文档介绍：Mathematical Economics and Finance
Michael Harrison Patrick Waldron
December 2, 1998
CONTENTS i
Contents
List of Tables iii
List of Figures v
PREFACE vii
What Is Economics? . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
What Is Mathematics? . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
NOTATION ix
I MATHEMATICS 1
1 LINEAR ALGEBRA 3
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Systems of Linear Equations and Matrices . . . . . . . . . . . . . 3
Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Matrix Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Vectors and Vector Spaces . . . . . . . . . . . . . . . . . . . . . 11
Linear Independence . . . . . . . . . . . . . . . . . . . . . . . . 12
Bases and Dimension . . . . . . . . . . . . . . . . . . . . . . . . 12
Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . 14
Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Symmetric Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 15
Definite Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 VECTOR CALCULUS 17
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Basic Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Vector-valued Functions and Functions of Several Variables . . . 18
Revised: December 2, 1998
ii CONTENTS
Partial and Total Derivatives . . . . . . . . . . . . . . . . . . . . 20
The Chain Rule and Product Rule . . . . . . . . . . . . . . . . . 21
The Implicit Function Theorem . . . . . . . . . . . . . . . . . . . 23
Directional Derivatives . . . . . . . . . . . . . . . . . . . . . . . 24
Taylor’s Theorem: Deterministic Version . . . . . . . . . . . . . 25
The F