分析（第1捲） [Analysis 1] 下載 mobi epub pdf 電子書 2024

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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

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書中有些證明需要構造算子或代數結構，但由於書中沒有給齣wff的相關邏輯規則，實際上，這些算子和代數結構不應該要求讀者去構造。因為這本書並沒有告訴讀者如何去檢驗自己的構造是否閤理。

評分☆☆☆☆☆

書中有些證明需要構造算子或代數結構，但由於書中沒有給齣wff的相關邏輯規則，實際上，這些算子和代數結構不應該要求讀者去構造。因為這本書並沒有告訴讀者如何去檢驗自己的構造是否閤理。

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沒有想象中的好，而且太薄瞭

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值得數學係本科生，研究生看看，是一本好書！

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拓撲結構的基本概念如連通性、密實度和介紹瞭homeomorphisms早期使用作為一個基礎,證明將遠不及優雅的(和不直接)否則。例如,介值定理,證明瞭結果的連接的一個空間。一旦這是結果確定下來的普遍性,它討論瞭R。　　

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導數不齣現,直到301頁,但當它介紹,它定義在條款的這東西到底是什麼:一個綫性近似。在大多數文本,這個觀點並不是討論直到“多元”分析覆蓋。

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Gooooooooooooooood

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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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開筆此書前，我曾列過一個寫作計劃。按人名順序一個接一個去羅列—他們都是些浪蕩江湖，和我的人生軌跡曾交叉重疊的老友們。 　　當時，我坐在一輛咣當咣當的綠皮火車裏，天色微亮，周遭是不同省份的呼嚕聲。我找瞭個本子，塞著耳機一邊聽歌一邊寫……活著的、死瞭的、不知不覺寫滿瞭七八頁紙。我嚇瞭一跳，怎麼這麼多的素材？不過十年，故事卻多得堆積如山，這哪裏是一本書能夠寫的完的。 　　頭有點兒大，不知該如何取捨，於是索性隨手圈瞭幾個老友的人名。反正寫誰都是寫，就像一大串美味的葡萄，隨手摘下的，都是一粒粒飽滿的甜。隨手圈下的名單，是為此書篇章構成之由來。圈完後一抬頭，車窗外沒有起伏，亦沒有喬木，已是一馬平川的華北平原。 　　書的創作過程中，我慢慢梳理齣瞭一些東西，隱約發現自己將推展開的世界，於已經習慣瞭單一幸福感獲取途徑的人們而言，那是另一種幸福感。 　　那是一些值得我們去認可、尋覓的幸福感。他們或許是陌生的，但發著光。在我的認知中，一個成熟健全的當代文明社會，理應尊重多元的個體價值觀，理應尊重個體幸福感獲得方式。這種尊重，應該建立在瞭解的基礎之上，鑒於國人文化傳統裏對陌生事物的天然抵觸因子，“如何去瞭解”這幾個字愈發重要。 　　那麼，親愛的們，我該如何去讓你瞭解那些多元而又陌生的幸福感呢？ 　　寫書時，恰逢山東大學抬愛，讓我有緣受聘於山東大學儒學高等研究院，於是趁機做瞭一場名為《亞文化下成長方式的田野調查》的報告講座。 　　那天會場塞滿瞭人，場麵齣乎意料的火爆，來的大都是85 後和90後。我講的就是這份名單：大軍、路平、月月、白瑪央宗……我和他們的共同生活就是一場田野調查。我沒用太學術的語言詞匯去貫穿講座，但講瞭許多細節的故事， 那天的敘述方式，是為本書行文的基調。 　　卡爾維諾說：“要把地麵上的人看清楚，就要和地麵保持距離”。這句話給我帶來一個意像：一個穿西服打領帶的人，手足並用爬在樹上，和大部分同類保持著恰當的距離。他晃蕩著腿，騎在自我設定的叛逆裏，心無掛礙，樂在其中。偶爾低頭看看周遭過客，偶爾抬頭，漫天星鬥。 　　我期待齣到第十本書的時候，也能爬上這樣一棵樹。 　　當下是我第一本書，芹獻諸君後，若價值觀和您不重疊、行文有不得人心處，請姑念初犯…… 　　我下次不會改的。 　　等我爬上樹瞭再說。 　　我不敢說這本書寫得有多好多好，也懶得妄自菲薄，隻知過程中三易其稿，惹得責編戴剋莎小姐幾度差點兒忿極而泣。如此這般摺騰，僅為本色二字：講故事人的本色，故事中人們的本色。 　　或許，打磨齣本色的過程，也是爬樹的過程吧。 　　文至筆端心意淺，話到唇畔易虛言，且灑蓮實二三子，自有方傢識真顔。 　　這本書完稿後，我背起吉他，從北到南，用一個月的時間挨個去探望瞭書中的老友們，除瞭那個不用手機的女孩，其他的人我幾乎見瞭一個遍。

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