实分析及其在经济学中的应用
2013-1
世界图书出版公司
Efe A.Ok
802
无
This is primarily a textbook on mathematical analysis for
graduate students in economics. While there are a large number of
excellent textbooks on this broad topic in the mathematics
literature， most ofthese texts are overly advanced relative to the
needs of the vast majority of economics students and concentrate on
various topics that are not readily helpful for studying economic
theory. Moreover， it seems that most economics students lack the
time or courage to enroll in a math course at the graduate
level. Sometimes this is not even for bad reasons， for only few
math departments offer classes that are designed for the parhcular
needs of economists. Unfortunately，more often than not， the
consequent lack ofmathematical background cre-ates problems for the
students at a later stage of their education， since an exceedingly
large fraction ofeconomic theory is impenetrable without some
rigorous background in real analysis. The present text aims at
providing a remedy for this inconvenient situation.
Preface
Prerequisites
Basic Conventions
PART Ⅰ SET THEORY
CHAPTER A Preliminaries of Real Analysis
A.1 Elements ofSet Theory
A.1.1 Sets
A.1.2 Relations
A.1.3 Equivalence Relations
A.1.4 O0rder Relations
A.1.5 Functions
A.1.6 Sequences, Vectors, and Matrices
A.1.7 A Glimpse ofAdvanced Set Theory: The Axiom of Choice
A.2 Real Numbers
A.2.1 Ordered Fields
A.2.2 Natural Numbers, Integers, and Rationals
A.2.3 Real Numbers
A.2.4 Intervals and R
A.3 Real Sequences
A.3.1 Convergent Sequences
A.3.2 Monotonic Sequences
A.3.3 Subsequential Limits
A.3.4 Infinite Series
A.3.5 Rear.rangement oflnfinite Series
A.3.6 Infinite Products
A.4 Real Functions
A.4.1 Basic Definitions
A.4.2 Limits, ContinLuty, and Differentiation
A.4.3 Riemann Integration
A.4.4 Exponential, Logarithmic, and Trigonometric Functions
A.4.5 Concave and Convex Functions
A.4.6 Quasiconcave and Quasiconvex Functions
CHAPTER B Countability
B.1 Countable and Uncountable Sets
B.2 Losets and Q
B.3 Some More Advanced Set Theory
B.3.1 The Cardinality Ordering
B.3.2 The Well-Ordering Principle
B.4 Application: Ordinal utility Theor）r
B.4.1 Preference Relations
B.4.2 Utilitv ReDresentation of Complete Preference
Relations
B.4.3 Utility Representation oflncomplete Preference
Relations
PART Ⅱ ANALYSIS ON METRIC SPACES
CHAPTER C Metric Spaces
C.1 Basic Notions
C.1.1 Metric Spaces: Definition and Examples
C.1.2 0pen and Closed Sets
C.1.3 Convergent Sequences
……
PART Ⅲ ANALYSIS ON LINEAR SPACES
PART Ⅳ ANALYSIS ON METRIC/NORMED LINEAR SPACES
Hints for Selected Exercises
References
Clossary of Selected Symbols
Index
无
大家在阅读高档次期刊论文时，难免会有犯糊涂，看不懂的时候，实际上是我们的数学功底不够，而这本书正好是提供这方面训练的，数学是必备基础，这本书里面的数学原理紧扣经济学原理，对于想用数学思考经济学的人来说是有很大助益的！
很好的书，值得多读几遍，对掌握基本经济理论的帮助很大。
高微老师推荐的，实分析里面的基础内容。印刷很满意！