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Fundamental methods of mathematical economics / Alpha C. Chiang

Chiang, Alpha C.
Material type: materialTypeLabelBook; Format: print Publisher: New York [etc.] : McGraw-Hill, 1984Edition: 3ª ed.Description: 788 p.ISBN: 0-07-010813-7.Subject(s): Matemáticas -- Métodos
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Monografías 07. BIBLIOTECA CIENCIAS SOCIALES
518/CHI/fun (Browse shelf)   Shelving location | Bibliomaps® PREST. LIBROS 3700047148
Monografías 07. BIBLIOTECA CIENCIAS SOCIALES
518/CHI/fun (Browse shelf)   Shelving location | Bibliomaps® PREST. LIBROS 370004720X
Monografías 07. BIBLIOTECA CIENCIAS SOCIALES
518/CHI/fun (Browse shelf)   Shelving location | Bibliomaps® PREST. LIBROS 3700047264
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Enhanced descriptions from Syndetics:

The best-selling, best known text in Mathematical Economics course, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. The book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.

Bibliografía

Table of contents provided by 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)

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