Preface I PRELIMINARIES Essentials of Logic and Set Theory Essentials of Set TheoryEssentials of LogicMathematical ProofsMathematical InductionReview Exercises   Algebra The Real NumbersInteger PowersRules of AlgebraFractionsFractional PowersInequalitiesIntervals and Absolute ValuesSign DiagramsSummation NotationRules for SumsNewton's Binomial FormulaDouble Sums Review Exercises Solving Equations Solving EquationsEquations and Their ParametersQuadratic EquationsSome Nonlinear EquationsUsing Implication ArrowsTwo Linear Equations in Two UnknownsReview Exercises Functions of One Variable   IntroductionDefinitionsGraphs of FunctionsLinear FunctionsLinear ModelsQuadratic FunctionsPolynomialsPower FunctionsExponential FunctionsLogarithmic Functions  Review Exercises Properties of Functions   Shifting GraphsNew Functions From OldInverse FunctionsGraphs of EquationsDistance in The PlaneGeneral Functions Review Exercises II SINGLE-VARIABLE CALCULUS Differentiation Slopes of CurvesTangents and DerivativesIncreasing and Decreasing FunctionsEconomic ApplicationsA Brief Introduction to LimitsSimple Rules for DifferentiationSums, Products, and QuotientsThe Chain RuleHigher-Order DerivativesExponential FunctionsLogarithmic Functions Review Exercises Derivatives in Use Implicit DifferentiationEconomic ExamplesThe Inverse Function TheoremLinear ApproximationsPolynomial ApproximationsTaylor's FormulaElasticitiesContinuityMore on LimitsThe Intermediate Value TheoremInfinite SequencesL'Hôpital's Rule Review Exercises Review Exercises Concave and Convex Functions IntuitionDefinitionsGeneral PropertiesFirst Derivative TestsSecond Derivative TestsInflection Points Review Exercises Optimization Extreme PointsSimple Tests for Extreme PointsEconomic ExamplesThe Extreme and Mean Value TheoremsFurther Economic ExamplesLocal Extreme Points Review Exercises Integration Indefinite IntegralsArea and Definite IntegralsProperties of Definite IntegralsEconomic ApplicationsIntegration by PartsIntegration by SubstitutionInfinite Intervals of Integration Review Exercises Topics in Finance and Dynamics Interest Periods and Effective RatesContinuous CompoundingPresent ValueGeometric SeriesTotal Present ValueMortgage RepaymentsInternal Rate of ReturnA Glimpse at Difference EquationsEssentials of Differential EquationsSeparable and Linear Differential Equations Review Exercises III MULTI-VARIABLE ALGEBRA Matrix Algebra Matrices and VectorsSystems of Linear EquationsMatrix AdditionAlgebra of VectorsMatrix MultiplicationRules for Matrix MultiplicationThe TransposeGaussian EliminationGeometric Interpretation of VectorsLines and Planes Review Exercises Determinants, Inverses, and Quadratic Forms Determinants of Order 2Determinants of Order 3 Determinants in GeneralBasic Rules for DeterminantsExpansion by CofactorsThe Inverse of a MatrixA General Formula for The InverseCramer's RuleThe Leontief ModeEigenvalues and EigenvectorsDiagonalizationQuadratic Forms Review Exercises IV MULTI-VARIABLE CALCULUS Multivariable Functions Functions of Two VariablesPartial Derivatives with Two VariablesGeometric RepresentationSurfaces and DistanceFunctions of More VariablesPartial Derivatives with More VariablesConvex SetsConcave and Convex FunctionsEconomic ApplicationsPartial Elasticities Review Exercises Partial Derivatives in Use A Simple Chain RuleChain Rules for Many VariablesImplicit Differentiation Along A Level CurveLevel SurfacesElasticity of SubstitutionHomogeneous Functions of Two Variables Homogeneous and Homothetic FunctionsLinear ApproximationsDifferentialsSystems of EquationsDifferentiating Systems of Equations Review Exercises Multiple Integrals Double Integrals Over Finite RectanglesInfinite Rectangles of IntegrationDiscontinuous Integrands and Other ExtensionsIntegration Over Many Variables Review Exercises V MULTI-VARIABLE OPTIMIZATION Unconstrained Optimization Two Choice Variables: Necessary ConditionsTwo Choice Variables: Sufficient ConditionsLocal Extreme PointsLinear Models with Quadratic ObjectivesThe Extreme Value TheoremFunctions of More VariablesComparative Statics and the Envelope Theorem Review Exercises Equality Constraints The Lagrange Multiplier MethodInterpreting the Lagrange MultiplierMultiple Solution CandidatesWhy Does the Lagrange Multiplier Method Work?Sufficient ConditionsAdditional Variables and ConstraintsComparative Statics Review Exercises Linear Programming A Graphical ApproachIntroduction to Duality TheoryThe Duality TheoremA General Economic InterpretationComplementary Slackness Review Exercises Nonlinear Programming Two Variables and One ConstraintMany Variables and Inequality ConstraintsNonnegativity Constraints Review Exercises Appendix Geometry The Greek Alphabet Bibliography Solutions to the Exercises Index Publisher's Acknowledgments

Acquire the key mathematical skills you need to master and succeed in economics  Essential Mathematics for Economic Analysis, 6th edition by Sydsaeter, Hammond, Strom and Carvajal is a global best-selling text that provides an extensive introduction to all the mathematical tools you need to study economics at intermediate level.  This book has been applauded for its scope and covers a broad range of mathematical knowledge, techniques and tools, progressing from elementary calculus to more advanced topics. With a wealth of practice examples, questions and solutions integrated throughout, as well as opportunities to apply them in specific economic situations, this book will help you develop key mathematical skills as your course progresses. Key features: - Numerous exercises and worked examples throughout each chapter allow you to practise skills and improve techniques. - Review exercises at the end of each chapter test your understanding of a topic, allowing you to progress with confidence. - Solutions to exercises are provided in the book and online, showing you the steps needed to arrive at the correct answer. 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. Pearson, the world’s learning company.

Hallmark features of this title A wide range of mathematical techniques offers your students essential knowledge from theory to practice. Some of the topics studied in the book include Algebra, functions, optimisation, derivatives, and linear and non-linear programming.The text further discusses the practical application of mathematical knowledge, introducing your students to the economist way of thinking. A clear pedagogical structure supports better understanding. Numerous exercises and worked examples throughout each chapter allow students to practice skills and improve techniques.Review exercises at the end of each chapter to test your students' understanding of a topic, allowing them to progress confidently.Solutions to exercises are provided in the book and online.

New and updated features of this title Updated extensive content coverage, exercises, and worked examples NEW! A new Chapter 8 considers concave and convex functions of one variable, including results on supergradients of concave functions and subgradients of convex functions that play a key role in the theory of optimisation. NEW! A new Chapter 16 on multiple integrals. REVISED! Chapter 13 has been extended to include eigenvalues and quadratic forms. REVISED! Numerous exercises and worked examples throughout each chapter allow your students to practice skills and improve techniques. REVISED! Review exercises at the end of each chapter to test your students' understanding of a topic before they progress with confidence. A revised structure enhances student engagement NEW! Matrix algebra is introduced earlier in this edition and now precedes the chapter on multivariate calculus. This allows new tools to be used in the treatment of multivariate calculus and in the last four chapters, now devoted exclusively to optimization. NEW! The chapter on constrained optimisation has been divided to form two new chapters: Chapters 18 & 20. REVISED! Solutions to exercises are provided in the book and online, breaking down the steps needed to arrive at the correct answer.