Further Mathematics for Economic Analysis

ISBN-10: 0273713280
ISBN-13: 9780273713289
Edition: 2nd 2008
List price: $224.40 Buy it from $100.84 Rent it from $32.21
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Book details

List price: $224.40
Edition: 2nd
Copyright year: 2008
Publisher: Prentice Hall PTR
Publication date: 12/4/2008
Binding: Paperback
Pages: 632
Size: 7.25" wide x 9.25" long x 1.25" tall
Weight: 2.266
Language: English

Preface
Topics in Linear Algebra
Review of Basic Linear Algebra
Linear Independence
The Rank of a Matrix
Main Results on Linear Systems
Eigenvalues
Diagonalization
Quadratic Forms
Quadratic Forms with Linear Constraints
Partitioned Matrices and Their Inverses
Multivariable Calculus
Gradients and Directional Derivatives
Convex Sets
Concave and Convex Functions I
Concave and Convex Functions II
Quasiconcave and Quasiconvex Functions
Taylor's Formula
Implicit and Inverse Function Theorems
Degrees of Freedom and Functional Dependence
Differentiability
Existence and Uniqueness of Solutions of Systems of Equations
Static Optimization
Extreme Points
Local Extreme Points
Equality Constraints: The Lagrange Problem
Local Second-Order Conditions
Inequality Constraints: Nonlinear Programming
Sufficient Conditions
Comparative Statics
Nonnegativity Constraints
Concave Programming
Precise Comparative Statics Results
Existence of Lagrange Multipliers
Topics in Integration
Review of One-Variable Integration
Leibniz's Formula
The Gamma Function
Multiple Integrals over Product Domains
Double Integrals over General Domains
The Multiple Riemann Integral
Change of Variables
Generalized Double Integrals
Differential Equations I: First-Order Equations in One Variable
Introduction
The Direction is Given: Find the Path!
Separable Equations
First-Order Linear Equations
Exact Equations and Integrating Factors
Transformation of Variables
Qualitative Theory and Stability
Existence and Uniqueness
Differential Equations II: Second-Order Equations and Systems in the Plane
Introduction
Linear Differential Equations
Constant Coefficients
Stability for Linear Equations
Simultaneous Equations in the Plane
Equilibrium Points for Linear Systems
Phase Plane Analysis
Stability for Nonlinear Systems
Saddle Points
Differential Equations III: Higher-Order Equations
Linear Differential Equations
The Constant Coefficients Case
Stability of Linear Differential Equations
Systems of Differential Equations
Stability for Nonlinear Systems
Qualitative Theory
A Glimpse at Partial Differential Equations
Calculus of Variations
The Simplest Problem
The Euler Equation
Why the Euler Equation is Necessary
Optimal Savings
More General Terminal Conditions
Control Theory: Basic Techniques
The Basic Problem
A Simple Case
Regularity Conditions
The Standard Problem
The Maximum Principle and the Calculus of Variations
Adjoint Variables as Shadow Prices
Sufficient Conditions
Variable Final Time
Current Value Formulations
Scrap Values
Infinite Horizon
Phase Diagrams
Control Theory with Many Variables
Several Control and State Variables
Some Examples
Infinite Horizon
Existence Theorems and Sensitivity
A Heuristic Proof of the Maximum Principle
Mixed Constraints
Pure State Constraints
Generalizations
Difference Equations
First-Order Difference Equations
Economic Applications
Second-Order Difference Equations
Linear Equations with Constant Coefficients
Higher-Order Equations
Systems of Difference Equations
Stability of Nonlinear Difference Equations
Discrete Time Optimization
Dynamic Programming
The Euler Equation
Infinite Horizon
The Maximum Principle
More Variables
Stochastic Optimization
Infinite Horizon Stationary Problems
Topology and Separation
Point Set Topology in R<sup>n</sup>
Topology and Convergence
Continuous Functions
Maximum Theorems
Convex Sets
Separation Theorems
Productive Economies and Frobenius's Theorem
Correspondences and Fixed Points
Correspondences
A General Maximum Theorem
Fixed Points for Contraction Mappings
Brouwer's and Kakutani's Fixed Point Theorems
Equilibrium in a Pure Exchange Economy
Sets, Completeness, and Covergence
Sets and Functions
Least Upper Bound Principle
Sequences of Real Numbers
Infimum and Supremum of Functions
Trigonometric Functions
Basic Definitions and Results
Differentiating Trigonometric Functions
Complex Numbers
Answers
References
Index

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