151-0301/04 – Mathematics B (Mat B)

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 languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
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
REZ0011 Anonymizovaná Osoba
CTV0004 Anonymizovaná Osoba
SED05 Ing. Bc. Monika Poledníková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
RUC05 RNDr. Pavel Rucki, Ph.D.
ZAH0001 Marek Zahradníček
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: 2011/2012 Summer semester, validity until: 2015/2016 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 40 (40) 20
                Písemka Written test 40  20 2
        Examination Examination 60 (60) 31 3
                Písemná zkouška Written examination 50  26 3
                Ústní zkouška Oral examination 10  5 3
Mandatory attendence participation:

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

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2011/2012 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
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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
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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

Assessment of instruction



2022/2023 Summer
2021/2022 Summer
2020/2021 Summer
2019/2020 Summer
2018/2019 Summer
2017/2018 Summer
2016/2017 Summer
2015/2016 Summer
2014/2015 Summer
2013/2014 Summer
2012/2013 Summer
2011/2012 Summer
2010/2011 Summer