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Last Edition
ISBN 13: 9781292074610
Imprint: Pearson Education Limited
Language: English
Authors: Knut Sydsaeter
Pub Date: 10/2016
Pages: 832
Illus: Illustrated
Weight: 1,380.00 grams
Size: h 187 x 246 mm
Product Type: Softcover
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- • 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. .
- 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
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