151-0401/03 – Mathematics B (MBKS)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits4
Subject guarantorMgr. Marian Genčev, Ph.D.Subject version guarantorRNDr. Simona Pulcerová, Ph.D., MBA
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction2006/2007Year of cancellation2009/2010
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
HRU61 RNDr. Jana Hrubá, Ph.D.
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
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 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

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

Studenti mají ke každému učivu test, mohou si tak sami ověřit, zda probranému učivu porozuměli či nikoliv. Také mají vzor závěrečné písemné zkoušky, kde si mohou opět vyzkoušet, zda by u zkoušky uspěli či nikoliv.

E-learning

Other requirements

Prerequisities

Subject codeAbbreviationTitleRequirement
151-0400 MatKomb Mathematics A Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Témata výkladu zpracovaných v podobě multimediálních studijních opor: 1. Neurčitý integrál – definice a vlastnosti, základní vzorce, pravidla integrování, metody integrace: substituční metoda, metoda per partes, integrace racionální lomené funkce, rozklad na parciální zlomky, integrace některých iracionálních funkcí, integrace některých goniometrických funkcí. 2. Určitý integrál – motivace a jeho zavedení, definice a vlastnosti, Newton- Leibnizova formule, obsah rovinného obrazce, nevlastní integrál. 3. Funkce dvou proměnných – úvod a základní pojmy, definiční obor, obor hodnot, graf, parciální derivace prvního řádu, parciální derivace vyšších řádů, extrémy funkce dvou proměnných: lokální extrémy, vázané extrémy. 4. Obyčejné diferenciální rovnice 1. řádu – úvod a základní pojmy, obecné řešení, partikulární řešení, separovatelná diferenciální rovnice, homogenní diferenciální rovnice, lineární diferenciální rovnice homogenní a nehomogenní (metoda variace konstanty).

Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2009/2010 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration K Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6210R004) European Integration (02) European Integration K Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (01) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration K Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6210R004) European Integration (02) European Integration K Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (01) Public Economics and Administration K Czech Šumperk 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner