分析

分析

(德) 阿莫恩 (Amann,H.) , 著

出版社:世界图书出版公司北京公司

年代:2012

定价:89.0

书籍简介:

这是一部三卷集的分析学习入门书籍,本书是第一卷。由于其在表述上的清晰性和现代特色,使得本书在众多同类图书中获得比较高的认可度,尤其是在基本概念讲述方面使得本书更胜一筹。本书在多变量和单变量的讲述方面浑然一体,没有进行刻意区分,重点强调了拓扑的基本知识,并将复分析基本观点也包括在里面。本书是学习分析基础教程的学生和老师的宝典。书中众多的例子,练习和补充材料使得本书也可以作为自学材料以及更高级学习的准备,也是物理和数学研究的基础。

书籍目录:

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

内容摘要:

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.

书籍规格:

书籍详细信息
书名分析站内查询相似图书
9787510048005
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出版地北京出版单位世界图书出版公司北京公司
版次影印本印次1
定价(元)89.0语种英文
尺寸26 × 19装帧平装
页数 440 印数

书籍信息归属:

分析是世界图书出版公司北京公司于2012.6出版的中图分类号为 O17 的主题关于 分析(数学)-英文 的书籍。