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Applied mathematics in economics
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ISBN: 978-606-28-0223-3
DOI: 10.5682/9786062802233
Publisher year: 2015
Edition: III, revizuita
Pages: 312
Publisher: Editura Universitara
Author: Gratiela Ghic
Product Code:
9786062802233
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Applied mathematics in economics
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GRATIELA GHIC
Doctor of Economics, Associate Professor at the Faculty of International Relations of the Christian University Dimitrie Cantemir, Bucharest.
Areas of competence: mathematical modeling of economic processes, financial mathematics, operational research, economic and financial analysis.
Doctor of Economics, Associate Professor at the Faculty of International Relations of the Christian University Dimitrie Cantemir, Bucharest.
Areas of competence: mathematical modeling of economic processes, financial mathematics, operational research, economic and financial analysis.
Chapter I
Elements of linear algebra / 9
1.1. Vector spaces / 9
1.2. Linear dependence and independence. Generator system. Base / 15
1.3. Base change. The motto of substitution. Pivot method / 23
1.4. Applications of the pivot method in the matrix / 25
1.5. Vector space morphisms / 33
1.6. Vector subspaces / 35
1.7. Functional on vector spaces / 39
Chapter II
Linear programming elements / 53
2.1. Formulation of a linear programming problem and its mathematical model / 53
2.2. Model matrix formulation (PPL) / 57
2.3. Convex sets and functions / 60
2.4. Solutions of a linear programming problem / 61
2.5. Graphic solving method (PPL) / 64
2.6. The simplex algorithm / 72
2.6.1. The primal simplex algorithm / 76
2.6.2. Determining an initial basic solution / 79
2.7. Duality in linear programming / 89
2.7.1. PPL formulation - dual. Fundamental theorem of duality / 89
2.7.2. Economic interpretations of duality / 94
2.7.3. Dual simplex algorithm (ASD) / 99
2.8. Reoptimization and parameterization in linear programming / 103
2.8.1. Reoptimizations in linear programming / 103
2.8.2. Parameterization in linear programming / 118
2.9. Transport problem / 122
2.9.1. The mathematical model of the transport problem / 123
2.9.2. Solving algorithm / 127
2.9.3. Degeneration in transport problems / 133
2.9.4. Transport problem with maximum objective function / 136
2.9.5. The transport problem with the impossibility of using some routes / 136
2.9.6. Transport problem with intermediate distribution centers (Transfer problem) / 137
2.9.7. Transport problems with related centers / 138
2.9.8. Distribution problems. Labor force allocation / 139
2.9.9. Linear models of distribution and transfer of funds / 140
Chapter III
Elements of mathematical analysis. Economic applications / 148
Multivariate functions / 148
3.1.1. Metrics. Metric spaces / 148
3.1.2. Norm. Standard spaces / 149
3.1.3. Scalar product. Euclidean space / 150
3.1.4. Elements of topology / 151
3.1.5. Limits of real functions of several variables / 154
3.1.6. Continuity of functions of several variables / 155
3.1.7. Differential theory of real functions of several real variables / 156
3.1.8. Optimization of functions without restrictions / 167
3.1.9. Optimization of the functions of several variables conditioned by equality type restrictions / 171
3.2. Microeconomic analysis of the consumer and the producer / 172
3.2.1. The decision to the producer in conditions of perfect competition / 172
3.2.2. Consumer decision optimization / 178
3.3. Integral calculation complements / 207
3.3.1. Improper integrals / 207
3.3.2. Eulerian integrals / 210
Chapter IV
Basic elements of probability theory / 213
4.1. Random events / 213
4.1.1. Operations with events / 214
4.1.2. Event field / 215
4.1.3. Definition of probability / 217
4.1.4. Conditional probability / 218
4.1.5. Fundamental probabilistic calculation formulas / 219
4.2. Classical probability schemes / 220
4.3. Random variables (stochastic) / 229
4.4. Numerical characteristics of random variables / 239
4.4.1. Average of a random variable / 239
4.4.2. Dispersion of a random variable / 240
4.4.3. Moments of higher order / 242
4.4.4. Characteristic function / 243
4.4.5. Covariance and correlation coefficient of two random variables / 244
4.5. Theoretical laws of distribution. Indicators / 246
Chapter V
Elements of financial mathematics / 261
5.1. Interest / 261
5.1.1. Simple interest / 263
5.1.2. Compound interest / 271
5.2. Discount operations / 281
5.3. Installed plates / 290
5.4. Repayment of loans / 303
Bibliography / 311
Elements of linear algebra / 9
1.1. Vector spaces / 9
1.2. Linear dependence and independence. Generator system. Base / 15
1.3. Base change. The motto of substitution. Pivot method / 23
1.4. Applications of the pivot method in the matrix / 25
1.5. Vector space morphisms / 33
1.6. Vector subspaces / 35
1.7. Functional on vector spaces / 39
Chapter II
Linear programming elements / 53
2.1. Formulation of a linear programming problem and its mathematical model / 53
2.2. Model matrix formulation (PPL) / 57
2.3. Convex sets and functions / 60
2.4. Solutions of a linear programming problem / 61
2.5. Graphic solving method (PPL) / 64
2.6. The simplex algorithm / 72
2.6.1. The primal simplex algorithm / 76
2.6.2. Determining an initial basic solution / 79
2.7. Duality in linear programming / 89
2.7.1. PPL formulation - dual. Fundamental theorem of duality / 89
2.7.2. Economic interpretations of duality / 94
2.7.3. Dual simplex algorithm (ASD) / 99
2.8. Reoptimization and parameterization in linear programming / 103
2.8.1. Reoptimizations in linear programming / 103
2.8.2. Parameterization in linear programming / 118
2.9. Transport problem / 122
2.9.1. The mathematical model of the transport problem / 123
2.9.2. Solving algorithm / 127
2.9.3. Degeneration in transport problems / 133
2.9.4. Transport problem with maximum objective function / 136
2.9.5. The transport problem with the impossibility of using some routes / 136
2.9.6. Transport problem with intermediate distribution centers (Transfer problem) / 137
2.9.7. Transport problems with related centers / 138
2.9.8. Distribution problems. Labor force allocation / 139
2.9.9. Linear models of distribution and transfer of funds / 140
Chapter III
Elements of mathematical analysis. Economic applications / 148
Multivariate functions / 148
3.1.1. Metrics. Metric spaces / 148
3.1.2. Norm. Standard spaces / 149
3.1.3. Scalar product. Euclidean space / 150
3.1.4. Elements of topology / 151
3.1.5. Limits of real functions of several variables / 154
3.1.6. Continuity of functions of several variables / 155
3.1.7. Differential theory of real functions of several real variables / 156
3.1.8. Optimization of functions without restrictions / 167
3.1.9. Optimization of the functions of several variables conditioned by equality type restrictions / 171
3.2. Microeconomic analysis of the consumer and the producer / 172
3.2.1. The decision to the producer in conditions of perfect competition / 172
3.2.2. Consumer decision optimization / 178
3.3. Integral calculation complements / 207
3.3.1. Improper integrals / 207
3.3.2. Eulerian integrals / 210
Chapter IV
Basic elements of probability theory / 213
4.1. Random events / 213
4.1.1. Operations with events / 214
4.1.2. Event field / 215
4.1.3. Definition of probability / 217
4.1.4. Conditional probability / 218
4.1.5. Fundamental probabilistic calculation formulas / 219
4.2. Classical probability schemes / 220
4.3. Random variables (stochastic) / 229
4.4. Numerical characteristics of random variables / 239
4.4.1. Average of a random variable / 239
4.4.2. Dispersion of a random variable / 240
4.4.3. Moments of higher order / 242
4.4.4. Characteristic function / 243
4.4.5. Covariance and correlation coefficient of two random variables / 244
4.5. Theoretical laws of distribution. Indicators / 246
Chapter V
Elements of financial mathematics / 261
5.1. Interest / 261
5.1.1. Simple interest / 263
5.1.2. Compound interest / 271
5.2. Discount operations / 281
5.3. Installed plates / 290
5.4. Repayment of loans / 303
Bibliography / 311
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