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• Cover Page
• Schaum’s Outline of Introduction to Mathematical Economics
• Copyright Page
• Preface
• Contents
• Chapter 1 Review
• 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
• 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’hôpital’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
• Footnote
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