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ESSENTIAL MATHEMATICS FOR ECONOMIC ANALYSIS
An extensive introduction to all the mathematical tools an economist needs is provided in this worldwide bestseller.
"The scope of the book is to be applauded" Dr Michael Reynolds, University of Bradford
"Excellent book on calculus with several economic applications" Mauro Bambi, University of York
New to this edition:
The introductory chapters have been restructured to more logically fit with teaching.
Several new exercises have been introduced, as well as fuller solutions to existing ones.
More coverage of the history of mathematical and economic ideas has been added, as well as of the scientists who developed them.
New example based on the 2014 UK reform of housing taxation illustrating how a discontinuous function can have significant economic consequences.
The associated material in MyMathLab has been expanded and improved.
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 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 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.
Sydsaeter Essential Mathematics for Economic Analysis - 5e TOC Ch01: Essentials of Logic and Set Theory 1.1 Essentials of set theory 1.2 Some aspects of logic 1.3 Mathematical proofs 1.4 Mathematical induction Ch02: 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 Summation 2.9 Rules for sums 2. 10 Newton's binomial formula 2. 11 Double sums Ch03: Solving Equations 3.1 Solving equations 3.2 Equations and their parameters 3.3 Quadratic equations 3.4 Nonlinear equations 3.5 Using implication arrows 3.6 Two linear equations in two unknowns Ch04: Functions of One Variable 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 Ch05: 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 Ch06: Differentiation 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 The Chain Rule 6.9 Higher-order derivatives 6. 10 Exponential functions 6. 11 Logarithmic functions Ch07: Derivatives in Use 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 Elasticities 7.8 Continuity 7.9 More on limits 7. 10 The intermediate value theorem and Newton's method 7. 11 Infinite sequences 7. 12 L'Hopital's Rule Ch08: Single-Variable Optimization 8.1 Extreme points 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 Ch09: Integration 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 Ch10: Topics in Financial Mathematics 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 Ch11: Functions of Many Variables 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 Ch12: Tools for Comparative Statics 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 Ch13: Multivariable Optimization 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 The general case 13.7 Comparative statics and the envelope theorem Ch14: Constrained Optimization 14.1 The Lagrange Multiplier Method 14.2 Interpreting the Lagrange multiplier 14.3 Multiple 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 Ch15: Matrix and Vector Algebra 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 Ch16: Determinants and Inverse Matrices 16.1 Determinants of order 2 16.2 Determinants of order 3 16.3 Determinants in general 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 Ch17: Linear Programming 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