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
LOR21 Mgr. Kristina Lorencová
OND10 Mgr. Ivana Onderková, Ph.D.
CTV0004 Anonymizovaná Osoba
REZ0011 Anonymizovaná Osoba
SED05 Ing. Bc. Monika Poledníková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
RUC05 RNDr. Pavel Rucki, Ph.D.
S1A20 prof. RNDr. Dana Šalounová, 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 five main topics listed in the syllabus. 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 able to solve systems of linear equations and apply them to describe the basic problems of network analysis. (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. (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. (4) The student will be able to solve selected ordinary differential equations of the 1st and 2nd order. (5) The student will be able to use basic rules and formulas to calculate the difference of the sequence and to assess the dynamic of monotonic sequences, will be able to solve linear difference equations of the 1st and 2nd order.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The course is primarily 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 - fulfill all assigned tasks, written test Exam - compulsory written part, 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.

Prerequisities

Subject codeAbbreviationTitleRequirement
151-0300 Mat A Mathematics A Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Systems of linear equations. Gaussian elimination, Cramer's rule,network analysis and further applications. 2. Basic rules and formulas for indefinite integrals, method of substitution. 3. Integration by parts, integration of selected rational functions. 4. Definite integral. Areas of regions bounded by continuous curves. 5. Definite integrals of discontinuous functions, improper integrals. 6. Real functions of more real variables. Graph, domain, level curves, homgeneous functions. 7. Partial derivatives, total differential. Tangent plane. 8. Local extrema of functions of two variables. Constrained extrema (substitution, Lagrange's multiplier). 9. Ordinary differential equations. Separable and linear equations. 10. Second order linear differential equations, undetermined coefficients. 11. Introduction to difference calculus. 12. First- and second-order linear difference equations, undetermined coefficients.

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 points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 40 (40) 20
                Písemka Written test 40  20
        Examination Examination 60 (60) 31
                Písemná zkouška Written examination 50  26
                Ústní zkouška Oral examination 10  5
Mandatory attendence parzicipation:

Show history

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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 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