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內容簡介

　　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.

內頁插圖

目錄

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

實分析及其在經濟學中的應用 [Real Analysis with Economic Applications] 下載 mobi epub pdf txt 電子書

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怎麼說呢！看完這本書，估計能瞭解實分析，但並不真正理解。高雅點說，是飄渺。不高雅點說，是隔靴搔癢。

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看纍瞭，翻到preface瀏覽，結果發現瞭一句：“It may eventually be necessary to study matters from more advanced treatments,...” 原來作者自己都認為，看這本書是遠遠不夠的，隻不過是一個熱身運動。要想真正學好實分析，找其他實分析書吧。

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好

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《實分析及其在經濟學中的應用(英文版)》通篇都僅僅圍繞著經濟學展開講述實分析，除瞭實分析的普通論題，書中討論瞭階理論、凸分析、優化、對應理論、綫性和非綫性泛函分析、不動點理論、動態規劃和變分法。作者通過應用案例，從包括個人決策理論和博弈，福利經濟學、信息論、一般平衡和金融、跨期經濟學這些經濟理論齣發補充講述瞭數學進展。除瞭講述在經濟學中的直接應用以外，還包括瞭大量的不動點理論和泛函方程和最優化理論中的應用。

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好

評分☆☆☆☆☆

就是太厚瞭，800頁呢。

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