高等微积分（英文影印版）
原书名：Advanced Calculus: A Course in Mathematical Analysis
- 作者：Patrick M. Fitzpatrick
- 译者：
- 版次：2
- ISBN：9787111193494
- 出版时间：2006-07
- 出版社：机械工业出版社
- 定价：￥76.00 元
图书简介
数学分析已经根植于自然科学和社会科学的各个学科分支之中。微积分作为数学分析的基础，不仅要为全部数学方法和算法工具提供方法论，同时还要为人们灌输逻辑思维的方法。本书在实现这一目标中取得了引人注目的成果，读者从中不仅可以获得微积分的知识，还会受到数学科学思维的训练。
本书一方面按传统的和严格的演绎形式介绍微积分的所有主题，另一方面强调主题的相关性和统一性，从整体的、系统的高度来组织材料。书中以最清晰、最简洁的方式介绍了数学分析的基本概念，除了包含必不可少的论题 (如实数、收敛序列、连续函数与极限、初等函数、积分、多元函数等) 以外，还包含其他一些重要的论题 (如求积分的逼近方法、魏尔斯特拉斯逼近定理、度量空间等)。另外，全书贯穿了许多具有启发性的例题以及激发求知欲的练习题。
作者简介
图书目录
Preface
Preliminaries
1 TOOLS FOR ANALYSIS
2 CONVERGENT SEQUENCES
3 CONTINUOUS FUNCTIONS
4 DIFFERENTIATION
5 ELEMENTARY FUNCTIONS AS SOLUTIONS OF DIFFERENTIAL EQUATIONS
6 INTEGRATION:TWO FUNDAMENTAL THEOREMS
7 INTEGRATION:fURTHER TOPICS
8 APPROXIMATION BY TAYLOR POLYNOMIALS
9 SEQUENCES AND SERIES OF FUNCTIONS
10 THE EUCLIDEAN SPACE
11 CONTINUITY,COMPACTNESS,AND CONNECTEDESS
12 METRIC SPACES
13 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES
14 LOCAL APPROXIMATION OF REAL-VALUED FUNCTIONS
15 APPROXIMATING NONLINEAR MAPPINGS BY LINEAR MAPPINGS
16 IMAGES AND INVERSES:THE INVERSE FUNCTION THEOREM
17 THE IMPLICIT FUNCTION THEOREM AND ITS APPLICATIONS
18 INTEGRATING FUNTIONS OF SEVERAL VARIABLES
19 ITERATED INTEGRATION AND CHANGES OF VARIABLES
20 LINE AND SURFACE INTEGRALS
A CONSEQUENCES OF THE FIELD AND POSITIVITY AXIOMS
B LINEAR ALGEBRA
Index
Preliminaries
1 TOOLS FOR ANALYSIS
2 CONVERGENT SEQUENCES
3 CONTINUOUS FUNCTIONS
4 DIFFERENTIATION
5 ELEMENTARY FUNCTIONS AS SOLUTIONS OF DIFFERENTIAL EQUATIONS
6 INTEGRATION:TWO FUNDAMENTAL THEOREMS
7 INTEGRATION:fURTHER TOPICS
8 APPROXIMATION BY TAYLOR POLYNOMIALS
9 SEQUENCES AND SERIES OF FUNCTIONS
10 THE EUCLIDEAN SPACE
11 CONTINUITY,COMPACTNESS,AND CONNECTEDESS
12 METRIC SPACES
13 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES
14 LOCAL APPROXIMATION OF REAL-VALUED FUNCTIONS
15 APPROXIMATING NONLINEAR MAPPINGS BY LINEAR MAPPINGS
16 IMAGES AND INVERSES:THE INVERSE FUNCTION THEOREM
17 THE IMPLICIT FUNCTION THEOREM AND ITS APPLICATIONS
18 INTEGRATING FUNTIONS OF SEVERAL VARIABLES
19 ITERATED INTEGRATION AND CHANGES OF VARIABLES
20 LINE AND SURFACE INTEGRALS
A CONSEQUENCES OF THE FIELD AND POSITIVITY AXIOMS
B LINEAR ALGEBRA
Index
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