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内容简介

　　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.

内页插图

目录

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

前言/序言

实分析及其在经济学中的应用 [Real Analysis with Economic Applications] 电子书 下载 mobi epub pdf txt

评分☆☆☆☆☆

相对于数学类的实分析教材，本书减少了较多与经济学不相关的内容，对经济学的学生来说针对性更明显。

评分☆☆☆☆☆

相对于数学类的实分析教材，本书减少了较多与经济学不相关的内容，对经济学的学生来说针对性更明显。

评分☆☆☆☆☆

看了20页，感觉写得不够友好。这书不太适合自学，必须有老师教才行。

评分☆☆☆☆☆

评分☆☆☆☆☆

就是太厚了，800页呢。

评分☆☆☆☆☆

看累了，翻到preface浏览，结果发现了一句：“It may eventually be necessary to study matters from more advanced treatments,...” 原来作者自己都认为，看这本书是远远不够的，只不过是一个热身运动。要想真正学好实分析，找其他实分析书吧。

评分☆☆☆☆☆

评分☆☆☆☆☆

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评分☆☆☆☆☆

《实分析及其在经济学中的应用(英文版)》通篇都仅仅围绕着经济学展开讲述实分析，除了实分析的普通论题，书中讨论了阶理论、凸分析、优化、对应理论、线性和非线性泛函分析、不动点理论、动态规划和变分法。作者通过应用案例，从包括个人决策理论和博弈，福利经济学、信息论、一般平衡和金融、跨期经济学这些经济理论出发补充讲述了数学进展。除了讲述在经济学中的直接应用以外，还包括了大量的不动点理论和泛函方程和最优化理论中的应用。

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