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

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

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

内页插图

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] epub pdf mobi txt 电子书 下载 2025

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

评分☆☆☆☆☆

Hilbert space（希尔伯特空间）的定义是一个complete的inner product space。LZ所说的空间是l^2，只是一种Hilbert空间的例子。

评分☆☆☆☆☆

开笔此书前，我曾列过一个写作计划。按人名顺序一个接一个去罗列—他们都是些浪荡江湖，和我的人生轨迹曾交叉重叠的老友们。 　　当时，我坐在一辆咣当咣当的绿皮火车里，天色微亮，周遭是不同省份的呼噜声。我找了个本子，塞着耳机一边听歌一边写……活着的、死了的、不知不觉写满了七八页纸。我吓了一跳，怎么这么多的素材？不过十年，故事却多得堆积如山，这哪里是一本书能够写的完的。 　　头有点儿大，不知该如何取舍，于是索性随手圈了几个老友的人名。反正写谁都是写，就像一大串美味的葡萄，随手摘下的，都是一粒粒饱满的甜。随手圈下的名单，是为此书篇章构成之由来。圈完后一抬头，车窗外没有起伏，亦没有乔木，已是一马平川的华北平原。 　　书的创作过程中，我慢慢梳理出了一些东西，隐约发现自己将推展开的世界，于已经习惯了单一幸福感获取途径的人们而言，那是另一种幸福感。 　　那是一些值得我们去认可、寻觅的幸福感。他们或许是陌生的，但发着光。在我的认知中，一个成熟健全的当代文明社会，理应尊重多元的个体价值观，理应尊重个体幸福感获得方式。这种尊重，应该建立在了解的基础之上，鉴于国人文化传统里对陌生事物的天然抵触因子，“如何去了解”这几个字愈发重要。 　　那么，亲爱的们，我该如何去让你了解那些多元而又陌生的幸福感呢？ 　　写书时，恰逢山东大学抬爱，让我有缘受聘于山东大学儒学高等研究院，于是趁机做了一场名为《亚文化下成长方式的田野调查》的报告讲座。 　　那天会场塞满了人，场面出乎意料的火爆，来的大都是85 后和90后。我讲的就是这份名单：大军、路平、月月、白玛央宗……我和他们的共同生活就是一场田野调查。我没用太学术的语言词汇去贯穿讲座，但讲了许多细节的故事， 那天的叙述方式，是为本书行文的基调。 　　卡尔维诺说：“要把地面上的人看清楚，就要和地面保持距离”。这句话给我带来一个意像：一个穿西服打领带的人，手足并用爬在树上，和大部分同类保持着恰当的距离。他晃荡着腿，骑在自我设定的叛逆里，心无挂碍，乐在其中。偶尔低头看看周遭过客，偶尔抬头，漫天星斗。 　　我期待出到第十本书的时候，也能爬上这样一棵树。 　　当下是我第一本书，芹献诸君后，若价值观和您不重叠、行文有不得人心处，请姑念初犯…… 　　我下次不会改的。 　　等我爬上树了再说。 　　我不敢说这本书写得有多好多好，也懒得妄自菲薄，只知过程中三易其稿，惹得责编戴克莎小姐几度差点儿忿极而泣。如此这般折腾，仅为本色二字：讲故事人的本色，故事中人们的本色。 　　或许，打磨出本色的过程，也是爬树的过程吧。 　　文至笔端心意浅，话到唇畔易虚言，且洒莲实二三子，自有方家识真颜。 　　这本书完稿后，我背起吉他，从北到南，用一个月的时间挨个去探望了书中的老友们，除了那个不用手机的女孩，其他的人我几乎见了一个遍。

评分☆☆☆☆☆

没有想象中的好，而且太薄了

评分☆☆☆☆☆

评分☆☆☆☆☆

Hilbert space（希尔伯特空间）的定义是一个complete的inner product space。LZ所说的空间是l^2，只是一种Hilbert空间的例子。

评分☆☆☆☆☆

拓扑结构的基本概念如连通性、密实度和介绍了homeomorphisms早期使用作为一个基础,证明将远不及优雅的(和不直接)否则。例如,介值定理,证明了结果的连接的一个空间。一旦这是结果确定下来的普遍性,它讨论了R。　　

评分☆☆☆☆☆

这种方法最初要求更多的读者和他的抽象能力,但在评审者的意见,是绝对的最好方法主体。我真的不知道什么是真正的初学者在数学也能想出来但替代方法是定义事物反复在越来越通用上下文最分析文本做。

评分☆☆☆☆☆

Hilbert space（希尔伯特空间）的定义是一个complete的inner product space。LZ所说的空间是l^2，只是一种Hilbert空间的例子。

评分☆☆☆☆☆

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。

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