Essential mathematics for economic analysis [electronic resource] / Knut Sydsæter Peter Hammond and Arne Strom.

Includes index.

Previous ed.: Harlow: Financial Times Prentice Hall, 2008.

Text on inside cover.

Machine generated contents note: -- 1.1.The Real Numbers -- 1.2.Integer Powers -- 1.3.Rules of Algebra -- 1.4.Fractions -- 1.5.Fractional Powers -- 1.6.Inequalities 1 -- 1.7.Intervals and Absolute Values -- Review Problems for Chapter 1 -- 2.1.How to Solve Simple Equations -- 2.2.Equations with Parameters -- 2.3.Quadratic Equations -- 2.4.Linear Equations in Two Unknowns -- 2.5.Nonlinear Equations -- Review Problems for Chapter 2 -- 3.1.Summation Notation -- 3.2.Rules for Sums. Newton's Binomial Formula -- 3.3.Double Sums -- 3.4.A Few Aspects of Logic -- 3.5.Mathematical Proofs -- 3.6.Essentials of Set Theory -- 3.7.Mathematical Induction -- Review Problems for Chapter 3 -- 4.1.Introduction -- 4.2.Basic 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 Problems for Chapter -- 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. Circles -- 5.6.General Functions -- Review Problems for Chapter 5 -- 6.1.Slopes of Curves -- 6.2.Tangents and Derivatives -- 6.3.Increasing and Decreasing Functions -- 6.4.Rates of Change -- 6.5.A Dash of Limits -- 6.6.Simple Rules for Differentiation -- 6.7.Sums, Products, and Quotients -- 6.8.Chain Rule -- 6.9.Higher-Order Derivatives -- 6.10.Exponential Functions -- 6.11.Logarithmic Functions -- Review Problems for Chapter 6 -- 7.1.Implicit Differentiation -- 7.2.Economic Examples -- 7.3.Differentiating the Inverse -- 7.4.Linear Approximations -- 7.5.Polynomial Approximations -- 7.6.Taylor's Formula -- 7.7.Why Economists Use Elasticities -- 7.8.Continuity -- 7.9.More on Limits -- 7.10.Intermediate Value Theorem. Newton's Method -- 7.11.Infinite Sequences -- 7.12.L'Hôpital's Rule -- Review Problems for Chapter 7 -- 8.1.Introduction 8.2.Simple Tests for Extreme Points -- 8.3.Economic Examples -- 8.4.The Extreme Value Theorem -- 8.5.Further Economic Examples -- 8.6.Local Extreme Points -- 8.7.Inflection Points -- Review Problems for Chapter 8 -- 9.1.Indefinite Integrals -- 9.2.Area and Definite Integrals -- 9.3.Properties of Definite Integrals -- 9.4.Economic Applications -- 9.5.Integration by Parts -- 9.6.Integration by Substitution -- 9.7.Infinite Intervals of Integration -- 9.8.A Glimpse at Differential Equations -- 9.9.Separable and Linear Differential Equations -- Review Problems for Chapter 9 -- 10.1.Interest Periods and Effective Rates -- 10.2.Continuous Compounding -- 10.3.Present Value -- 10.4.Geometric Series -- 10.5.Total Present Value -- 10.6.Mortgage Repayments -- 10.7.Internal Rate of Return -- 10.8.A Glimpse at Difference Equations -- Review Problems for Chapter 10 -- 11.1.Functions of Two Variables -- 11.2.Partial Derivatives with Two Variables 11.3.Geometric Representation -- 11.4.Surfaces and Distance -- 11.5.Functions of More Variables -- 11.6.Partial Derivatives with More Variables -- 11.7.Economic Applications -- 11.8.Partial Elasticities -- Review Problems for Chapter 11 -- 12.1.A Simple Chain Rule -- 12.2.Chain Rules for Many Variables -- 12.3.Implicit Differentiation along a Level Curve -- 12.4.More General Cases -- 12.5.Elasticity of Substitution -- 12.6.Homogeneous Functions of Two Variables -- 12.7.Homogeneous and Homothetic Functions -- 12.8.Linear Approximations -- 12.9.Differentials -- 12.10.Systems of Equations -- 12.11.Differentiating Systems of Equations -- Review Problems for Chapter 12 -- 13.1.Two Variables: Necessary Conditions -- 13.2.Two Variables: Sufficient Conditions -- 13.3.Local Extreme Points -- 13.4.Linear Models with Quadratic Objectives -- 13.5.The Extreme Value Theorem -- 13.6.Three or More Variables -- 13.7.Comparative Statics and the Envelope Theorem Review Problems for Chapter 13 -- 14.1.The Lagrange Multiplier Method -- 14.2.Interpreting the Lagrange Multiplier -- 14.3.Several Solution Candidates -- 14.4.Why the Lagrange Method Works -- 14.5.Sufficient Conditions -- 14.6.Additional Variables and Constraints -- 14.7.Comparative Statics -- 14.8.Nonlinear Programming: A Simple Case -- 14.9.Multiple Inequality Constraints -- 14.10.Nonnegativity Constraints -- Review Problems for Chapter 14 -- 15.1.Systems of Linear Equations -- 15.2.Matrices and Matrix Operations -- 15.3.Matrix Multiplication -- 15.4.Rules for Matrix Multiplication -- 15.5.The Transpose -- 15.6.Gaussian Elimination -- 15.7.Vectors -- 15.8.Geometric Interpretation of Vectors -- 15.9.Lines and Planes -- Review Problems for Chapter 15 -- 16.1.Determinants of Order 2 -- 16.2.Determinants of Order 3 -- 16.3.Determinants of Order n -- 16.4.Basic Rules for Determinants -- 16.5.Expansion by Cofactors -- 16.6.The Inverse of a Matrix 16.7.A General Formula for the Inverse -- 16.8.Cramer's Rule -- 16.9.The Leontief Model -- Review Problems for Chapter 16 -- 17.1.A Graphical Approach -- 17.2.Introduction to Duality Theory -- 17.3.The Duality Theorem -- 17.4.A General Economic Interpretation -- 17.5.Complementary Slackness -- Review Problems for Chapter 17.

This text provides an invaluable introduction to the mathematical tools that undergraduate economists need. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics that are usually taught in undergraduate courses on mathematics for economists.