Schaum's outline of theory and problems of introduction to mathematical economics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1992
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Schaum's outline series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Frühere Aufl. u.d.T.: Dowling, Edward T.: Schaum's outline of theory and problems of mathematics for economists |
| Beschreibung: | IX, 485 S. |
| ISBN: | 0070176744 |
Internformat
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| 245 | 1 | 0 | |a Schaum's outline of theory and problems of introduction to mathematical economics |c Edward T. Dowling |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1992 | |
| 300 | |a IX, 485 S. | ||
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Datensatz im Suchindex
| _version_ | 1804125960436449280 |
|---|---|
| adam_text | Contents
Chapter 1 REVIEW 1
1.1 Exponents 1
1.2 Polynomials 2
1.3 Factoring 3
1.4 Equations: Linear and Quadratic 3
1.5 Completing the Square 4
1.6 Simultaneous Equations 5
1.7 Functions 6
1.8 Graphs, Slopes, and Intercepts 7
1.9 Graphs of Nonlinear Functions 8
Chapter 2 ECONOMIC APPLICATIONS OF GRAPHS AND EQUATIONS 20
2.1 Isocost Lines 20
2.2 Supply and Demand Analysis 20
2.3 Income Determination Models 21
2.4 IS LM Analysis 22
2.5 Production Possibilities Frontiers 22
Chapter 3 THE DERIVATIVE AND THE RULES OF DIFFERENTIATION 39
3.1 Limits 39
3.2 Continuity 40
3.3 The Slope of a Curvilinear Function 41
3.4 The Derivative 42
3.5 Differentiability and Continuity 43
3.6 Derivative Notation 43
3.7 Rules of Differentiation 44
3.8 Higher Order Derivatives 46
3.9 Implicit Differentiation 47
Chapter 4 USES OF THE DERIVATIVE IN MATHEMATICS
AND ECONOMICS 65
4.1 Increasing and Decreasing Functions 65
4.2 Concavity and Convexity 65
4.3 Relative Extrema 66
4.4 Inflection Points 67
4.5 Curve Sketching 67
4.6 Optimization of Functions 68
4.7 Marginal Concepts 69
4.8 Optimizing Economic Functions 70
4.9 Price Elasticity of Demand and Supply 70
4.10 Relationship among Total, Marginal, and Average Concepts 72
v
vi CONTENTS
Chapter 5 CALCULUS OF MULTIVARIABLE FUNCTIONS 100
5.1 Functions of Several Variables and Partial Derivatives 100
5.2 Rules of Partial Differentiation 101
5.3 Second Order Partial Derivatives 102
5.4 Optimization of Multivariable Functions 103
5.5 Constrained Optimization with Lagrange Multipliers 105
5.6 Significance of the Lagrange Multiplier 106
5.7 Differentials 106
5.8 Total and Partial Differentials 107
5.9 Total Derivatives 107
5.10 Implicit and Inverse Function Rules 109
Chapter 6 CALCULUS OF MULTIVARIABLE FUNCTIONS IN ECONOMICS 127
6.1 Marginal Productivity 127
6.2 Income Determination Multipliers 127
6.3 Partial Elasticities 128
6.4 Differentials and Incremental Changes 129
6.5 Optimization of Multivariable Functions in Economics 130
6.6 Constrained Optimization of Multivariable Functions in Economics 131
6.7 Inequality Constraints 132
6.8 Homogeneous Production Functions 133
6.9 Returns to Scale 133
6.10 Optimization of Cobb Douglas Production Functions 134
6.11 Optimization of Constant Elasticity of Substitution Production Functions 135
Chapter 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 162
7.1 Exponential Functions 162
7.2 Logarithmic Functions 162
7.3 Properties of Exponents and Logarithms 164
7.4 Natural Exponential and Logarithmic Functions 164
7.5 Solving Natural Exponential and Logarithmic Functions 165
7.6 Logarithmic Transformation of Nonlinear Functions 166
Chapter 8 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
IN ECONOMICS 176
8.1 Interest Compounding 176
8.2 Effective vs. Nominal Rates of Interest 177
8.3 Discounting 177
8.4 Discounting a Future Stream of Income 178
8.5 Converting Exponential to Natural Exponential Functions 178
8.6 Estimating Growth Rates from Data Points 180
Chapter 9 DIFFERENTIATION OF EXPONENTIAL AND LOGARITHMIC
FUNCTIONS 190
9.1 Rules of Differentiation 190
9.2 Higher Order Derivatives 192
9.3 Partial Derivatives 193
9.4 Optimization of Exponential and Logarithmic Functions 193
9.5 Logarithmic Differentiation 194
CONTENTS vii
9.6 Alternative Measures of Growth 195
9.7 Optimal Timing 195
9.8 Derivation of a Cobb Douglas Demand Function Using a
Logarithmic Transformation 196
Chapter 10 THE FUNDAMENTALS OF LINEAR (OR MATRIX) ALGEBRA .... 215
10.1 The Role of Linear Algebra 215
10.2 Definitions and Terms 215
10.3 Addition and Subtraction of Matrices 216
10.4 Scalar Multiplication 217
10.5 Vector Multiplication 217
10.6 Multiplication of Matrices 218
10.7 Commutative, Associative, and Distributive Laws in
Matrix Algebra 219
10.8 Identity and Null Matrices 220
10.9 Matrix Expression of a System of Linear Equations 221
10.10 Row Operations 222
10.11 Augmented Matrix 222
10.12 Gaussian Method of Solving Linear Equations 223
Chapter 11 MATRIX INVERSION 244
11.1 Determinants and Nonsingularity 244
11.2 Third Order Determinants 244
11.3 Minors and Cofactors 246
11.4 Laplace Expansion and Higher Order Determinants 246
11.5 Properties of a Determinant 247
11.6 Cofactor and Adjoint Matrices 247
11.7 Inverse Matrices 248
11.8 Solving Linear Equations with the Inverse 249
11.9 Cramer s Rule for Matrix Solutions 250
11.10 The Gaussian Method of Inverting a Matrix 251
Chapter 12 SPECIAL DETERMINANTS AND MATRICES AND THEIR
USE IN ECONOMICS 280
12.1 TheJacobian 280
12.2 TheHessian 281
12.3 The Discriminant 281
12.4 Higher Order Hessians 282
12.5 The Bordered Hessian for Constrained Optimization 283
12.6 Derivation of a Marshallian Demand Function 285
12.7 Input Output Analysis 286
12.8 Characteristic Roots and Vectors (Eigenvalues, Eigenvectors) 287
12.9 Transformation Matrix 289
Chapter 13 LINEAR PROGRAMMING: A GRAPHIC APPROACH 317
13.1 Graphic Solutions 317
13.2 The Extreme Point Theorem 318
13.3 Slack and Surplus Variables 319
13.4 The Basis Theorem 320
viii CONTENTS
Chapter 14 LINEAR PROGRAMMING: THE SIMPLEX ALGORITHM 331
14.1 Simplex Algorithm: Maximization 331
14.2 Marginal Value or Shadow Pricing 333
14.3 Simplex Algorithm: Minimization 334
Chapter 75 LINEAR PROGRAMMING: THE DUAL 347
15.1 TheDual 347
15.2 Rules of Transformation to Obtain the Dual 347
15.3 The Dual Theorems 348
15.4 Advantages of the Dual 349
15.5 Shadow Prices in the Dual 350
15.6 Shadow Prices and the Lagrangian Multiplier 350
Chapter 16 INTEGRAL CALCULUS: THE INDEFINITE INTEGRAL 357
16.1 Integration 357
16.2 Rules of Integration 357
16.3 Initial Conditions and Boundary Conditions 359
16.4 Integration by Substitution 359
16.5 Integration by Parts 360
16.6 Economic Applications 362
Chapter 17 INTEGRAL CALCULUS: THE DEFINITE INTEGRAL 373
17.1 Area under a Curve 373
17.2 The Definite Integral 373
17.3 The Fundamental Theorem of Calculus 374
17.4 Properties of Definite Integrals 374
17.5 Area between Curves 376
17.6 Improper Integrals 376
17.7 L Hopital s Rule 377
17.8 Present Value of Cash Flows 378
17.9 Consumers and Producers Surplus 378
17.10 The Definite Integral and Probability 379
Chapter 18 DIFFERENTIAL EQUATIONS 392
18.1 Definitions and Concepts 392
18.2 General Formula for First Order Linear Differential
Equations 392
18.3 Exact Differential Equations and Partial Integration 394
18.4 Integrating Factors 395
18.5 Rules for the Integrating Factor 395
18.6 Separation of Variables 395
18.7 Bernoulli Equations 397
18.8 Economic Applications 397
Chapter 19 DIFFERENCE EQUATIONS 418
19.1 Definitions and Concepts 418
19.2 General Formula for First Order Linear Difference
Equations 4jg
CONTENTS ix
19.3 Stability Conditions 419
19.4 Lagged Income Determination Model 420
19.5 The Cobweb Model 421
19.6 The Harrod Model 422
Chapter 20 SECOND ORDER DIFFERENTIAL EQUATIONS AND
DIFFERENCE EQUATIONS 431
20.1 Second Order Differential Equations 431
20.2 Second Order Difference Equations 432
20.3 Characteristic Roots 433
20.4 Conjugate Complex Numbers 434
20.5 Trigonometric Functions 434
20.6 Derivatives of Trigonometric Functions 436
20.7 Transformation of Imaginary and Complex Numbers 436
20.8 Stability Conditions 437
Chapter 21 THE CALCULUS OF VARIATIONS 449
21.1 Dynamic Optimization 449
21.2 Distance between Two Points on a Plane 449
21.3 Euler s Equation and Conditions for Dynamic Optimization 450
21.4 Finding Candidates for Extremals 452
21.5 Dynamic Optimization Subject to Functional Constraints 453
21.6 Variational Notation 455
21.7 Applications to Economics 456
INDEX 477
|
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| indexdate | 2024-07-09T18:09:51Z |
| institution | BVB |
| isbn | 0070176744 |
| language | English |
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| physical | IX, 485 S. |
| publishDate | 1992 |
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| publisher | McGraw-Hill |
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| series2 | Schaum's outline series |
| spelling | Dowling, Edward T. Verfasser aut Schaum's outline of theory and problems of introduction to mathematical economics Edward T. Dowling 2. ed. New York [u.a.] McGraw-Hill 1992 IX, 485 S. txt rdacontent n rdamedia nc rdacarrier Schaum's outline series Frühere Aufl. u.d.T.: Dowling, Edward T.: Schaum's outline of theory and problems of mathematics for economists Calcul économique ram Mathématiques économiques ram Mathématiques ram Wiskundige economie gtt Mathematik Economics, Mathematical Mathematics Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007696677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dowling, Edward T. Schaum's outline of theory and problems of introduction to mathematical economics Calcul économique ram Mathématiques économiques ram Mathématiques ram Wiskundige economie gtt Mathematik Economics, Mathematical Mathematics Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 |
| title | Schaum's outline of theory and problems of introduction to mathematical economics |
| title_auth | Schaum's outline of theory and problems of introduction to mathematical economics |
| title_exact_search | Schaum's outline of theory and problems of introduction to mathematical economics |
| title_full | Schaum's outline of theory and problems of introduction to mathematical economics Edward T. Dowling |
| title_fullStr | Schaum's outline of theory and problems of introduction to mathematical economics Edward T. Dowling |
| title_full_unstemmed | Schaum's outline of theory and problems of introduction to mathematical economics Edward T. Dowling |
| title_short | Schaum's outline of theory and problems of introduction to mathematical economics |
| title_sort | schaum s outline of theory and problems of introduction to mathematical economics |
| topic | Calcul économique ram Mathématiques économiques ram Mathématiques ram Wiskundige economie gtt Mathematik Economics, Mathematical Mathematics Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Calcul économique Mathématiques économiques Mathématiques Wiskundige economie Mathematik Economics, Mathematical Mathematics Wirtschaftsmathematik |
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