Descripciones mejoradas de Syndetics:

It has been 20 years since the last edition of this classic text. Kevin Wainwright, a long time user of the text (British Columbia University and Simon Fraser University), has executed the perfect revision---he has updated examples, applications and theory without changing the elegant, precise presentation style of Alpha Chiang. Readers will find the wait was worthwhile.

Tabla de contenidos provista por Syndetics

• Preface(p. x)
• Part 1 Introduction
• 1 The Nature of Mathematical Economics(p. 3)
• 1.1 Mathematical versus Nonmathematical Economics(p. 3)
• 1.2 Mathematical Economics versus Econometrics(p. 5)
• 2 Economic Models(p. 7)
• 2.1 Ingredients of a Mathematical Model(p. 7)
• 2.2 The Real-Number System(p. 10)
• 2.3 The Concept of Sets(p. 11)
• 2.4 Relations and Functions(p. 17)
• 2.5 Types of Function(p. 23)
• 2.6 Functions of Two or More Independent Variables(p. 29)
• 2.7 Levels of Generality(p. 31)
• Part 2 Static (or Equilibrium) Analysis
• 3 Equilibrium Analysis in Economics(p. 35)
• 3.1 The Meaning of Equilibrium(p. 35)
• 3.2 Partial Market Equilibrium--A Linear Model(p. 36)
• 3.3 Partial Market Equilibrium--A Nonlinear Model(p. 40)
• 3.4 General Market Equilibrium(p. 46)
• 3.5 Equilibrium in National-Income Analysis(p. 52)
• 4 Linear Models and Matrix Algebra(p. 54)
• 4.1 Matrices and Vectors(p. 55)
• 4.2 Matrix Operations(p. 58)
• 4.3 Notes on Vector Operations(p. 67)
• 4.4 Commutative, Associative, and Distributive Laws(p. 76)
• 4.5 Identity Matrices and Null Matrices(p. 79)
• 4.6 Transposes and Inverses(p. 82)
• 5 Linear Models and Matrix Algebra (Continued)(p. 88)
• 5.1 Conditions for Nonsingularity of a Matrix(p. 88)
• 5.2 Test of Nonsingularity by Use of Determinant(p. 92)
• 5.3 Basic Properties of Determinants(p. 98)
• 5.4 Finding the Inverse Matrix(p. 103)
• 5.5 Cramer's Rule(p. 107)
• 5.6 Application to Market and National-Income Models(p. 112)
• 5.7 Leontief Input-Output Models(p. 115)
• 5.8 Limitations of Static Analysis(p. 124)
• Part 3 Comparative-Static Analysis
• 6 Comparative Statics and the Concept of Derivative(p. 127)
• 6.1 The Nature of Comparative Statics(p. 127)
• 6.2 Rate of Change and the Derivative(p. 128)
• 6.3 The Derivative and the Slope of a Curve(p. 131)
• 6.4 The Concept of Limit(p. 132)
• 6.5 Digression on Inequalities and Absolute Values(p. 141)
• 6.6 Limit Theorems(p. 145)
• 6.7 Continuity and Differentiability of a Function(p. 147)
• 7 Rules of Differentiation and Their Use in Comparative Statics(p. 155)
• 7.1 Rules of Differentiation for a Function of One Variable(p. 155)
• 7.2 Rules of Differentiation Involving Two or More Functions of the Same Variable(p. 159)
• 7.3 Rules of Differentiation Involving Functions of Different Variables(p. 169)
• 7.4 Partial Differentiation(p. 174)
• 7.5 Applications to Comparative-Static Analysis(p. 178)
• 7.6 Note on Jacobian Determinants(p. 184)
• 8 Comparative-Static Analysis of General-Function Models(p. 187)
• 8.1 Differentials(p. 188)
• 8.2 Total Differentials(p. 194)
• 8.3 Rules of Differentials(p. 196)
• 8.4 Total Derivatives(p. 198)
• 8.5 Derivatives of Implicit Functions(p. 204)
• 8.6 Comparative Statics of General-Function Models(p. 215)
• 8.7 Limitations of Comparative Statics(p. 226)
• Part 4 Optimization Problems
• 9 Optimization: A Special Variety of Equilibrium Analysis(p. 231)
• 9.1 Optimum Values and Extreme Values(p. 232)
• 9.2 Relative Maximum and Minimum: First-Derivative Test(p. 233)
• 9.3 Second and Higher Derivatives(p. 239)
• 9.4 Second-Derivative Test(p. 245)
• 9.5 Digression on Maclaurin and Taylor Series(p. 254)
• 9.6 Nth-Derivative Test for Relative Extremum of a Function of One Variable(p. 263)
• 10 Exponential and Logarithmic Functions(p. 268)
• 10.1 The Nature of Exponential Functions(p. 269)
• 10.2 Natural Exponential Functions and the Problem of Growth(p. 274)
• 10.3 Logarithms(p. 282)
• 10.4 Logarithmic Functions(p. 287)
• 10.5 Derivatives of Exponential and Logarithmic Functions(p. 292)
• 10.6 Optimal Timing(p. 298)
• 10.7 Further Applications of Exponential and Logarithmic Derivatives(p. 302)
• 11 The Case of More than One Choice Variable(p. 307)
• 11.1 The Differential Version of Optimization Conditions(p. 308)
• 11.2 Extreme Values of a Function of Two Variables(p. 310)
• 11.3 Quadratic Forms--An Excursion(p. 319)
• 11.4 Objective Functions with More than Two Variables(p. 332)
• 11.5 Second-Order Conditions in Relation to Concavity and Convexity(p. 337)
• 11.6 Economic Applications(p. 353)
• 11.7 Comparative-Static Aspects of Optimization(p. 364)
• 12 Optimization with Equality Constraints(p. 369)
• 12.1 Effects of a Constraint(p. 370)
• 12.2 Finding the Stationary Values(p. 372)
• 12.3 Second-Order Conditions(p. 379)
• 12.4 Quasiconcavity and Quasiconvexity(p. 387)
• 12.5 Utility Maximization and Consumer Demand(p. 400)
• 12.6 Homogeneous Functions(p. 410)
• 12.7 Least-Cost Combination of Inputs(p. 418)
• 12.8 Some Concluding Remarks(p. 431)
• Part 5 Dynamic Analysis
• 13 Economic Dynamics and Integral Calculus(p. 435)
• 13.1 Dynamics and Integration(p. 436)
• 13.2 Indefinite Integrals(p. 437)
• 13.3 Definite Integrals(p. 447)
• 13.4 Improper Integrals(p. 454)
• 13.5 Some Economic Applications of Integrals(p. 458)
• 13.6 Domar Growth Model(p. 465)
• 14 Continuous Time: First-Order Differential Equations(p. 470)
• 14.1 First-Order Linear Differential Equations with Constant Coefficient and Constant Term(p. 470)
• 14.2 Dynamics of Market Price(p. 475)
• 14.3 Variable Coefficient and Variable Term(p. 480)
• 14.4 Exact Differential Equations(p. 483)
• 14.5 Nonlinear Differential Equations of the First Order and First Degree(p. 489)
• 14.6 The Qualitative-Graphic Approach(p. 493)
• 14.7 Solow Growth Model(p. 496)
• 15 Higher-Order Differential Equations(p. 502)
• 15.1 Second-Order Linear Differential Equations with Constant Coefficients and Constant Term(p. 503)
• 15.2 Complex Numbers and Circular Functions(p. 511)
• 15.3 Analysis of the Complex-Root Case(p. 523)
• 15.4 A Market Model with Price Expectations(p. 529)
• 15.5 The Interaction of Inflation and Unemployment(p. 535)
• 15.6 Differential Equations with a Variable Term(p. 541)
• 15.7 Higher-Order Linear Differential Equations(p. 544)
• 16 Discrete Time: First-Order Difference Equations(p. 549)
• 16.1 Discrete Time, Differences, and Difference Equations(p. 550)
• 16.2 Solving a First-Order Difference Equation(p. 551)
• 16.3 The Dynamic Stability of Equilibrium(p. 557)
• 16.4 The Cobweb Model(p. 561)
• 16.5 A Market Model with Inventory(p. 566)
• 16.6 Nonlinear Difference Equations--The Qualitative-Graphic Approach(p. 569)
• 17 Higher-Order Difference Equations(p. 576)
• 17.1 Second-Order Linear Difference Equations with Constant Coefficients and Constant Term(p. 577)
• 17.2 Samuelson Multiplier-Acceleration Interaction Model(p. 585)
• 17.3 Inflation and Unemployment in Discrete Time(p. 591)
• 17.4 Generalizations to Variable-Term and Higher-Order Equations(p. 596)
• 18 Simultaneous Differential Equations and Difference Equations(p. 605)
• 18.1 The Genesis of Dynamic Systems(p. 605)
• 18.2 Solving Simultaneous Dynamic Equations(p. 608)
• 18.3 Dynamic Input-Output Models(p. 616)
• 18.4 The Inflation-Unemployment Model Once More(p. 623)
• 18.5 Two-Variable Phase Diagrams(p. 628)
• 18.6 Linearization of a Nonlinear Differential-Equation System(p. 638)
• 18.7 Limitations of Dynamic Analysis(p. 646)
• Part 6 Mathematical Programming
• 19 Linear Programming(p. 651)
• 19.1 Simple Examples of Linear Programming(p. 652)
• 19.2 General Formulation of Linear Programs(p. 661)
• 19.3 Convex Sets and Linear Programming(p. 665)
• 19.4 Simplex Method: Finding the Extreme Points(p. 671)
• 19.5 Simplex Method: Finding the Optimal Extreme Point(p. 676)
• 19.6 Further Notes on the Simplex Method(p. 682)
• 20 Linear Programming (Continued)(p. 688)
• 20.1 Duality(p. 688)
• 20.2 Economic Interpretation of a Dual(p. 696)
• 20.3 Activity Analysis: Micro Level(p. 700)
• 20.4 Activity Analysis: Macro Level(p. 709)
• 21 Nonlinear Programming(p. 716)
• 21.1 The Nature of Nonlinear Programming(p. 716)
• 21.2 Kuhn-Tucker Conditions(p. 722)
• 21.3 The Constraint Qualification(p. 731)
• 21.4 Kuhn-Tucker Sufficiency Theorem: Concave Programming(p. 738)
• 21.5 Arrow-Enthoven Sufficiency Theorem: Quasiconcave Programming(p. 744)
• 21.6 Economic Applications(p. 747)
• 21.7 Limitations of Mathematical Programming(p. 754)
• The Greek Alphabet(p. 756)
• Mathematical Symbols(p. 757)
• A Short Reading List(p. 760)
• Answers to Selected Exercise Problems(p. 763)
• Index(p. 781)