# 151-0401/01 – Mathematics B (MBKS)

 Gurantor department Department of Mathematical Methods in Economics Credits 4 Subject guarantor Mgr. Marian Genčev, Ph.D. Subject version guarantor RNDr. Simona Pulcerová, Ph.D., MBA Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 1999/2000 Year of cancellation 2009/2010 Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
BAU20 RNDr. Danuše Bauerová, Ph.D.
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 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.

### 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, tečná rovina k ploše, 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). 5. Diferenční rovnice 1. řádu – úvod a základní pojmy, obecné řešení, partikulární řešení, lineární diferenční rovnice s konstantními koeficienty a speciální pravou stranou.

### Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (145) 51 3
Examination Examination 100  0 3
Exercises evaluation Credit 45  0 3
Mandatory attendence participation:

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

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2006/2007 (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

### Assessment of instruction

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