Editura Universitara 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: Universitară

Author: Gratiela Ghic

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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.

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

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