网站首页  软件下载  游戏下载  翻译软件  电子书下载  电影下载  电视剧下载  教程攻略

请输入您要查询的图书:

 

书名 分析方法(修订版)
分类 科学技术-自然科学-数学
作者 (美)斯特里沙兹
出版社 世界图书出版公司
下载
简介
编辑推荐

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。本书则向你阐述了有关其分析方法。主要内容包括实数体系结构;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;隐函数等。

目录

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

随便看

 

霍普软件下载网电子书栏目提供海量电子书在线免费阅读及下载。

 

Copyright © 2002-2024 101bt.net All Rights Reserved
更新时间:2025/6/14 4:06:44