Schaum's Outline of Calculus for Business, Economics and Finance, Fourth Edition (Schaum's Outlines)

Cover
Title Page
Copyright Page
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 Func tions
	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’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
CHAPTER 22 Series in Economics: Descriptive Statistics and Linear Regression
	22.1 Series
	22.2 Properties of Summations
	22.3 Descriptive Statistics: Frequency, Mean, and Variance
	22.4 Probability: The Discrete Case
	22.5 The Weighted Average
	22.6 The Expected Value
	22.7 Economic Applications: Regression Analysis
EXCEL PRACTICE
	Excel Practice A
	Excel Practice B
Additional Practice Problems
Additional Practice Problems: Solutions
Index