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 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
