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Mathematics B

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code151-0301/04
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
151-0300Mathematics A
Name of Lecturer(s)Personal IDName
SOB33RNDr. Simona Pulcerová, Ph.D., MBA
GEN02Mgr. Marian Genčev, Ph.D.
Summary
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
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
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
Required Reading:
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:
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.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit40 (40)40
                PísemkaWritten test40 20
        ExaminationExamination60 (60)15
                Písemná zkouškaWritten examination30 15
                Ústní zkouškaOral examination30 0