Course Unit Code | 151-0301/04 |
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Number of ECTS Credits Allocated | 5 ECTS credits |
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Type of Course Unit * | Compulsory |
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Level of Course Unit * | First Cycle |
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Year of Study * | First Year |
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Semester when the Course Unit is delivered | Summer Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 151-0300 | Mathematics A |
Name of Lecturer(s) | Personal ID | Name |
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| ARE30 | Ing. Orlando Arencibia Montero, Ph.D. |
| SOB33 | RNDr. Simona Pulcerová, Ph.D., MBA |
| GEN02 | Mgr. Marian Genčev, Ph.D. |
Summary |
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The course is focused on the practical mastery of selected mathematical methods in the field of linear algebra and calculus, which form the basis for further quantitative considerations in related subjects. The student will also be acquainted with the derivation of basic theoretical findings. This enables the development of logical skills, which form the basis for analytical and critical thinking. For better motivation of students, the presentation in lectures is always connected with appropriate economic problems. |
Learning Outcomes of the Course Unit |
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The students will be able to master the basic techniques specified by the three main topics (see below, items 1-3). Also, they will be able to freely, but logically correct, discuss selected theoretical units that will allow talented individuals to excel. The student will also have an overview of basic application possibilities of the discussed apparatus in the field of economics.
(1) The student will be introduced to the basics of linear algebra and its application possibilities in economics.
(2) The student will be able to apply the basic rules and formulas for the calculation of integrals, use them to calculate the area of planar regions, and for calculating of improper integrals and integrals of discontinuous functions. The student will be able to discuss the relating application possibilities in economics.
(3) The student will be able to find local extrema of functions of two variables without/with constraints, level curves and total differential, will be able to decide whether the given function is homogeneous. The student will be able to discuss the relating application possibilities and to mention appropriate generalizations for functions of 'n' real variables. |
Course Contents |
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1. Basic operations with matrices, calculation of 2nd- and 3rd order determinants.
2. Matrix invesrsion, specific matrix equations. Applications in economics.
3. Systems of linear equations. Gaussian elimination, Cramer's rule,network analysis and further applications.
4. Basic rules and formulas for indefinite integrals, method of substitution. Applications in economics.
5. Integration by parts, integration of selected rational functions. Applications in economics.
6. Definite integral. Areas of regions bounded by continuous curves. Applications in economics.
7. Definite integrals of discontinuous functions, improper integrals. Applications in economics.
8. Real functions of more real variables. Graph, domain, level curves, homgeneous functions. Applications in economics.
9. Partial derivatives, total differential. Tangent plane. Applications in economics.
10. Local extrema of functions of two variables. Constrained extrema (substitution, Lagrange's multiplier). Applications in economics. |
Recommended or Required Reading |
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Required Reading: |
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LARSON, Ron a David C. FALVO. Elementary linear algebra. 6th ed. Belmont: Brooks/Cole Cengage Lerning, 2010. ISBN 978-0-495-82923-2.
TAN, Soo Tang. Multivariable calculus. International ed. Belmont: Brooks/Cole Cengage Learning, 2010. ISBN 978-0-495-83150-1.
HOY, Michael, LIVERNOIS, John Richard and MCKENNA, C. J. Mathematics for economics. Cambridge: The MIT Press, 2022. ISBN 9780262046626. |
GENČEV, Marian a Pavel RUCKI. Cvičebnice z matematiky nejen pro ekonomy I. Ostrava: Facuty of Economics, VŠB-TU Ostrava, 2017. Series of textbooks, Faculty of Economics, VŠB-TU Ostrava, 2017, vol. 32. ISBN 978-80-248-4100-7.
GENČEV, Marian. Matematika A. Ostrava: VŠB-TU Ostrava, 2013. Series of textbooks, v. 5 (2013). ISBN 978-80-248-3154-1.
GENČEV, Marian. Matematika B. Ostrava: VŠB-TU Ostrava, 2013. Series of textbooks, v. 6 (2013). ISBN 978-80-248-3157-2. |
Recommended Reading: |
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STEWART, James. Calculus: metric version. Eighth edition. [Boston]: Cengage Learning, [2016]. ISBN 978-1-305-26672-8. |
ŠALOUNOVÁ, Dana a Alena POLOUČKOVÁ. Úvod do lineární algebry. Ostrava: VŠB - Technická univerzita Ostrava, 2002. ISBN 80-248-0199-X.
MOUČKA, Jiří a Petr RÁDL. Matematika pro studenty ekonomie. 2., upravené a doplněné vydání. Praha: Grada Publishing, 2015. Expert. ISBN 978-80-247-5406-2.
KLŮFA, Jindřich. Matematika pro bakalářské studium na VŠE. Vydání I. Jesenice: Ekopress, 2019. ISBN 9788087865538.
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Planned learning activities and teaching methods |
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Lectures, Individual consultations, Tutorials, Other activities |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 40 (40) | 40 |
Písemka | Written test | 40 | 20 |
Examination | Examination | 60 (60) | 15 |
Písemná zkouška | Written examination | 30 | 15 |
Ústní zkouška | Oral examination | 30 | 0 |