# 151-0401/04 – Mathematics B (MBKS)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor Mgr. Marian Genčev, Ph.D. Subject version guarantor Mgr. Marian Genčev, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 2010/2011 Year of cancellation 2020/2021 Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
GEN02 Mgr. Marian Genčev, Ph.D.
KUB33 Mgr. Aleš Kubíček
S1A20 prof. RNDr. Dana Šalounová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time 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.

### Way of continuous check of knowledge in the course of semester

Written exam - max. 100 pts, - min. 51 pts

### Other requirements

According to teacher's instructions.

### Prerequisities

Subject codeAbbreviationTitleRequirement
151-0400 MatKomb Mathematics A Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

I. Systems of linear equations and analytic geometry ---------------------------------------------------- - basic concepts, - Gaussian elimination, Frobenius' theorem, - Cramer's rule, - use of systems of linear equations for determining the mutual position of - two planes in E3, - two lines in E2 and E3, - plane and a line in E3 - basic applications in economics II. Integral calculus --------------------- Indefinite integral - definition and properties, - basic integration formulas and rules, - per partes, substitution, - integration of rational functions (partial fractions), - basic applications in economics Definite integral - the problem of calculating the area of a region bounded by continuous curves - definitions a properties of the definite integral, - Newton-Leibniz' formula, - basic applications in economics Generalized and improper integral - improper integral of the first and second kind, - Gaussian integral (for information only), - calculating improper integrals by limits, - generalized definite integrals (the case of discontinuous functions), - basic applications in economics and connection with statistics III. Functions of two real variables ------------------------------------ - definitions of basic concepts, - domain and its visualization, - homogeneous functions of order 's', - partial derivatives and their geometric interpretation - tangent plane, - total differential, differentiable functions, approximations of number expressions, - local extremes, - constrained local extremes - method of substitution, - Lagrange's multiplier, - basic applications in economics IV. Ordinary differential equations (ODE) ----------------------------------------- - definition of ODE, - order of ODE, - solution of ODE (general, particular, singular, extraordinary), - basic types of first-order ODE's - separated, - separable, - linear first-order DE (variation of constants), - second-order linear DE with constant coefficients and special right-hand side (undetermined coefficients), - basic applications in economics V. Difference calculus and difference equations ----------------------------------------------- Introduction to difference calculus - difference of order 'k', - basic formulas and rules for calculating the differences, - the sign of the first-order difference as the indicator of the sequence monotonicity, - the sign of the second-order difference as the indicator of the sequence monotonicity dynamics, - relation of summation and difference Ordinary difference equations (ODifE) - definition of the ODifE - order of the ODifE - solution of the ODifE (general, particular) - first- and second-order ODifE with constant coefficients and special right-hand side (undetermined coefficients) - basic applications in economics

### Conditions for subject completion

Part-time form (validity from: 2010/2011 Summer semester, validity until: 2020/2021 Summer semester)
Min. number of pointsMax. počet pokusů
Examination Examination 100  51 3
Mandatory attendence participation: Passing succesfully the exam test.

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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
2020/2021 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration K Czech Ostrava 2 Compulsory study plan
2018/2019 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2017/2018 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2017/2018 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2016/2017 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2016/2017 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2015/2016 (B6202) Economic Policy and Administration K Czech Valašské Meziříčí 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2014/2015 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2014/2015 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2013/2014 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2013/2014 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2012/2013 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2012/2013 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan
2011/2012 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management K Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration K Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration K Czech Šumperk 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - EKF - K - cs 2020/2021 Part-time Czech Optional EKF - Faculty of Economics stu. block
Subject block without study plan - EKF - K - cs 2019/2020 Part-time Czech Optional EKF - Faculty of Economics stu. block