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Mathematics for Economists. Applications - Tatiana Corina Dosescu, Bogdan Nicolae Toader
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ISBN: 978-606-591-300-4
DOI: 10.5682/9786065913004
Publisher year: 2011
Edition: I
Pages: 146
Publisher: Editura Universitara
Author: Bogdan Nicolae Toader, Tatiana Corina Dosescu
Product Code:
9786065913004
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This paper was designed as a guide for the activity of the seminars courses "Applied Mathematics in Economics" and "Financial Mathematics" held at the Faculty of Tourism and Commercial Management and the Faculty of Finance, Banking and Accounting at the Christian University "Dimitrie Cantemir". As a result, it is addressed, with predilection, to the students of these faculties, but it can also be useful to the students from other faculties with economic profile. The paper has a predominantly didactic character and covers the material that is the object of the seminar held in the first year within the mentioned faculties. Each chapter contains:
1) a theoretical brief, in which are exposed the notions and the necessary methods for solving the exercises.
2) a set of completely solved exercises. In the presentation of the solutions we tried to give as many explanations as possible in order to accustom the students with mathematical reasoning. Whenever it was the case, we emphasized the algorithmic aspect of some problem-solving methods. The applications are chosen so as to contribute to the understanding and deepening of the theory.
3) a set of proposed exercises. Since understanding a solution does not mean mastering the method, the proposed exercises, which are very similar to those solved, are meant to invite students to practice the methods presented on their own.
1) a theoretical brief, in which are exposed the notions and the necessary methods for solving the exercises.
2) a set of completely solved exercises. In the presentation of the solutions we tried to give as many explanations as possible in order to accustom the students with mathematical reasoning. Whenever it was the case, we emphasized the algorithmic aspect of some problem-solving methods. The applications are chosen so as to contribute to the understanding and deepening of the theory.
3) a set of proposed exercises. Since understanding a solution does not mean mastering the method, the proposed exercises, which are very similar to those solved, are meant to invite students to practice the methods presented on their own.
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Matematici pentru economişti. Aplicaţii
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TATIANA CORINA DOSESCU
BOGDAN NICOLAE TOADER
BOGDAN NICOLAE TOADER
Foreword / 7
Chapter 1. Linear systems / 9
1. Theoretical brief / 9
2. Solved exercises / 12
3. Proposed exercises / 17
Chapter 2. Elements of vector computation / 19
1. Vector space (Rn, R) / 19
2. Solved exercises / 22
3. Proposed exercises / 32
Chapter 3. Gauss-Jordan method / 35
1. Theoretical brief / 35
2. Solved exercises / 37
3. Proposed exercises / 40
Chapter 4. The simplex algorithm / 41
1. Theoretical brief / 41
2. Solved exercises / 47
3. Proposed exercises / 54
Chapter 5. The simple algorithm. Penalty method / 55
1. Theoretical brief / 55
2. Solved exercises / 56
3. Proposed exercises / 61
Chapter 6. Balanced transport problem / 63
1. Theoretical brief / 63
2. Solved exercises / 67
3. Proposed exercises / 76
Chapter 7. Unbalanced transport problem / 77
1. Theoretical brief / 77
2. Solved exercises / 78
3. Proposed exercises / 85
Chapter 8. Numerical series / 87
1. Theoretical brief / 87
2. Solved exercises / 89
3. Proposed exercises / 95
Chapter 9. Series with positive terms / 97
1. Theoretical brief / 97
2. Solved exercises / 99
3. Proposed exercises / 103
Chapter 10. Series of powers / 105
1. Theoretical brief / 105
2. Solved exercises / 107
3. Proposed exercises / 111
Chapter 11. Extremes of functions / 113
1. Theoretical brief / 113
2. Solved exercises / 116
3. Proposed exercises / 119
Chapter 12. Adjusting the observation data / 121
1. Theoretical brief / 121
2. Solved exercises / 123
3. Proposed exercises / 125
Chapter 13. Improper integrals / 127
1. Theoretical Breviary / 127
2. Solved exercises / 129
3. Proposed exercises / 134
Chapter 14. Eulerian Integrals / 135
1. Theoretical brief / 135
2. Solved exercises / 136
3. Proposed exercises / 140
Annex A. Matrix and determinants / 141
Bibliography / 145
Chapter 1. Linear systems / 9
1. Theoretical brief / 9
2. Solved exercises / 12
3. Proposed exercises / 17
Chapter 2. Elements of vector computation / 19
1. Vector space (Rn, R) / 19
2. Solved exercises / 22
3. Proposed exercises / 32
Chapter 3. Gauss-Jordan method / 35
1. Theoretical brief / 35
2. Solved exercises / 37
3. Proposed exercises / 40
Chapter 4. The simplex algorithm / 41
1. Theoretical brief / 41
2. Solved exercises / 47
3. Proposed exercises / 54
Chapter 5. The simple algorithm. Penalty method / 55
1. Theoretical brief / 55
2. Solved exercises / 56
3. Proposed exercises / 61
Chapter 6. Balanced transport problem / 63
1. Theoretical brief / 63
2. Solved exercises / 67
3. Proposed exercises / 76
Chapter 7. Unbalanced transport problem / 77
1. Theoretical brief / 77
2. Solved exercises / 78
3. Proposed exercises / 85
Chapter 8. Numerical series / 87
1. Theoretical brief / 87
2. Solved exercises / 89
3. Proposed exercises / 95
Chapter 9. Series with positive terms / 97
1. Theoretical brief / 97
2. Solved exercises / 99
3. Proposed exercises / 103
Chapter 10. Series of powers / 105
1. Theoretical brief / 105
2. Solved exercises / 107
3. Proposed exercises / 111
Chapter 11. Extremes of functions / 113
1. Theoretical brief / 113
2. Solved exercises / 116
3. Proposed exercises / 119
Chapter 12. Adjusting the observation data / 121
1. Theoretical brief / 121
2. Solved exercises / 123
3. Proposed exercises / 125
Chapter 13. Improper integrals / 127
1. Theoretical Breviary / 127
2. Solved exercises / 129
3. Proposed exercises / 134
Chapter 14. Eulerian Integrals / 135
1. Theoretical brief / 135
2. Solved exercises / 136
3. Proposed exercises / 140
Annex A. Matrix and determinants / 141
Bibliography / 145
This paper was designed as a guide for the activity of the seminars courses "Applied Mathematics in Economics" and "Financial Mathematics" held at the Faculty of Tourism and Commercial Management and the Faculty of Finance, Banking and Accounting at the Christian University "Dimitrie Cantemir". As a result, it is addressed, with predilection, to the students of these faculties, but it can also be useful to the students from other faculties with economic profile. The paper has a predominantly didactic character and covers the material that is the object of the seminar held in the first year within the mentioned faculties. Each chapter contains:
1) a theoretical brief, in which are exposed the notions and the necessary methods for solving the exercises.
2) a set of completely solved exercises. In the presentation of the solutions we tried to give as many explanations as possible in order to accustom the students with mathematical reasoning. Whenever it was the case, we emphasized the algorithmic aspect of some problem-solving methods. The applications are chosen so as to contribute to the understanding and deepening of the theory.
3) a set of proposed exercises. Since understanding a solution does not mean mastering the method, the proposed exercises, which are very similar to those solved, are meant to invite students to practice the methods presented on their own.
Severe time restrictions (a one-semester seminar, after all) imposed a very strict selection of the material presented. For those who want to learn more about the topics covered in this book, the bibliography offers some titles that can be especially useful.
Certain notions and results regarding matrices and small order determinants, which will be used, often tacitly, during the lessons, are gathered in Annex A. Finally, for the questions of elementary mathematical analysis, which are supposed to be known, we recommend consulting high school textbooks for 11th and 12th grades.
Reminding students that a math book is read patiently and with a pencil in hand, to redo calculations and demonstrations, we wish them much success!
The Authors
1) a theoretical brief, in which are exposed the notions and the necessary methods for solving the exercises.
2) a set of completely solved exercises. In the presentation of the solutions we tried to give as many explanations as possible in order to accustom the students with mathematical reasoning. Whenever it was the case, we emphasized the algorithmic aspect of some problem-solving methods. The applications are chosen so as to contribute to the understanding and deepening of the theory.
3) a set of proposed exercises. Since understanding a solution does not mean mastering the method, the proposed exercises, which are very similar to those solved, are meant to invite students to practice the methods presented on their own.
Severe time restrictions (a one-semester seminar, after all) imposed a very strict selection of the material presented. For those who want to learn more about the topics covered in this book, the bibliography offers some titles that can be especially useful.
Certain notions and results regarding matrices and small order determinants, which will be used, often tacitly, during the lessons, are gathered in Annex A. Finally, for the questions of elementary mathematical analysis, which are supposed to be known, we recommend consulting high school textbooks for 11th and 12th grades.
Reminding students that a math book is read patiently and with a pencil in hand, to redo calculations and demonstrations, we wish them much success!
The Authors
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