数学分析(英文版第2版)(经典原版书库)
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品牌: 〔美〕阿波斯托尔
基本信息·出版社：机械工业出版社
·页码：493 页
·出版日期：2004年
·ISBN：7111146891
·条形码：9787111146896
·包装版本：第1版
·装帧：平装
·开本：16开
·丛书名：经典原版书库
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内容简介《数学分析》(英文版第2版)是一部现代数学名著。自20世纪70年代面世以来，一直受到西方学术界、教育界的广泛推崇，被许多知名大学指定为教材。相比于同类书籍，它的特点在于：选取的论据更适子教学使用。论证详尽，可读性更强。习题丰富，覆盖各个方面、各级难度。可根据教学需要选用不同章节。
作者简介Tom M. Apostol是加州理工学院数学系荣誉教授。他于1946年在华盛顿大学西雅图分校获得数学硕士学位，于1948年在加州大学伯克利分校获得数学博士学位。他的著述很多，除本书外，还著有《Calculus,Multi-Variable Calculus and Algebra with Applications》、《Calculus,One-Variable Calculus with an Introduction to Linear Algebra》等。
目录
Chapter 1 The Real and Complex Number Systems
1.1 Introduction
1.2 The field axioms
1.3 The order axioms
1.4 Geometric representation of real numbers
1.5 Intervals
1.6 Integers
1.7 The unique factorization of real numbers
1.8 Rational numbers
1.9 Irrational numbers
1.10 Upper bounds ,maximum element,least upper bound
1.11 The completeness axiom
1.12 Some properties of the supremum
1.13 Properties of the integers deduced from the completeness axiom
1.14 the Archimedean property of the real-number systen
1.15 Rational numbers with finite decimal representation
1.16 Finite decimal approximations to real numbers
1.17 Infinite decimal representation of the real-numbers
1.18 Absolute values and the triangle inequality
1.19 The Cauchy-Schwarz inequality
1.20 Plus and minus infinity and the extended real number system R*
1.21 Compex numbers
1.22 geometric representation of complex numbers
1.23 The imaginary unit
1.24 Absolute value of a complex number
1.25 Impossinbility of ordering the complex numbers
1.26 Complex exponentials
1.27 Further properties of complex exponentials
1.28 The argument of a complex number
1.29 Integral powers and roots of complex numbers
1.30 Complex logarithms
1.31 Complex powers
1.32 Complex sines and cosines
1.33 Infinity and the extended complex plane C*
Exercises
Chapter 2 Some Basic Notions of Set Theory
Chapter 3 elements of Point Set topology
Chapter 4 Limits and Continuity
Chapter 5 Derivatives
Chapter 6 Functions of bounded Variation and Rectifiable Curves
Chapter 7 The Riemann-Stieltjes Integral
Chapter 8 Infinite Series and Infinite Products
Chapter 9 Sequences of Functions
Chapter 10 The Lebesgu Integral
Chapter 11 Fourier Series and fourier Integrals
Chapter 12 Multivariable Differential Calculus
Chapter 13 Implicit Functions and Extremum Problems
Chapter 14 Multiple Riemann Integrals
Chapter 15 Multiple Lebesgue Integrals
Chapter 16 Cauchy's Theorem and the Residue Calculus
Index of Special Symbols
Index
……[看更多目录]