Efnisyfirlit

• Cover Page
• Title Page
• Copyright Page
• About the Authors
• 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
    • 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 More on Limits
    • 7.11 More on Limits
    • 7.12 More on Limits
    • 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

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