## Schaum's outline of theory and problems of introduction to mathematical economics

Author: Dowling, Edward T. Publisher: McGraw-Hill, 2001.Edition: 3rd ed.Language: EnglishDescription: 523 p. ; 28 cm.ISBN: 9780071358965Type of document: BookBibliography/Index: Includes indexItem type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|

Asia Campus Textbook Collection (PhD) |
HB135 .D69 2001
(Browse shelf) 900183895 |
Consultation only | 900183895 |

Includes index

Digitized

Schaum's Outline of Introduction to Mathematical Economics Schaum's Outline of Introduction to Mathematical Economics CHAPTER Review 1 1.1 Exponents. 1.2 Polynomials. 1.3 Equations: Linear and Quadratic. l.4 Simultaneous Equations. 1.5 Functions. 1.6 Graphs, Slopes, and Intercepts. CHAPTER 2 Economic Applications of Graphs and Equations 2.1 Isocost Lines. 2.2 Supply and Demand Analysis. 2.3 Income Determination Models. 2.4 IS-LM Analysis. 14 CHAPTER 3 The Derivative and the Rules of Differentiation 3.1 Limits. 3.2 Continuity. 3.3 The Slope of a Curvilinear Function. 3.4 The Derivative. 3.5 Differentiability and Continuity. 3.6 Derivative Notation. 3.7 Rules of Differentiation. 3.8 Higher-Order Derivatives 3.9 Implicit Differentiation. 32 CHAPTER 4 Uses of the Derivative i n Mathematics and Economics 58 4.1 Increasing and Decreasing Functions. 4.2 Concavity and Convexity. 4.3 Relative Extrema. 4.4 Inflection Points. 4.5 Optimization of Functions. 4.6 Successive-DerivativeTest for Optimization. 4.7 Marginal Concepts. 4.8 Optimizing Economic Functions. 4.9 Relationship among Total, Marginal, and Average Concepts. CHAPTER 5 Calculus of Multivariable Functions 5.1 Functions of Several Variables and Partial Derivatives. 5.2 Rules of Partial Differentiation. 5.3 Second-Order Partial Derivatives. 5.4 Optimization of Multivariable Functions. 5.5 Constrained Optimization with Lagrange Multipliers. 5.6 Significance of the Lagrange Multiplier. 5.7 Differentials. 5.8 Total and Partial Differentials. 5.9 Total Derivatives. 5.10 Implicit and Inverse Function Rules. 82 CHAPTER 6 Calculus of Multivariable Functions i n Economics 110 6.1 Marginal Productivity. 6.2 Income Determination Multipliers and Comparative Statics. 6.3 Income and Cross Price Elasticities of Demand. 6.4 Differentials and Incremental Changes. 6.5 Optimization of Multivariable Functions in Economics. 6.6 Constrained Optimization of Multivariable Functions in Economics. 6 7 Homogeneous Production . Functions. 68 Returns to Scale. 69 Optimization of . . Cobb-Douglas Production Functions. 6 1 Optimization of .0 Constant Elasticity of Substitution Production Functions. CHAPTER 7 Exponential and Logarithmic Functions 71 Exponential Functions. 72 Logarithmic Functions. . . 73 Properties of Exponents and Logarithms. 74 Natural . . Exponential and Logarithmic Functions. 75 Solving Natural Exponential and Logarithinic Functions. 76 Logarithmic . Transformation of Nonlinear Functions. 146 CHAPTER Exponential and Logarithmic Functions i n Economics 81 Interest Compounding. 82 Effective vs. Nominal Rates of . . Interest. 83 Discounting. 84 Converting Exponential to . . Natural Exponential Functions. 85 Estimating Growth Rates . from Data Points. 160 Differentiation of Exponential and Logarithmic Functions 91 Rules of Differentiation. 92 Higher-Order Derivatives. . . 93 Partial Derivatives. 94 Optimization of Exponential and . . Logarithmic Functions. 95 Logarithmic Differentiation. . 96 Alternative Measures of Growth. 97 Optimal Timing. . . 98 Derivation of a Cobb-Douglas Demand Function Using a . Logarithmic Transformation. 173 The Fundamentals of Linear (or Matrix) Algebra 1. The Role of Linear Algebra. 1. Definitions and 01 02 199 03 Terms. 1 . Addition and Subtraction of Matrices. 1 . Scalar Multiplication. 1 . Vector Multiplication. 04 05 1. Multiplication of Matrices. 1 . Commutative, Associative, 06 07 and Distributive Laws in Matrix Algebra. 1. Identity and 08 Null Matrices. 1 . Matrix Expression of a System of Linear 09 Equations. CHAPTER 11 Matrix Inversion 1 . Determinants and Nonsingplarity. 1. Third-Order 11 12 Determinants. 1. Minors and Cofactors. 1 . Laplace 13 14 Expansion and Higher-Order Determinants. 1L5 Properties of a Determinant. 1. Cofactor and Adjoint Matrices. 16 1 . Inverse Matrices. l . Solving Linear Equations with the 17 l8 Inverse. 1. Cramer's Rule for Matrix Solutions. l9 224 CHAPTE Special Determinants and Matrices and Their Use i n Economics 12.1 The Jacobian. 12.2 The Hessian. 12.3 The Discriminant. 12.4 Higher-Order Hessians. 12.5 The Bordered Hessian for Constrained Optimization. 12.6 Input-Output Analysis. 12.7 Characteristic Roots and Vectors (Eigenvalues, Eigenvectors). 254 R Comparative Statics and Concave Programming 13.1 Introduction to Comparative Statics. 13.2 Comparative Statics with One Endogenous Variable. 13.3 Comparative Statics with More Than One Endogenous Variable. 13.4 Comparative Statics for Optimization Problems. 13.5 Comparative Statics Used in Constrained Optimization. 13.6 The Envelope Theorem. 13.7 Concave Programming and Inequality Constraints. 284 APTER 14 Integral Calculus: The Indefinite Integral 14.1 Integration. 14.2 Rules of Integration. 14.3 Initial Conditions and Boundary Conditions. 14.4 Integration by Substitution. 14.5 Integration by Parts. 14.6 Economic Applications. 326 ER 15 Integral Calculus: The Definite Integral 342 15.1 Area Under a Curve. 15.2 The Definite Integral. 15.3 The Fundamental Theorem of Calculus. 15.4 Properties of Definite Integrals. 15.5 Area Between Curves. 15.6 Improper Integrals. 15.7 L'HBpital's Rule. 15.8 Consumers' and Producers' Surplus. 15.9 The Definite Integral and Probability. First-Order Differential Equations 362 16.1 Definitions and Concepts. 16.2 General Formula for First-Order Linear Differential Equations. 16.3 Exact Differential Equations and Partial Integration. 16.4 Integrating Factors. 16.5 Rules for the Integrating Factor. 16.6 Separation of Variables. 16.7 Economic Applications. 16.8 Phase Diagrams for Differential Equations. CHAPTER 17 First-Order Difference Equations 17.1 Definitions and Concepts. 17.2 General Formula for First-Order Linear Difference Equations. 17.3 Stability Conditions. 17.4 Lagged Income Determination Model. 17.5 The Cobweb Model. 17.6 The Harrod Model. 17.7 Phase Diagrams for Difference Equations. \ 391 CHAPTER 18 Second-Order Differential'Equations and Difference Equations 1 . Second-Order Differential Equations. 1 . Second-Order 81 82 83 Difference Equations. 1 . Characteristic Roots. 1 . Conjugate Complex Numbers. 1 . Trigonometric 84 85 86 Functions. 1 . Derivatives of Trigonometric Functions. 1 . Transformation of Imaginary and Complex Numbers. 87 1 . Stability Conditions. 88 408 Simultaneous Differential and Difference Equations 428 1 . Matrix Solution of Simultaneous Differential Equations, 91 Part 1. 1 . Matrix Solution of Simultaneous Differential 92 Equations, Part 2. 1 . Matrix Solution of Simultaneous 93 94 Difference Equations, Part 1. 1 . Matrix Solution of Simultaneous Difference Equations, Part 2. 1. Stability and 95 Phase Diagrams for Simultaneous Differential Equations. CHAPTER 20 The Calculus of Variations 2 . Dynamic Optimization. 2 . Distance Between l k o 01 02 Points on a Plane. 2 . Euler's Equation and the Necessary 03 Condition for Dynamic Optimization. 2 . Finding Candidates 04 for Extremals. 2 . The Sufficiency Conditions for the 05 Calculus of Variations. 2 . Dynamic Optimization Subject to 06 Functional Constraints. 2 . Variational Notation. 07 2 . Applications to Economics. 08 460 CHAPTER 21 Optimal Control Theory 2 . Terminology. 2 . The Hamiltonian and the Necessary 11 12 Conditions for Maximization in Optimal Control Theory. 2. Sufficiency Conditions for Maximization in Optimal 13 Control. 2 . Optimal Control Theory with a Free 14 l5 Endpoint. 2. Inequality Constraints in the Endpoints. 2 . The Current-Valued Hamiltonian. 16 493 Index

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