# 151-0301/04 – Mathematics B (Mat B)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor Mgr. Marian Genčev, Ph.D. Subject version guarantor Mgr. Marian Genčev, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2010/2011 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 Mgr. Marian Genčev, Ph.D.
HRD0001 Mgr. Zdeněk Hrdina
HRU61 RNDr. Jana Hrubá, Ph.D.
KUB33 Mgr. Aleš Kubíček
CTV0004 Anonymizovaná Osoba
REZ0011 Anonymizovaná Osoba
SED05 Ing. Bc. Monika Poledníková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
RUC05 RNDr. Pavel Rucki, 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:

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 unexcused absence Exam - compulsory written part (passing rate of at least 50%, samples available in LMS), - optional oral part (exam 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, other conditions without modification.

### Prerequisities

Subject codeAbbreviationTitleRequirement
151-0300 Mat 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: 2016/2017 Winter semester, validity until: 2020/2021 Summer semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 40 (40) 20
Písemka Written test 40  20 2
Průběžná písemka 1 Written test 0  0 1
Examination Examination 60 (60) 31 3
Písemná zkouška Written examination 42  22 3
Ústní zkouška Oral examination 18  9 3
Mandatory attendence participation: One unexcused absence in seminars.

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Conditions for subject completion and attendance at the exercises within ISP:

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2023/2024 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2023/2024 (B0414A050001) Marketing (S02) Marketing and business P Czech Šumperk 1 Compulsory study plan
2023/2024 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0311A050015) Informatics in Economy P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2022/2023 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
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2022/2023 (B0414A050001) Marketing (S02) Marketing and business P Czech Šumperk 1 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0311A050015) Informatics in Economy P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0411A050001) Accounting and Taxes P Czech Valašské Meziříčí 1 Compulsory study plan
2021/2022 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
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2020/2021 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
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2020/2021 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0411A050001) Accounting and Taxes P Czech Valašské Meziříčí 1 Compulsory study plan
2020/2021 (B0311A050015) Informatics in Economy P Czech Ostrava 1 Compulsory study plan
2020/2021 (B6209) Systems Engineering and Informatics (6209R017) Informatics in Economics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
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2019/2020 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
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2019/2020 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
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2018/2019 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2018/2019 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2018/2019 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2018/2019 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2016/2017 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2016/2017 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2016/2017 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2015/2016 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration P Czech Uherské Hradiště 1 Compulsory study plan
2014/2015 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2014/2015 (B6209) Systems Engineering and Informatics P Czech Uherské Hradiště 1 Compulsory study plan
2013/2014 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
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2013/2014 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2013/2014 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2011/2012 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2011/2012 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2011/2012 (B6234) Quantitative Methods and Decision Making in Economics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2010/2011 (B6207) Quantitative Methods in Economics P Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2010/2011 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6208R101) Sports Management (02) Sports Management P Czech Uherské Hradiště 1 Compulsory study plan
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### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - EKF - P - cs 2023/2024 Full-time Czech Optional EKF - Faculty of Economics stu. block
Subject block without study plan - EKF - P - cs 2021/2022 Full-time Czech Optional EKF - Faculty of Economics stu. block
Subject block without study plan - EKF - P - cs 2020/2021 Full-time Czech Optional EKF - Faculty of Economics stu. block