分析（第1卷） [Analysis 1] epub pdf mobi txt 电子书 下载 2024

分析（第1卷） [Analysis 1] epub pdf mobi txt 电子书 下载 2024

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分析（第1卷） [Analysis 1] epub pdf mobi txt 电子书 下载 2024

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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 2024

分析（第1卷） [Analysis 1] 下载 epub mobi pdf txt 电子书 2024

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二、书有很多分类，不要局限于某一类，尤其是不要耽溺于通俗小说

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总的来说,它们的证明简洁和逻辑但需要一些耐心跟随。当做出一个论点,作者经常引用前题一个b。c和定理x y。没有显式地声明校长z,他们正在使用,即使它可能有一个名字。因此,作为一个读者,你要么必须愿意遵循面包屑他们提供或确保你明白为什么他们的论证工作。这真的不是一个批评,只是一个观察。因为这个原因虽然,如果你打算买卷的工作,您N必须买卷N - 1。在每一卷,作者承认的序言中,他们的是太多的材料覆盖在一个学期;事实上,至少有足够的材料在每个卷为一个学年工作的价值。

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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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　　 读者对象：数学及相关专业的大学高年级学生和研究生。

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没有想象中的好，而且太薄了

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书中的很多对于产业介绍和机械制图方面的知识很完整，很系统。但是某些部分关于计算机配置的部分稍微落后。同时，部分机械草图有些小错误。但是，基本上对于想挑战自己的机械制图的工程师们来说，是很好的sample.

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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。

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