分析（第1捲） [Analysis 1] 下載 mobi epub pdf 電子書 2025

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內容簡介

　　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.

內頁插圖

目錄

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捲） [Analysis 1] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

沒有想象中的好，而且太薄瞭

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比如我們10歲以前，阿拉丁神燈這一類兒童書籍能夠打動我們，也能夠讓我們開始學著認識這個世界。然而當我們長大一些之後，能夠打動我們或者對我們有巨大幫助的書籍，會變化。所以第一個建議是：根據自己當前的人生階段、認知水平來思考自己應該看哪一類書，比如說初入職場的人，去學習具體的工作技能（如Excel的使用）會比研讀管理學理論要更為有益，因為對於這個階段的你來說，技能性的東西可以現學現練，很快就能把書裏的東西轉化為自己能力的一部分。

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Hilbert space當然可以是有限維的，但是有限維的不很好玩。以為哪怕隻是一個topological vector space (over C or R) （就是一個嚮量空間和一個拓撲，而這個拓撲使得嚮量空間上的兩種運算連續），如果是有限維，那也和C^n或R^n是一樣的。（homeomorphic)

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二、書有很多分類，不要局限於某一類，尤其是不要耽溺於通俗小說

評分☆☆☆☆☆

沒有想象中的好，而且太薄瞭

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　　 讀者對象：數學及相關專業的大學高年級學生和研究生。

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書中的很多對於産業介紹和機械製圖方麵的知識很完整，很係統。但是某些部分關於計算機配置的部分稍微落後。同時，部分機械草圖有些小錯誤。但是，基本上對於想挑戰自己的機械製圖的工程師們來說，是很好的sample.

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Hilbert space（希爾伯特空間）的定義是一個complete的inner product space。LZ所說的空間是l^2，隻是一種Hilbert空間的例子。

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