Essential Mathematics for Economic Analysis

The late Knut Sydsaeter was Emeritus Professor of Mathematics in the Economics Department at the University of Oslo, where he had taught mathematics for economists for over 45 years. Peter Hammond is currently Professor of Economics at the University of Warwick, where he moved in 2007 after becoming an Emeritus Professor at Stanford University. He has taught mathematics for economists at both universities, as well as at the universities of Oxford and Essex. Arne Strom is Associate Professor Emeritus at the University of Oslo and has extensive experience in teaching mathematics for economists in the Department of Economics there. Andres Carvajal is an Associate Professor in the Department of Economics at University of California, Davis.

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'Hopital'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 Infinite Intervals of Integration 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