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Essential Mathematics for Economic Analysis

Essential Mathematics for Economic Analysis

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Provide your students with the key mathematical tools to master Economics.

Essential Mathematics for Economic Analysis will support your teaching as you provide your students with all the mathematical tools necessary to study Economics.

The plethora of features and practice examples in this edition will allow your students to excel in their course.

Knut Sydsaeter (1937-2012) was Emeritus Professor of Mathematics in the Economics Department at the University of Oslo, where he had taught mathematics to economists for over 45 years.

Peter Hammond is currently a 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 the universities of Oxford and Essex.

Arne Strøm is Associate Professor Emeritus at the University of Oslo and has extensive experience in teaching mathematics to economists at the University Department of Economics.

Andrés Carvajal is an Associate Professor in the Department of Economics at the University of California, Davis.

Preface

I PRELIMINARIES

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

    Review Exercises

    2.  

  2. 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

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

    Review Exercises

  4. Functions of One Variable
       

    • Introduction
    • Definitions
    • Graphs of Functions
    • Linear Functions
    • Linear Models
    • Quadratic Functions
    • Polynomials
    • Power Functions
    • Exponential Functions
    • Logarithmic Functions

      •  

    Review Exercises

  5. 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

    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.

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

    Essential Mathematics for Economic Analysis, 6th edition by Sydsaeter, Hammond, Strøm, and Carvajal is a global best-selling text providing an extensive introduction to all the mathematical resources you need to study economics at an intermediate level.

    This book has been applauded for covering a broad range of mathematical knowledge, techniques, and tools, progressing from elementary calculus to more advanced topics.

    With a plethora of practice examples, questions, and solutions integrated throughout, this latest edition provides you a wealth of opportunities to apply them in specific economic situations, helping you develop key mathematical skills as your course progresses.

    Key features:

    • Numerous exercisesand worked examples throughout each chapter allow you to practice skills and improve techniques.
    • Review exercisesat the end of each chapter test your understanding of a topic, allowing you to progress with confidence.
    • Solutionsto exercises are provided in the book and online, showing you the steps needed to arrive at the correct answer.

    Pair this text with MyLab® Math

    MyLab® is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyMathLab personalises the learning experience and improves results for each student.

    If you would like to purchase both the physical text and MyMathLab, search for:

    9781292359342 Essential Mathematics for Economic Analysis, 6th edition with MyMathLab

    Package consists of:

    • 9781292359281 Essential Mathematics for Economic Analysis, 6th edition
    • 9781292359311 Essential Mathematics for Economic Analysis, 6th edition MyMathLab
    • 9781292359335 Essential Mathematics for Economic Analysis, 6th edition Pearson eText

    MyLab® Math is not included. Students, if MyLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

    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.

    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.

    Additional information

    Dimensions 1.50 × 7.40 × 9.70 in
    Imprint

    Format

    ISBN-13

    ISBN-10

    Author

    , , ,

    Subjects

    economics, higher education, business and economics, Quantitative Business, Mathematical Economics