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Essential mathematics for economic analysis

Author: Sydsaeter, Knut ; Hammond, PeterPublisher: Prentice Hall, 2008. ; Financial Times, 2008.Edition: 3rd ed.Language: EnglishDescription: 721 p. : Ill. ; 25 cm.ISBN: 9780273713241Type of document: BookBibliography/Index: Includes index
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Book Asia Campus
Textbook Collection (PhD)
Print HB135 .S93 2008
(Browse shelf)
900187718
Consultation only 900187718
Book Europe Campus
Main Collection
Print HB135 .S93 2008
(Browse shelf)
001194947
Available 001194947
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Includes index

Digitized

Essential Mathematics for Economic Analysis Essential Mathematics for Economic Analysis Preface ix I 4 I0 15 19 24 29 32 1 lntroductory Topics I: Algebra 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 The Real Numbers Integer Powers Rules of Algebra Fractions Fractional Powers Inequalities Intervals and Absolute Values Review Problems for Chapter 1 3.3 3.4 3.5 3.6 3.7 Double Sums A Few Aspects of Logic Mathematical Proofs Essentials of Set Theory Mathematical Induction Review Problems for Chapter 3 59 61 67 69 74 76 4 Functions of One Variable 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 79 79 80 86 89 96 99 105 112 114 120 124 2 lntroductory Topics II: Equations 2.1 2.2 2.3 2.4 2.5 How to Solve Simple Equations Equations with Parameters Quadratic Equations Linear Equations in Two Unknowns Nonlinear Equations Review Problems for Chapter 2 35 35 38 41 46 48 49 Introduction Basic Definitions Graphs of Functions Linear Functions Linear Models Quadratic Functions Polynomials Power Functions Exponential Functions Logarithmic Functions Review Problems for Chapter 4 5 Properties of Functions 5.1 5.2 5.3 5.4 5.5 127 127 132 136 143 146 3 lntroductory Topics Ill: Miscellaneous 3.1 Summation Notation 3.2 Rules for Sums. Newton's Binomial Formula 51 51 55 Shifting Graphs New Functions from Old Inverse Functions Graphs of Equations Distance in the Plane. Circles 5.6 General Functions Review Problems for Chapter 5 150 153 9 Integration 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 Indefinite Integrals Area and Definite Integrals Properties of Definite lntegrals Economic Applications Integration by Parts Integration by Substitution Infinite Intervals of Integration A Glimpse at Differential Equations Separable and Linear Differential Equations Review Problems for Chapter 9 291 6 Differentiation 6.1 Slopes of Curves 6.2 The Derivative. Tangents 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 6.1 0 Exponential Functions 6.1 1 Logarithmic Functions Review Problems for Chapter 6 155 155 157 163 165 169 174 178 184 189 194 197 203 10 Interest Rates and Present Values 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 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 Review Problems for Chapter 10 7 Derivatives in Use 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 Implicit Differentiation Economic Examples Differentiating the Inverse Linear Approximations Polynomial Approximations Taylor's Formula Why Economists Use Elasticities Continuity More on Limits Intermediate Value Theorem. Newton's Method 7.1 1 Infinite Sequences 7.12 L HBpital's Rule ' Review Problems for Chapter 7 205 205 210 21 3 21 6 22 1 224 228 232 236 244 248 250 254 1 1 Functions of Many Variables I I. I 1 1.2 11.3 11.4 11.5 11.6 11.7 1 1.8 Functions of Two Variables Partial Derivatives with Two Variables Geometric Representation Surfaces and Distance Functions of More Variables Partial Derivatives with More Variables Economic Applications Partial Elasticities Review Problems for Chapter 11 8 Single-Variable Optimization 8.1 8.2 8.3 8.4 8.5 8.6 8.7 Introduction Simple Tests for Extreme Points Economic Examples The Extreme Value Theorem Further Economic Examples Local Extreme Points Inflection Points Review Problems for Chapter 8 12 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 General Homogeneous and Homothetic Functions 12.8 Linear Approximations 12.9 Differentials 12. LO Systems of Equations 12-11 Differentiating Systems of Equations Review Problems for Chapter 12 420 423 427 432 436 44 1 444 450 15.6 15.7 15.8 15.9 Gaussian Elimination Vectors Geometric lnterpretation of Vectors Lines and Planes Review Problems for Chapter 15 16 Determinants and Inverse Matrices 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 Determinants of Order 2 Determinants of Order 3 Determinants of Order n Basic Rules for Determinants Expansion by Cofactors The Inverse of a Matrix A General Formula for the Inverse Cramer's Rule The Leontief Model Review Problems for Chapter 16 13 Multivariable Optimization 13.1 Two Variables: Necessary Conditions 13.2 Two Variables: Sufficient Conditions 13.3 Local Extreme Points 13.4 Linear Models with Qyadratic 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 17 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 Review Problems for Chapter 17 14 Constrained Optimization 489 14.1 14.2 14.3 14.4 The Lagrange Multiplier Method Interpreting the Lagrange Multiplier Several Solution Candidates Why the Lagrange Multiplier Method Works 14.5 Sufficient Conditions 14.6 More Variables and More Constraints 14.7 Comparative Statics 14.8 Nonlinear Programming: A Simple Case 14.9 More on Nonlinear Programming Review Problems for Chapter 14 489 496 499 501 505 508 5 14 5 17 523 530 Appendix: Geometry The Greek Alphabet Answers to the Problems Index 15 Matrix and Vector Algebra 15.1 15.2 15.3 15.4 15.5 Systems of Linear Equations Matrices and Matrix Operations Matrix Multiplication Rules for Matrix Multiplication The Transpose 533 533 537 540 545 55 1

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