151-0502/02 – Mathematics B (MathB)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits5
Subject guarantorMgr. Marian Genčev, Ph.D.Subject version guarantorMgr. Marian Genčev, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
GEN02 Mgr. Marian Genčev, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

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.

Compulsory literature:

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. STEWART, James Michael. Multivariable calculus, International Metric Edition. Cengage Learning, 2019. ISBN 978-0-357-11350-9.

Recommended literature:

LAY, David C., LAY, Steven R. and MCDONALD, Judith. Linear algebra and its applications. Harlow, Essex: Pearson Education Limited, 2022. ISBN 978-0-135-88280-1. HOY, Michael, LIVERNOIS, John Richard and MCKENNA, C. J. Mathematics for economics. Cambridge: The MIT Press, 2022. ISBN 9780262046626.

Way of continuous check of knowledge in the course of semester

Credit - passing the written credit test (passing score of at least 50%), - maximum one unexcused absence Exam - compulsory written part (passing rate of at least 50%), - optional oral part

E-learning

LMS, MS Teams, https://www.vsb.cz/e-vyuka/cs/subject/151-0301/04

Other requirements

According to teacher's requests in accoradnce with official conditions. Conditions for ISP: Optional attendance at seminars, other conditions without modification.

Prerequisities

Subject codeAbbreviationTitleRequirement
151-0500 Math A Mathematics A Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Full-time form (validity from: 2021/2022 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40 (40) 40
                Písemka Written test 40  20 2
        Examination Examination 60 (60) 15 3
                Písemná zkouška Written examination 30  15 3
                Ústní zkouška Oral examination 30  0 3
Mandatory attendence participation: Maximal one unexcused absence.

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Conditions for subject completion and attendance at the exercises within ISP: Attendance at the seminar is not obligatory.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2024/2025 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2023/2024 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2023/2024 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2023/2024 (B0412A050006) Finance P English Ostrava 1 Compulsory study plan
2023/2024 (B0413A050047) Business Administration P English Ostrava 1 Compulsory study plan
2022/2023 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2022/2023 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2022/2023 (B0412A050006) Finance P English Ostrava 1 Compulsory study plan
2022/2023 (B0413A050047) Business Administration P English Ostrava 1 Compulsory study plan
2021/2022 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2021/2022 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2021/2022 (B0412A050006) Finance P English Ostrava 1 Compulsory study plan
2020/2021 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2020/2021 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2020/2021 (B0412A050006) Finance P English Ostrava 1 Compulsory study plan
2019/2020 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2019/2020 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2019/2020 (B0412A050006) Finance P English Ostrava 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2022/2023 Summer