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

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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发表于2024-11-22

商品介绍



出版社: 世界图书出版公司
ISBN:9787510048005
版次:1
商品编码:11154487
包装:平装
外文名称:Analysis 1
开本:16开
出版时间:2012-09-01
用纸:胶版纸
页数:426
正文语种:英文

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书籍描述

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

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

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

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

评分

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.

评分

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.

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。

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)。

评分

没有想象中的好,而且太薄了

评分

人都是有局限性的,「提升自我」这件事不只是技能上的提升,更核心的是视野、理念、思维方式这些意识世界里的东西。「读史使人明智,读诗使人灵秀,数学使人周密,科学使人深刻,伦理学使人庄重,逻辑修辞之学使人善辩:凡有所学,皆成性格。」第

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。

评分

Gooooooooooooooood

评分

不错的东西。。。。。。。。。。。。。

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

类似图书 点击查看全场最低价

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