# 151-0401/05 – Mathematics B (MBKS)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor doc. Mgr. Marian Genčev, Ph.D. Subject version guarantor doc. Mgr. Marian Genčev, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
FUN01 Mgr. Taťána Funioková, Ph.D.
GEN02 doc. Mgr. Marian Genčev, Ph.D.
KUB33 Mgr. Aleš Kubíček
S1A20 prof. RNDr. Dana Šalounová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 6+8

### 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

### 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:

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.

### Recommended literature:

STEWART, James. Calculus: metric version. Eighth edition. [Boston]: Cengage Learning, [2016]. ISBN 978-1-305-26672-8.

### Way of continuous check of knowledge in the course of semester

Credit - passing the written credit test (passing score of at least 50%, samples available in LMS) - maximum one unexcussed absence at seminars Exam - compulsory written part (passing rate of at least 50%, samples available in LMS), - optional oral part (themes available in LMS)

### 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 and lectures, other conditions without modification.

### Prerequisities

Subject codeAbbreviationTitleRequirement
151-0400 MatKomb 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

Part-time form (validity from: 2021/2022 Winter semester)
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: One unexcused absence at seminars.

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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
2023/2024 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2022/2023 (B0312A050001) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan
2022/2023 (B0312A050001) Public Economics and Administration K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 1 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S02) Business Administration K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S03) Management K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S01) International Economic Relations K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S02) Economic Development K Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - EKF - K - cs 2023/2024 Part-time Czech Optional EKF - Faculty of Economics stu. block