151-0401/01 – 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 introduction1999/2000Year of cancellation2009/2010
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
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

Knowledge, comprehension The student will be able... - to solve the systems of linear equations, to control basic terminology and related applications - to explain the concept of the primitive function and indefinite integral, to control the basic rules, formulas and techniques of integration - to define the definite integral (Darboux construction), to compute the definite integral with the help of Newton-Leibniz formula, to control the related basic geometric and economic applications - to define real functions of two real variables, to find the domain of functions of two variables and its visualization, to give the overview of basic functions of two variables used in economics, to explain the concept of homogenous functions of order 's' and to give the connections to economics - to define and to compute the partial derivatives with the help of their definitions and with the help of rules and formulas, to apply the partial derivatives for determining of local extremes (Hessian matrix), to define and interpret local extrema in a correct way, to discuss local extrema by means of their definition (inequality-type conditions, i.e., without the Hessian matrix), to find constrained extremes (Lagrange's multiplier) - to distinguish and to solve the basic types of differential and difference equations of 1st and 2nd order, to state the basic application possibilities in economics - to control the principles of difference calculus in connection with the monotonicity and dynamics of real sequences, to explain the connection between summation and difference

Teaching methods

Lectures
Individual consultations
Tutorials

Summary

The aim of the subject is to get acquainted with the basic knowledge of advanced mathematics, which is necessary for further studies of quantitative methods in economics. The subject’s structure and nature themselves have their importance as they help to develop logical thinking as well as the ability to enunciate thoughts accurately and to give clear argumentation when solving the practical problems. Formal prerequisites: Mathematics A

Compulsory literature:

[1] Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. [2] Tan T.S. Calculus: Multivariable Calculus. Brooks/Cole Cengage Learning, Belmont, 2010. [3] Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011.

Recommended literature:

[1] Stewart J.S. Calculus - Concepts and Contexts. Cengage Learning, 2010. [2] Canuto C., Tabacco A. Mathematical Analysis I. Springer Verlag, 2008. [3] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007. [4] Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.

Way of continuous check of knowledge in the course of semester

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, 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
(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
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