新書推薦：
《
“十五五”与2035中国
》
售價：HK$
74.8
《
被杀死的真理子 尸人庄谜案 作者今村昌弘全新青春冒险小说
》
售價：HK$
61.6
《
智能超越 AI浪潮下的全球涌动与中国破局
》
售價：HK$
75.9
《
忌物堂诡谈
》
售價：HK$
49.5
《
大学问·太平天国的文献和历史：海外新文献刊布和文献史事研究
》
售價：HK$
118.8
《
汗青堂丛书158：唐朝的灭亡与欧亚东部 藩镇体制的通史性研究
》
售價：HK$
77.0
《
真菌的秘密生活
》
售價：HK$
63.8
《
财之道丛书·资本主义的终结：经济增长与气候变化的悖论
》
售價：HK$
74.8
|
| 內容簡介： |
The present book strives for clarity and transparency. Right
來源：香港大書城megBookStore,http://www.megbook.com.hk
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.
|
| 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
|
|
購物車/收銀台(0) | 在線留言板
| 付款方式
| 運費計算
| 聯絡我們
| 幫助中心 |
加入書簽
HOME
新書上架
