Mathematics For Economists, 4/e

Contents:

Preface • Dependence of Chapters • Answers and Solutions • The Greek Alphabet

Chapter 1: LINEAR EQUATIONS • Straight line graphs • An economic application: supply and demand • Simultaneous equations • Input-output analysis • Problems on Chapter 1
Chapter 2: LINEAR INEQUALITIES • Inequalities • Economic applications • Linear programming • Problems on Chapter 2
Chapter 3: SETS AND FUNCTIONS • Sets • Real numbers • Functions • Mappings • Problems on Chapter 3
Chapter 4: QUADRATICS, INDICES AND LOGARITHMS • Quadratic functions and equations • Maximising and minimising quadratic functions • Indices • Logarithms • Problems on Chapter 4
Chapter 5: SEQUENCES, SERIES AND LIMITS • Sequences • Series • Geometric progressions in economics • Limits and continuity • Problems on Chapter 5
Chapter 6: INTRODUCTION TO DIFFERENTIATION • The derivative. • Linear approximations and differentiability. • Two useful rules • Derivatives in economics • Problems on Chapter 6
Chapter 7: METHODS OF DIFFERENTIATION • The product and quotient rules • The composite function rule • Monotonic functions • Inverse functions • Problems on Chapter 7 • Appendix to Chapter 7
Chapter 8: MAXIMA AND MINIMA • Critical point • The second derivative • Optimisation • Convexity and concavity • Problems on Chapter 8
Chapter 9: EXPONENTIAL AND LOGARITHMIC FUNCTIONS • The exponential function • Natural logarithms • Time in economics • Problems on Chapter 9 • Appendix to Chapter 9
Chapter 10: APPROXIMATIONS • Linear approximations and Newton's method • The mean value theorem • Quadratic approximations and Taylor's theorem • Taylor and Maclaurin series • Problems on Chapter 10 • Appendix to Chapter 10
Chapter 11: MATRIX ALGEBRA • Vectors • Matrices. • Matrix multiplication • Square matrices • Problems on Chapter 11
Chapter 12: SYSTEMS OF LINEAR EQUATIONS • Echelon matrices • More on Gaussian elimination • Inverting a matrix • Linear dependence and rank • Problems on Chapter 12
Chapter 13: DETERMINANTS AND QUADRATIC FORMS • Determinants • Transposition • Inner products • Quadratic forms and symmetric matrices • Problems on Chapter 13 • Appendix to Chapter 13
Chapter 14: FUNCTIONS OF SEVERAL VARIABLES • Partial derivatives • Approximations and the chain rule • An economic application: production functions • Homogeneous functions • Problems on Chapter 14 • Appendix to Chapter 14
Chapter 15: IMPLICIT RELATIONS • Implicit differentiation • Comparative statics • Generalising to higher dimensions • Problems on Chapter 15 • Appendix to Chapter 15
Chapter 16: OPTIMISATION WITH SEVERAL VARIABLES • Critical points and their classification • Global optima, concavity and convexity • Non-negativity constraints • Problems on Chapter 16 • Appendix to Chapter 16
Chapter 17: PRINCIPLES OF CONSTRAINED OPTIMISATION • Lagrange multipliers • Extensions and warnings • Economic applications • Quasi-concave functions • Problems on Chapter 17
Chapter 18: FURTHER TOPICS IN CONSTRAINED OPTIMISATION • The meaning of the multipliers • Envelope theorems • Non-negativity constraints again • Inequality constraints • Problems on Chapter 18
Chapter 19: INTEGRATION • Areas and integrals • Rules of integration • Integration in economics • Numerical integration • Problems on Chapter • Appendix to Chapter 19
Chapter 20: ASPECTS OF INTEGRAL CALCULUS • Methods of integration • Infinite integrals • Differentiation under the integral sign • Double integrals • Problems on Chapter 20
Chapter 21: PROBABILITY • Events and their probabilities • Conditional probability and independence • Random variables • The binomial, Poisson and exponential distributions • Problems on Chapter 21 • Appendix to Chapter 21
Chapter 22: EXPECTATION • Expected value • The variance and higher moments • Two or more random variables • Random samples and limit theorems • Problems on Chapter 22 • Appendix to Chapter 22
Chapter 23: INTRODUCTION TO DYNAMICS • Differential equations • Linear equations with constant coefficients • Harder first-order equations • Difference equations • Problems on Chapter 23
Chapter 24: THE CIRCULAR FUNCTIONS • Cycles, circles and trigonometry • Extending the definitions • Calculus with circular functions • Polar coordinates • Problems on Chapter 24
Chapter 25: COMPLEX NUMBERS • The complex number system • The trigonometric form • Complex exponentials and polynomials • Problems on Chapter 25
Chapter 26: FURTHER DYNAMICS • Second-order differential equations • Qualitative behaviour • Second-order difference equations • Problems on Chapter 26 • Appendix to Chapter 26
Chapter 27: EIGENVALUES AND EIGENVECTORS • Diagonalisable matrices • The characteristic polynomial • Eigenvalues of symmetric matrices • Problems on Chapter 27
Chapter 28: DYNAMIC SYSTEMS • Systems of difference equations • Systems of differential equations • Qualitative behaviour • Non-linear systems • Problems on Chapter 28 • Appendix to Chapter 28
Chapter 29: DYNAMIC OPTIMISATION IN DISCRETE TIME • The basic problem • Variants of the basic problem • Dynamic programming • Problems on Chapter 29 • Appendix to Chapter 29
Chapter 30: DYNAMIC OPTIMISATION IN CONTINUOUS TIME • The basic problem and its variants • The maximum principle • Two applications to resource economics • Problems with an infinite horizon • Problems on Chapter 30 • Appendix to Chapter 30
Chapter 31: INTRODUCTION TO ANALYSIS • Rigour • More on the real number system • Sequences of real numbers • More on limits and continuity • Problems on Chapter 31
Chapter 32: METRIC SPACES AND EXISTENCE THEOREMS • Metric spaces • Open, closed and compact sets • Continuous mappings • Fixed point theorems • Problems on Chapter 32 • Appendix to Chapter 32

Notes on Further Reading
Index

 

About the Authors:

Malcolm Pemberton is Senior Lecturer in Economics at University College London.
Nicholas Ra is Honorary Senior Lecturer in Economics at University College London.