分析方法 修订版
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作者： （美）斯特里沙兹著
出 版 社： 世界图书出版公司
出版时间： 2010-4-1字数：版次： 1页数： 739印刷时间： 2010-4-1开本： 24开印次： 1纸张： 胶版纸I S B N ： 9787510005565包装： 平装
数学主要讲述思想的方法，深入理解数学比掌握一大堆的定理、定义、问题和技术显得更为重要。理论和定义共同作用，本书在介绍实分析的时候结合详尽、广泛的阐释，使得读者完全理解分析基础和方法。目次：基础；实数体系结构；实线拓扑；连续函数；微分学；积分学；序列和函数级数；超函数；欧拉空间和矩阵空间；欧拉空间上的微分计算；常微分方程；傅里叶级数；隐函数、曲线和曲面；勒贝格积分；多重积分。
读者对象：数学专业的研究生以及相关的科研人员。
Preface
1 Preliminaries
1.1 The Logic of Quantifiers
1.2 Infinite Sets
1.3 Proofs
1.4 The Rational Number System
1.5 The Axiom of Choice*
2 Construction of the Real Number System
2.1 Cauchy Sequences
2.2 The Reals as an Ordered Field
2.3 Limits and Completeness
2.4 Other Versions and Visions
2.5 Summary
3 Topology of the Real Line
3.1 The Theory of Limits
3.2 Open Sets and Closed Sets
3.3 Compact Sets
3.4 Summary
4 Continuous Functions
4.1 Concepts of Continuity
5 Differential Calculus
5.1 Concepts of the Derivative
5.2 Properties of the Derivative
5.3 The Calculus of Derivatives
5.4 Higher Derivatives and Taylor's Theorem
5.5 Summary
6 Integral Calculus
6.1 Integrals of Continuous Functions
6.2 The Riemann Integral
6.3 Improper Integrals*
6.4 Summary
7 Sequences and Series of Functions
7.1 Complex Numbers
7.2 Numerical Series and Sequences
7.3 Uniform Convergence
7.4 Power Series
7.5 Approximation by Polynomials
7.6 Equicontinuity
7.7 Summary
8 Transcendental Functions
8.1 The Exponential and Logarithm
8.2 Trigonometric Functions
8.3 Summary
9 Euclidean Space and Metric Spaces
9.1 Structures on Euclidean Space
9.2 Topology of Metric Spaces
9.3 Continuous Functions on Metric Spaces
9.4 Summary
10 Differential Calculus in Euclidean Space
10.1 The Differential
10.2 Higher Derivatives
10.3 Summary
11 Ordinary Differential Equations
11.1 Existence and Uniqueness
11.2 Other Methods of Solution*
11.3 Vector Fields and Flows*
11.4 Summary
12 Fourier Series
12.1 Origins of Fourier Series
12.2 Convergence of Fourier Series
12.3 Summary
13 Implicit Functions, Curves, and Surfaces
13.1 The Implicit Function Theorem
13.2 Curves and Surfaces
13.3 Maxima and Minima on Surfaces
13.4 Arc Length
13.5 Summary
14 The Lebesgue Integral
14.1 The Concept of Measure
14.2 Proof of Existence of Measures*
14.3 The Integral
14.4 The Lebesgue Spaces L1 and L2
14.5 Summary
15 Multiple Integrals
15.1 Interchange of Integrals
15.2 Change of Variable in Multiple Integrals
15.3 Summary
Index
