Cover image for Mathematics for economics
Title:
Mathematics for economics
Author:
Hoy, Michael, 1953 September 22-
Edition:
Second edition.
Publication Information:
Cambridge, Mass. : MIT Press, [2001]

©2001
Physical Description:
xiv, 1129 pages : illustrations ; 24 cm
General Note:
Includes index.
Language:
English
ISBN:
9780262082945

9780262582070
Format :
Book

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Summary

Summary

This paperback edition is not available in the U.S. and Canada. This book offers a comprehensive presentation of the mathematics required to tackle problems in economic analysis. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. To develop the student's problem-solving skills, the book works through a large number of examples and economic applications. The second edition includes simple game theory, l'Hôpital's rule, Leibniz's rule, and a more intuitive development of the Hamiltonian. An instructor's manual is available.


Table of Contents

Prefacep. xiii
I Introduction and Fundamentals
1 Introductionp. 3
1.1 What Is an Economic Model?p. 3
1.2 How to Use This Bookp. 8
1.3 Conclusionp. 9
2 Review of Fundamentalsp. 11
2.1 Sets and Subsetsp. 11
2.2 Numbersp. 23
2.3 Some Properties of Point Sets in Rnp. 33
2.4 Functionsp. 43
2.5 Proof, Necessary and Sufficient Conditions *p. 60
3 Sequences, Series, and Limitsp. 67
3.1 Definition of a Sequencep. 67
3.2 Limit of a Sequencep. 70
3.3 Present-Value Calculationsp. 75
3.4 Properties of Sequencesp. 84
3.5 Seriesp. 89
II Univariate Calculus and Optimization
4 Continuity of Functionsp. 115
4.1 Continuity of a Function of One Variablep. 115
4.2 Economic Applications of Continuous and Discontinuous Functionsp. 125
4.3 Intermediate-Value Theoremp. 143
5 The Derivative and Differential for Functions of One Variablep. 155
5.1 Definition of a Tangent Linep. 155
5.2 Definition of the Derivative and the Differentialp. 162
5.3 Conditions for Differentiabilityp. 169
5.4 Rules of Differentiationp. 175
5.5 Higher-Order Derivatives: Concavity and Convexity of a Functionp. 208
5.6 Taylor Series Formula and the Mean-Value Theoremp. 218
6 Optimization of Functions of One Variablep. 227
6.1 Necessary Conditions for Unconstrained Maxima and Minimap. 227
6.2 Second-Order Conditionsp. 253
6.3 Optimization over an Intervalp. 265
III Linear Algebra
7 Systems of Linear Equationsp. 279
7.1 Solving Systems of Linear Equationsp. 279
7.2 Linear Systems in n-Variablesp. 293
8 Matricesp. 317
8.1 General Notationp. 317
8.2 Basic Matrix Operationsp. 324
8.3 Matrix Transpositionp. 340
8.4 Some Special Matricesp. 345
9 Determinants and the Inverse Matrixp. 353
9.1 Defining the Inversep. 353
9.2 Obtaining the Determinant and Inverse of a 3 x 3 Matrixp. 370
9.3 The Inverse of an n x n Matrix and Its Propertiesp. 376
9.4 Cramer's Rulep. 386
10 Some Advanced Topics in Linear Algebra *p. 405
10.1 Vector Spacesp. 405
10.2 The Eigenvalue Problemp. 421
10.3 Quadratic Formsp. 436
IV Multivariate Calculus
11 Calculus for Functions of n-Variablesp. 455
11.1 Partial Differentiationp. 455
11.2 Second-Order Partial Derivativesp. 469
11.3 The First-Order Total Differentialp. 477
11.4 Curvature Properties: Concavity and Convexityp. 498
11.5 More Properties of Functions with Economic Applicationsp. 513
11.6 Taylor Series Expansion *p. 534
12 Optimization of Functions of n-Variablesp. 545
12.1 First-Order Conditionsp. 545
12.2 Second-Order Conditionsp. 560
12.3 Direct Restrictions on Variablesp. 569
13 Constrained Optimizationp. 585
13.1 Constrained Problems and Approaches to Solutionsp. 585
13.2 Second-Order Conditions for Constrained Optimizationp. 616
13.3 Existence, Uniqueness, and Characterization of Solutionsp. 622
14 Comparative Staticsp. 631
14.1 Introduction to Comparative Staticsp. 631
14.2 General Comparative-Statics Analysisp. 643
14.3 The Envelope Theoremp. 660
15 Concave Programming and the Kuhn-Tucker Conditionsp. 677
15.1 The Concave-Programming Problemp. 677
15.2 Many Variables and Constraintsp. 686
V Integration and Dynamic Methods
16 Integrationp. 701
16.1 The Indefinite Integralp. 701
16.2 The Riemann (Definite) Integralp. 709
16.3 Properties of Integralsp. 721
16.4 Improper Integralsp. 733
16.5 Techniques of Integrationp. 742
17 An Introduction to Mathematics for Economic Dynamicsp. 753
17.1 Modeling Timep. 754
18 Linear, First-Order Difference Equationsp. 763
18.1 Linear, First-Order, Autonomous Difference Equationsp. 763
18.2 The General, Linear, First-Order Difference Equationp. 780
19 Nonlinear, First-Order Difference Equationsp. 789
19.1 The Phase Diagram and Qualitative Analysisp. 789
19.2 Cycles and Chaosp. 799
20 Linear, Second-Order Difference Equationsp. 811
20.1 The Linear, Autonomous, Second-Order Difference Equationp. 811
20.2 The Linear, Second-Order Difference Equation with a Variable Termp. 838
21 Linear, First-Order Differential Equationsp. 849
21.1 Autonomous Equationsp. 849
21.2 Nonautonomous Equationsp. 870
22 Nonlinear, First-Order Differential Equationsp. 879
22.1 Autonomous Equations and Qualitative Analysisp. 879
22.2 Two Special Forms of Nonlinear, First-Order Differential Equationsp. 888
23 Linear, Second-Order Differential Equationsp. 897
23.1 The Linear, Autonomous, Second-Order Differential Equationp. 897
23.2 The Linear, Second-Order Differential Equation with a Variable Termp. 919
24 Simultaneous Systems of Differential and Difference Equationsp. 929
24.1 Linear Differential Equation Systemsp. 929
24.2 Stability Analysis and Linear Phase Diagramsp. 951
24.3 Systems of Linear Difference Equationsp. 976
25 Optimal Control Theoryp. 999
25.1 The Maximum Principlep. 1002
25.2 Optimization Problems Involving Discountingp. 1014
25.3 Alternative Boundary Conditions on x(T)p. 1026
25.4 Infinite-Time Horizon Problemsp. 1040
25.5 Constraints on the Control Variablep. 1053
25.6 Free-Terminal-Time Problems (T Free)p. 1063
Appendix: Complex Numbers and Circular Functionsp. 1081
Answersp. 1091
Indexp. 1123