# Schaum's Outline of Introduction to Mathematical Economics

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## Description

More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice.

Outline format supplies a concise guide to the standard college courses in mathematical economics710 solved problemsClear, concise explanations of all mathematical economics conceptsSupplements the major bestselling textbooks in economics coursesAppropriate for the following courses: Introduction to Economics, Economics, Econometrics, Microeconomics, Macroeconomics, Economics Theories, Mathematical Economics, Math for Economists, Math for Social SciencesEasily understood review of mathematical economics Supports all the major textbooks for mathematical economics courses

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## Product details

- Paperback | 544 pages
- 208 x 272 x 25mm | 862g
- 24 Oct 2011
- McGraw-Hill Education - Europe
- MCGRAW-HILL Professional
- United States
- English
- 3rd edition
- 73 Illustrations, unspecified
- 0071762515
- 9780071762519
- 133,912

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## Table of contents

1.1 Exponents

1.2 Polynomials

1.3 Equations: Linear and Quadratic

1.4 Simultaneous Equations

1.5 Functions

1.6 Graphs, Slopes, and Intercepts

Chapter 2: Economic Applications of Graphs and Equations

2.1 Isocost Lines

2.2 Supply and Demand Analysis

2.3 Income Determination Models

2.4 IS-LM Analysis

Chapter 3: The Derivative and the Rules of Differentiation

3.1 Limits

3.2 Continuity

3.3 The Slope of a Curvilinear Function

3.4 The Derivative

3.5 Differentiability and Continuity

3.6 Derivative Notation

3.7 Rules of Differentiation

3.8 Higher-Order Derivatives

3.9 Implicit Differentiation

Chapter 4: Uses of the Derivative in Mathematics and Economics

4.1 Increasing and Decreasing Functions

4.2 Concavity and Convexity

4.3 Relative Extrema

4.4 Inflection Points

4.5 Optimization of Functions

4.6 Successive-Derivative Test for Optimization

4.7 Marginal Concepts

4.8 Optimizing Economic Functions

4.9 Relationship among Total, Marginal, and Average Concepts

Chapter 5: Calculus of Multivariable Functions

5.1 Functions of Several Variables and Partial Derivatives

5.2 Rules of Partial Differentiation

5.3 Second-Order Partial Derivatives

5.4 Optimization of Multivariable Functions

5.5 Constrained Optimization with Lagrange Multipliers

5.6 Significance of the Lagrange Multiplier

5.7 Differentials

5.8 Total and Partial Differentials

5.9 Total Derivatives

5.10 Implicit and Inverse Function Rules

Chapter 6: Calculus of Multivariable Functions in Economics

6.1 Marginal Productivity

6.2 Income Determination Multipliers and Comparative Statics

6.3 Income and Cross Price Elasticities of Demand

6.4 Differentials and Incremental Changes

6.5 Optimization of Multivariable Functions in Economics

6.6 Constrained Optimization of Multivariable Functions in Economics

6.7 Homogeneous Production Functions

6.8 Returns to Scale

6.9 Optimization of Cobb-Douglas Production Functions

6.10 Optimization of Constant Elasticity of Substitution Production Functions

Chapter 7: Exponential and Logarithmic Functions

7.1 Exponential Functions

7.2 Logarithmic Functions

7.3 Properties of Exponents and Logarithms

7.4 Natural Exponential and Logarithmic Functions

7.5 Solving Natural Exponential and Logarithmic Functions

7.6 Logarithmic Transformation of Nonlinear Functions

Chapter 8: Exponential and Logarithmic Functions in Economics

8.1 Interest Compounding

8.2 Effective vs. Nominal Rates of Interest

8.3 Discounting

8.4 Converting Exponential to Natural Exponential Functions

8.5 Estimating Growth Rates from Data Points

Chapter 9: Differentiation of Exponential and Logarithmic Functions

9.1 Rules of Differentiation

9.2 Higher-Order Derivatives

9.3 Partial Derivatives

9.4 Optimization of Exponential and Logarithmic Functions

9.5 Logarithmic Differentiation

9.6 Alternative Measures of Growth

9.7 Optimal Timing

9.8 Derivation of a Cobb-Douglas Demand Function Using a Logarithmic Transformation

Chapter 10: The Fundamentals of Linear (or Matrix) Algebra

10.1 The Role of Linear Algebra

10.2 Definitions and Terms

10.3 Addition and Subtraction of Matrices

10.4 Scalar Multiplication

10.5 Vector Multiplication

10.6 Multiplication of Matrices

10.7 Commutative, Associative, and Distributive Laws in Matrix Algebra

10.8 Identity and Null Matrices

10.9 Matrix Expression of a System of Linear Equations.

Chapter 11: Matrix Inversion

11.1 Determinants and Nonsingularity

11.2 Third-Order Determinants

11.3 Minors and Cofactors

11.4 Laplace Expansion and Higher-Order Determinants

11.5 Properties of a Determinant

11.6 Cofactor and Adjoint Matrices

11.7 Inverse Matrices

11.8 Solving Linear Equations with the Inverse

11.9 Cramer's Rule for Matrix Solutions

Chapter 12: Special Determinants and Matrices and Their Use in Economics

12.1 The Jacobian

12.2 The Hessian

12.3 The Discriminant

12.4 Higher-Order Hessians

12.5 The Bordered Hessian for Constrained Optimization

12.6 Input-Output Analysis

12.7 Characteristic Roots and Vectors (Eigenvalues, Eigenvectors)

Chapter 13: Comparative Statics and Concave Programming

13.1 Introduction to Comparative Statics

13.2 Comparative Statics with One Endogenous Variable

13.3 Comparative Statics with More Than One Endogenous Variable

13.4 Comparative Statics for Optimization Problems

13.5 Comparative Statics Used in Constrained Optimization

13.6 The Envelope Theorem

13.7 Concave Programming and Inequality Constraints

Chapter 14: Integral Calculus: The Indefinite Integral

14.1 Integration

14.2 Rules of Integration

14.3 Initial Conditions and Boundary Conditions

14.4 Integration by Substitution

14.5 Integration by Parts

14.6 Economic Applications

Chapter 15: Integral Calculus: The Definite Integral

15.1 Area Under a Curve

15.2 The Definite Integral

15.3 The Fundamental Theorem of Calculus

15.4 Properties of Definite Integrals

15.5 Area Between Curves

15.6 Improper Integrals

15.7 L'HUpital's Rule

15.8 Consumers' and Producers' Surplus

15.9 The Definite Integral and Probability

Chapter 16: First-Order Differential Equations

16.1 Definitions and Concepts

16.2 General Formula for First-Order Linear Differential Equations

16.3 Exact Differential Equations and Partial Integration

16.4 Integrating Factors

16.5 Rules for the Integrating Factor

16.6 Separation of Variables

16.7 Economic Applications

16.8 Phase Diagrams for Differential Equations

Chapter 17: First-Order Difference Equations

17.1 Definitions and Concepts

17.2 General Formula for First-Order Linear Difference Equations

17.3 Stability Conditions

17.4 Lagged Income Determination Model

17.5 The Cobweb Model

17.6 The Harrod Model

17.7 Phase Diagrams for Difference Equations

Chapter 18: Second-Order Differential Equations and Difference Equations

18.1 Second-Order Differential Equations

18.2 Second-Order Difference Equations

18.3 Characteristic Roots

18.4 Conjugate Complex Numbers

18.5 Trigonometric Functions

18.6 Derivatives of Trigonometric Functions

18.7 Transformation of Imaginary and Complex Numbers

18.8 Stability Conditions

Chapter 19: Simultaneous Differential and Difference Equations

19.1 Matrix Solution of Simultaneous Differential Equations, Part 1

19.2 Matrix Solution of Simultaneous Differential Equations, Part 2

19.3 Matrix Solution of Simultaneous Difference Equations, Part 1

19.4 Matrix Solution of Simultaneous Difference Equations, Part 2

19.5 Stability and Phase Diagrams for Simultaneous Differential Equations

Chapter 20: The Calculus of Variations

20.1 Dynamic Optimization

20.2 Distance Between Two Points on a Plane

20.3 Euler's Equation and the Necessary Condition for Dynamic Optimization

20.4 Finding Candidates for Extremals

20.5 The Sufficiency Conditions for the Calculus of Variations

20.6 Dynamic Optimization Subject to Functional Constraints

20.7 Variational Notation

20.8 Applications to Economics

Chapter 21: Optimal Control Theory

21.1 Terminology

21.2 The Hamiltonian and the Necessary Conditions for Maximization in Optimal Control Theory

21.3 Sufficiency Conditions for Maximization in Optimal Control

21.4 Optimal Control Theory with a Free Endpoint

21.5 Inequality Constraints in the Endpoints

21.6 The Current-Valued Hamiltonian

Index

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## About Edward Dowling

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