Essential Mathematics for Economic Analysis, 6th edition

Published by Pearson (April 15, 2021) © 2021

  • Knut Sydsaeter University of Oslo
  • Peter Hammond Stanford University
  • Arne Strom University of Oslo
  • Andrés Carvajal

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ISBN-13: 9781292359281
Essential Mathematics for Economic Analysis
Published 2021

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Acquire the key mathematical skills you need to master and succeed in Economics.

Essential Mathematics for Economic Analysis, 6th edition is a global best-selling text providing an extensive introduction to all the mathematical tools you need to study Economics at an intermediate level.

From elementary calculus to more advanced topics, this edition includes a plethora of practice examples, questions, and solutions integrated throughout, giving you a wealth of opportunities to apply them in specific economic situations and develop key mathematical skills as your course progresses.

Pair this text with MyMathLab®.

Preface

I PRELIMINARIES

  1. Essentials of Logic and Set Theory
    • Essentials of Set Theory
    • Essentials of Logic
    • Mathematical Proofs
    • Mathematical Induction

    Review Exercises

  2.  
  3. Algebra
    • The Real Numbers
    • Integer Powers
    • Rules of Algebra
    • Fractions
    • Fractional Powers
    • Inequalities
    • Intervals and Absolute Values
    • Sign Diagrams
    • Summation Notation
    • Rules for Sums
    • Newton's Binomial Formula
    • Double Sums

    Review Exercises

  4. Solving Equations
    • Solving Equations
    • Equations and Their Parameters
    • Quadratic Equations
    • Some Nonlinear Equations
    • Using Implication Arrows
    • Two Linear Equations in Two Unknowns

    Review Exercises

  5. Functions of One Variable
       
    • Introduction
    • Definitions
    • Graphs of Functions
    • Linear Functions
    • Linear Models
    • Quadratic Functions
    • Polynomials
    • Power Functions
    • Exponential Functions
    • Logarithmic Functions
    •  

    Review Exercises

  6. Properties of Functions
       
    • Shifting Graphs
    • New Functions From Old
    • Inverse Functions
    • Graphs of Equations
    • Distance in The Plane
    • General Functions

    Review Exercises

II SINGLE-VARIABLE CALCULUS

  1. Differentiation
    • Slopes of Curves
    • Tangents and Derivatives
    • Increasing and Decreasing Functions
    • Economic Applications
    • A Brief Introduction to Limits
    • Simple Rules for Differentiation
    • Sums, Products, and Quotients
    • The Chain Rule
    • Higher-Order Derivatives
    • Exponential Functions
    • Logarithmic Functions

    Review Exercises

  2. Derivatives in Use
    • Implicit Differentiation
    • Economic Examples
    • The Inverse Function Theorem
    • Linear Approximations
    • Polynomial Approximations
    • Taylor's Formula
    • Elasticities
    • Continuity
    • More on Limits
    • The Intermediate Value Theorem
    • Infinite Sequences
    • L'Hôpital's Rule Review Exercises

    Review Exercises

  3. Concave and Convex Functions
    • Intuition
    • Definitions
    • General Properties
    • First Derivative Tests
    • Second Derivative Tests
    • Inflection Points

    Review Exercises

  4. Optimization
    • Extreme Points
    • Simple Tests for Extreme Points
    • Economic Examples
    • The Extreme and Mean Value Theorems
    • Further Economic Examples
    • Local Extreme Points

    Review Exercises

  5. Integration
    • Indefinite Integrals
    • Area and Definite Integrals
    • Properties of Definite Integrals
    • Economic Applications
    • Integration by Parts
    • Integration by Substitution
    • Infinite Intervals of Integration

    Review Exercises

  6. Topics in Finance and Dynamics
    • Interest Periods and Effective Rates
    • Continuous Compounding
    • Present Value
    • Geometric Series
    • Total Present Value
    • Mortgage Repayments
    • Internal Rate of Return
    • A Glimpse at Difference Equations
    • Essentials of Differential Equations
    • Separable and Linear Differential Equations

    Review Exercises

III MULTI-VARIABLE ALGEBRA

  1. Matrix Algebra
    • Matrices and Vectors
    • Systems of Linear Equations
    • Matrix Addition
    • Algebra of Vectors
    • Matrix Multiplication
    • Rules for Matrix Multiplication
    • The Transpose
    • Gaussian Elimination
    • Geometric Interpretation of Vectors
    • Lines and Planes

    Review Exercises

  2. Determinants, Inverses, and Quadratic Forms
    • Determinants of Order 2
    • Determinants of Order 3
    • Determinants in General
    • Basic Rules for Determinants
    • Expansion by Cofactors
    • The Inverse of a Matrix
    • A General Formula for The Inverse
    • Cramer's Rule
    • The Leontief Mode
    • Eigenvalues and Eigenvectors
    • Diagonalization
    • Quadratic Forms

    Review Exercises

IV MULTI-VARIABLE CALCULUS

  1. Multivariable Functions
    • Functions of Two Variables
    • Partial Derivatives with Two Variables
    • Geometric Representation
    • Surfaces and Distance
    • Functions of More Variables
    • Partial Derivatives with More Variables
    • Convex Sets
    • Concave and Convex Functions
    • Economic Applications
    • Partial Elasticities

    Review Exercises

  2. Partial Derivatives in Use
    • A Simple Chain Rule
    • Chain Rules for Many Variables
    • Implicit Differentiation Along A Level Curve
    • Level Surfaces
    • Elasticity of Substitution
    • Homogeneous Functions of Two Variables
    • Homogeneous and Homothetic Functions
    • Linear Approximations
    • Differentials
    • Systems of Equations
    • Differentiating Systems of Equations

    Review Exercises

  3. Multiple Integrals
    • Double Integrals Over Finite Rectangles
    • Infinite Rectangles of Integration
    • Discontinuous Integrands and Other Extensions
    • Integration Over Many Variables

    Review Exercises

V MULTI-VARIABLE OPTIMIZATION

  1. Unconstrained Optimization
    • Two Choice Variables: Necessary Conditions
    • Two Choice Variables: Sufficient Conditions
    • Local Extreme Points
    • Linear Models with Quadratic Objectives
    • The Extreme Value Theorem
    • Functions of More Variables
    • Comparative Statics and the Envelope Theorem

    Review Exercises

  2. Equality Constraints
    • The Lagrange Multiplier Method
    • Interpreting the Lagrange Multiplier
    • Multiple Solution Candidates
    • Why Does the Lagrange Multiplier Method Work?
    • Sufficient Conditions
    • Additional Variables and Constraints
    • Comparative Statics

    Review Exercises

  3. Linear Programming
    • A Graphical Approach
    • Introduction to Duality Theory
    • The Duality Theorem
    • A General Economic Interpretation
    • Complementary Slackness

    Review Exercises

  4. Nonlinear Programming
    • Two Variables and One Constraint
    • Many Variables and Inequality Constraints
    • Nonnegativity Constraints

    Review Exercises

Appendix

  • Geometry
  • The Greek Alphabet
  • Bibliography
  • Solutions to the Exercises

    Index

    Publisher's Acknowledgments

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