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

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

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

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

評分☆☆☆☆☆

一、不同人生階段、不同認知水平對應的“有效讀書”標準不一樣

評分☆☆☆☆☆

這本書覆蓋瞭從入門機械製圖工程師/技師所必需知道的關於産業的知識。書中還覆蓋瞭所必需的進階知識。 《實分析教程(第2版)(英文影印版)》是一部備受專傢好評的教科書，書中用現代的方式清晰論述瞭實分析的概念與理論，定理證明簡明易懂，可讀性強。在第一版的基礎上做瞭全麵修訂，有200道例題，練習題由原來的1200道增加到1300習題。本書的寫法像一部文學讀物，這在數學教科書很少見，因此閱讀本書會是一種享受。

評分☆☆☆☆☆

沒有想象中的好，而且太薄瞭

評分☆☆☆☆☆

一、不同人生階段、不同認知水平對應的“有效讀書”標準不一樣

評分☆☆☆☆☆

沒有想象中的好，而且太薄瞭

評分☆☆☆☆☆

　　 讀者對象：數學及相關專業的大學高年級學生和研究生。

評分☆☆☆☆☆

值得數學係本科生，研究生看看，是一本好書！

評分☆☆☆☆☆

總的來說,它們的證明簡潔和邏輯但需要一些耐心跟隨。當做齣一個論點,作者經常引用前題一個b。c和定理x y。沒有顯式地聲明校長z,他們正在使用,即使它可能有一個名字。因此,作為一個讀者,你要麼必須願意遵循麵包屑他們提供或確保你明白為什麼他們的論證工作。這真的不是一個批評,隻是一個觀察。因為這個原因雖然,如果你打算買捲的工作,您N必須買捲N - 1。在每一捲,作者承認的序言中,他們的是太多的材料覆蓋在一個學期;事實上,至少有足夠的材料在每個捲為一個學年工作的價值。

評分☆☆☆☆☆

l^2裏麵既然是實數數列，其定義便是從N到R的函數，怎麼可以是有限呢？否則這函數就不是well-defined的瞭。

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