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• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• I PRELIMINARIES
• 1 Essentials of Logic and Set Theory
• 1.1 Essentials of Set Theory
• 1.2 Essentials of Logic
• 1.3 Mathematical Proofs
• 1.4 Mathematical Induction
• Review Exercises
• 2 Algebra
• 2.1 The Real Numbers
• 2.2 Integer Powers
• 2.3 Rules of Algebra
• 2.4 Fractions
• 2.5 Fractional Powers
• 2.6 Inequalities
• 2.7 Intervals and Absolute Values
• 2.8 Sign Diagrams
• 2.9 Summation Notation
• 2.10 Rules for Sums
• 2.11 Newton’s Binomial Formula
• 2.12 Double Sums
• Review Exercises
• 3 Solving Equations
• 3.1 Solving Equations
• 3.2 Equations and Their Parameters
• 3.3 Quadratic Equations
• 3.4 Some Nonlinear Equations
• 3.5 Using Implication Arrows
• 3.6 Two Linear Equations in Two Unknowns
• Review Exercises
• 4 Functions of One Variable
• 4.1 Introduction
• 4.2 Definitions
• 4.3 Graphs of Functions
• 4.4 Linear Functions
• 4.5 Linear Models
• 4.6 Quadratic Functions
• 4.7 Polynomials
• 4.8 Power Functions
• 4.9 Exponential Functions
• 4.10 Logarithmic Functions
• Review Exercises
• 5 Properties of Functions
• 5.1 Shifting Graphs
• 5.2 New Functions from Old
• 5.3 Inverse Functions
• 5.4 Graphs of Equations
• 5.5 Distance in the Plane
• 5.6 General Functions
• Review Exercises
• II SINGLE VARIABLE CALCULUS
• 6 Differentiation
• 6.1 Slopes of Curves
• 6.2 Tangents and Derivatives
• 6.3 Increasing and Decreasing Functions
• 6.4 Economic Applications
• 6.5 A Brief Introduction to Limits
• 6.6 Simple Rules for Differentiation
• 6.7 Sums, Products, and Quotients
• 6.8 The Chain Rule
• 6.9 Higher-Order Derivatives
• 6.10 Exponential Functions
• 6.11 Logarithmic Functions
• Review Exercises
• 7 Derivatives in Use
• 7.1 Implicit Differentiation
• 7.2 Economic Examples
• 7.3 The Inverse Function Theorem
• 7.4 Linear Approximations
• 7.5 Polynomial Approximations
• 7.6 Taylor’s Formula
• 7.7 Elasticities
• 7.8 Continuity
• 7.9 More on Limits
• 7.10 The Intermediate Value Theorem
• 7.11 Infinite Sequences
• 7.12 L’Hôpital’s Rule
• Review Exercises
• 8 Concave and Convex Functions
• 8.1 Intuition
• 8.2 Definitions
• 8.3 General Properties
• 8.4 First-Derivative Tests
• 8.5 Second-Derivative Tests
• 8.6 Inflection Points
• Review Exercises
• 9 Optimization
• 9.1 Extreme Points
• 9.2 Simple Tests for Extreme Points
• 9.3 Economic Examples
• 9.4 The Extreme and Mean Value Theorems
• 9.5 Further Economic Examples
• 9.6 Local Extreme Points
• Review Exercises
• 10 Integration
• 10.1 Indefinite Integrals
• 10.2 Area and Definite Integrals
• 10.3 Properties of Definite Integrals
• 10.4 Economic Applications
• 10.5 Integration by Parts
• 10.6 Integration by Substitution
• 10.7 Improper Integrals
• Review Exercises
• 11 Topics in Finance and Dynamics
• 11.1 Interest Periods and Effective Rates
• 11.2 Continuous Compounding
• 11.3 Present Value
• 11.4 Geometric Series
• 11.5 Total Present Value
• 11.6 Mortgage Repayments
• 11.7 Internal Rate of Return
• 11.8 A Glimpse at Difference Equations
• 11.9 Essentials of Differential Equations
• 11.10 Separable and Linear Differential Equations
• Review Exercises
• III MULTIVARIABLE ALGEBRA
• 12 Matrix Algebra
• 12.1 Matrices and Vectors
• 12.2 Systems of Linear Equations
• 12.3 Matrix Addition
• 12.4 Algebra of Vectors
• 12.5 Matrix Multiplication
• 12.6 Rules for Matrix Multiplication
• 12.7 The Transpose
• 12.8 Gaussian Elimination
• 12.9 Geometric Interpretation of Vectors
• 12.10 Lines and Planes
• Review Exercises
• 13 Determinants, Inverses, and Quadratic Forms
• 13.1 Determinants of Order 2
• 13.2 Determinants of Order 3
• 13.3 Determinants in General
• 13.4 Basic Rules for Determinants
• 13.5 Expansion by Cofactors
• 13.6 The Inverse of a Matrix
• 13.7 A General Formula for the Inverse
• 13.8 Cramer’s Rule
• 13.9 The Leontief Model
• 13.10 Eigenvalues and Eigenvectors
• 13.11 Diagonalization
• 13.12 Quadratic Forms
• Review Exercises
• IV MULTIVARIABLE CALCULUS
• 14 Functions of Many Variables
• 14.1 Functions of Two Variables
• 14.2 Partial Derivatives with Two Variables
• 14.3 Geometric Representation
• 14.4 Surfaces and Distance
• 14.5 Functions of n Variables
• 14.6 Partial Derivatives with Many Variables
• 14.7 Convex Sets
• 14.8 Concave and Convex Functions
• 14.9 Economic Applications
• 14.10 Partial Elasticities
• Review Exercises
• 15 Partial Derivatives in Use
• 15.1 A Simple Chain Rule
• 15.2 Chain Rules for Many Variables
• 15.3 Implicit Differentiation along a Level Curve
• 15.4 Level Surfaces
• 15.5 Elasticity of Substitution
• 15.6 Homogeneous Functions of Two Variables
• 15.7 Homogeneous and Homothetic Functions
• 15.8 Linear Approximations
• 15.9 Differentials
• 15.10 Systems of Equations
• 15.11 Differentiating Systems of Equations
• Review Exercises
• 16 Multiple Integrals
• 16.1 Double Integrals Over Finite Rectangles
• 16.2 Infinite Rectangles of Integration
• 16.3 Discontinuous Integrands and Other Extensions
• 16.4 Integration Over Many Variables
• V MULTIVARIABLE OPTIMIZATION
• 17 Unconstrained Optimization
• 17.1 Two Choice Variables: Necessary Conditions
• 17.2 Two Choice Variables: Sufficient Conditions
• 17.3 Local Extreme Points
• 17.4 Linear Models with Quadratic Objectives
• 17.5 The Extreme Value Theorem
• 17.6 Functions of More Variables
• 17.7 Comparative Statics and the Envelope Theorem
• Review Exercises
• 18 Equality Constraints
• 18.1 The Lagrange Multiplier Method
• 18.2 Interpreting the Lagrange Multiplier
• 18.3 Multiple Solution Candidates
• 18.4 Why Does the Lagrange Multiplier Method Work?
• 18.5 Sufficient Conditions
• 18.6 Additional Variables and Constraints
• 18.7 Comparative Statics
• Review Exercises
• 19 Linear Programming
• 19.1 A Graphical Approach
• 19.2 Introduction to Duality Theory
• 19.3 The Duality Theorem
• 19.4 A General Economic Interpretation
• 19.5 Complementary Slackness
• Review Exercises
• 20 Nonlinear Programming
• 20.1 Two Variables and One Constraint
• 20.2 Many Variables and Inequality Constraints
• 20.3 Nonnegativity Constraints
• Review Exercises
• Appendix
• Geometry
• The Greek Alphabet
• Bibliography
• Solutions to the Exercises
• Index
• Publisher’s Acknowledgements
• Back Cover