的情况定义在条款的收敛序列。作者也表明连续性所以定义也同样适用于一个赋范矢量空间(因为每个赋范矢量空间也是一个度量空间)。

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比如我们10岁以前，阿拉丁神灯这一类儿童书籍能够打动我们，也能够让我们开始学着认识这个世界。然而当我们长大一些之后，能够打动我们或者对我们有巨大帮助的书籍，会变化。所以第一个建议是：根据自己当前的人生阶段、认知水平来思考自己应该看哪一类书，比如说初入职场的人，去学习具体的工作技能（如Excel的使用）会比研读管理学理论要更为有益，因为对于这个阶段的你来说，技能性的东西可以现学现练，很快就能把书里的东西转化为自己能力的一部分。

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