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Description
Author
Contents
Teaching Materials
This book is a self-contained treatment of all the mathematics needed by undergraduate and beginning graduate students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra as well as easily accessible introductions to optimization and dynamics. The emphasis throughout is on intuitive argument and problem solving. All methods are illustrated by well-chosen examples and exercises selected from central areas of modern economic analysis.
The third edition of Mathematics for Economists features new sections on double integration and discrete-time dynamic programming, as well as an online solutions manual and answers to exercises. The book's careful arrangement into short chapters enables it to be used in a variety of course formats for students with and without prior knowledge of calculus, as well as for reference and self-study.
Malcolm Pemberton is a senior lecturer in the Department of Economics at University College London.
Nicholas Rau is a senior lecturer in the Department of Economics at University College London.
Nicholas Rau is a senior lecturer in the Department of Economics at University College London.
Preface
Dependence of Chapters
Answers and Solutions
The Greek Alphabet
1 LINEAR EQUATIONS
1.1 Straight line graphs
1.2 An economic application: supply and demand
1.3 Simultaneous equations
1.4 Input-output analysis
Problems on Chapter 1.
2 LINEAR INEQUALITIES
2.1 Inequalities
2.2 Economic applications
2.3 Linear programming
Problems on Chapter 2
3 SETS AND FUNCTIONS
3.1 Sets and numbers.
3.2 Functions.
3.3 Mappings.
Problems on Chapter 3.
Appendix to Chapter 3.
4 QUADRATICS, INDICES AND LOGARITHMS
4.1 Quadratic functions and equations
4.2 Maximising and minimising quadratic functions
4.3 Indices.
4.4 Logarithms.
Problems on Chapter 4.
5 SEQUENCES AND SERIES
5.1 Sequences.
5.2 Series.
5.3 Geometric progressions in economics
Problems on Chapter 5.
6 INTRODUCTION TO DIFFERENTIATION
6.1 The derivative.
6.2 Linear approximations and differentiability
6.3 Two useful rules.
6.4 Derivatives in economics
Problems on Chapter 6.
Appendix to Chapter 6.
7 METHODS OF DIFFERENTIATION
7.1 The product and quotient rules
7.2 The composite function rule
7.3 Monotonic functions.
7.4 Inverse functions.
Problems on Chapter 7.
Appendix to Chapter 7.
8 MAXIMA AND MINIMA
8.1 Critical points.
8.2 The second derivative
8.3 Optimisation.
8.4 Convexity and concavity
Problems on Chapter 8.
9 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
9.1 The exponential function
9.2 Natural logarithms.
9.3 Time in economics.
Problems on Chapter 9.
Appendix to Chapter 9.
10 APPROXIMATIONS
10.1 Linear approximations and Newton?s method
10.2 The mean value theorem
10.3 Quadratic approximations and Taylor?s theorem
10.4 Taylor series.
Problems on Chapter 10.
Appendix to Chapter 10.
11 MATRIX ALGEBRA
11.1 Vectors.
11.2 Matrices.
11.3 Matrix multiplication
11.4 Square matrices.
Problems on Chapter 11.
12 SYSTEMS OF LINEAR EQUATIONS
12.1 Echelon matrices.
12.2 More on Gaussian elimination
12.3 Inverting a matrix.
12.4 Linear dependence and rank
Problems on Chapter 12.
13 DETERMINANTS AND QUADRATIC FORMS
13.1 Determinants.
13.2 Transposition.
13.3 Inner products.
13.4 Quadratic forms and symmetric matrices
Problems on Chapter 13.
Appendix to Chapter 13.
14 FUNCTIONS OF SEVERAL VARIABLES
14.1 Partial derivatives.
14.2 Approximations and the chain rule
14.3 Production functions
14.4 Homogeneous functions
Problems on Chapter 14.
Appendix to Chapter 14.
15 IMPLICIT RELATIONS
15.1 Implicit differentiation
15.2 Comparative statics.
15.3 Generalising to higher dimensions
Problems on Chapter 15.
Appendix to Chapter 15.
16 OPTIMISATION WITH SEVERAL VARIABLES
16.1 Critical points and their classification
16.2 Global optima, concavity and convexity
16.3 Non-negativity constraints
Problems on Chapter 16.
Appendix to Chapter 16.
17 PRINCIPLES OF CONSTRAINED OPTIMISATION
17.1 Lagrange multipliers
17.2 Extensions and warnings
17.3 Economic applications
17.4 Quasi-concave functions
Problems on Chapter 17.
18 FURTHER TOPICS IN CONSTRAINED OPTIMISATION
18.1 The meaning of the multipliers
18.2 Envelope theorems.
18.3 Inequality constraints
Problems on Chapter 18.
19 INTEGRATION
19.1 Areas and integrals.
19.2 Rules of integration
19.3 Integration in economics
19.4 Numerical integration
Problems on Chapter 19.
Appendix to Chapter 19.
20 ASPECTS OF INTEGRAL CALCULUS
20.1 Methods of integration
20.2 Infinite integrals.
20.3 Differentiation under the integral sign
20.4 Double integrals.
Problems on Chapter 20.
21 INTRODUCTION TO DYNAMICS
21.1 Differential equations
21.2 Linear equations with constant coefficients
21.3 Harder first-order equations
21.4 Difference equations
Problems on Chapter 21.
22 THE CIRCULAR FUNCTIONS
22.1 Cycles, circles and trigonometry
22.2 Extending the definitions
22.3 Calculus with circular functions
22.4 Polar coordinates.
Problems on Chapter 22.
23 COMPLEX NUMBERS
23.1 The complex number system
23.2 The trigonometric form
23.3 Complex exponentials and polynomials
Problems on Chapter 23.
24 FURTHER DYNAMICS
24.1 Second-order differential equations
24.2 Qualitative behaviour
24.3 Second-order difference equations
Problems on Chapter 24.
Appendix to Chapter 24.
25 EIGENVALUES AND EIGENVECTORS
25.1 Diagonalisable matrices
25.2 The characteristic polynomial
25.3 Eigenvalues of symmetric matrices
Problems on Chapter 25.
Appendix to Chapter 25.
26 DYNAMIC SYSTEMS
26.1 Systems of difference equations
26.2 Systems of differential equations
26.3 Qualitative behaviour
26.4 Nonlinear systems.
Problems on Chapter 26.
Appendix to Chapter 26.
27 DYNAMIC OPTIMISATION IN DISCRETE TIME
27.1 The basic problem.
27.2 Variants of the basic problem
27.3 Dynamic programming.
Problems on Chapter 27.
Appendix to Chapter 27.
28 DYNAMIC OPTIMISATION IN CONTINUOUS TIME
28.1 The basic problem and its variants
28.2 The maximum principle
28.3 Two problems in resource economics
28.4 Problems with an infinite horizon
Problems on Chapter 28.
Appendix to Chapter 28.
29 INTRODUCTION TO ANALYSIS
29.1 Rigour.
29.2 More on the real number system
29.3 Sequences of real numbers
29.4 Continuity.
Problems on Chapter 29.
30 METRIC SPACES AND EXISTENCE THEOREMS
30.1 Metric spaces.
30.2 Open, closed and compact sets
30.3 Continuous mappings.
30.4 Fixed point theorems
Problems on Chapter 30.
Appendix to Chapter 30.
Notes on Further Reading
