# 151-0300/04 – Mathematics A (Mat A)

 Gurantor department Department of Mathematical Methods in Economics Credits 5 Subject guarantor RNDr. Pavel Rucki, Ph.D. Subject version guarantor RNDr. Pavel Rucki, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2018/2019 Year of cancellation Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
FUN01 Mgr. Taťána Funioková, Ph.D.
GEN02 Mgr. Marian Genčev, Ph.D.
HAN0001 Mgr. Vít Hanák
HRD0001 Mgr. Zdeněk Hrdina
HRU61 RNDr. Jana Hrubá, Ph.D.
KOZ214 Ing. Mgr. Petr Kozel, Ph.D.
LOR21 Mgr. Kristina Lorencová
MIH22 RNDr. Šárka Michalcová, Ph.D.
OND10 Mgr. Ivana Onderková, Ph.D.
CTV0004 Anonymizovaná Osoba
REZ0011 Anonymizovaná Osoba
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
RUC05 RNDr. Pavel Rucki, Ph.D.
S1A20 prof. RNDr. Dana Šalounová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent

### Subject aims expressed by acquired skills and competences

Knowledge • Define the function of one variable. • Find the domain and range and basic properties. • Draw graphs of elementary functions. • Compute limits and derivates of functions. • Find the properties of no elementary functions a draw theirs graphs. • Obtain easier imagine about economic functions. Comprehension • Express economic dependences using a mathematical function. • Explain the slope of a function. • Restate the terms “concavity” and “convexity” into the “degressive” and “progressive”. • Generalise the functions on the dependences in the real live. Applications • Relate economic and mathematical functions. • Discover the tools suitable for describing of dependences in economics and other sciences. • Develop the technique of graphs drawing.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Taught in Czech. The subject continues fulfilling general methodical and professional goals of Mathematics, i.e. to train the rational thinking and the ability to conceive and work with quantitative information concerning the real world. This is being done especially by mathematization of the practical as well as theoretical economic problems. This subject supplies the students’ education with realms of higher Mathematics which is applicable namely to the creation and investigation of economic models.

### Compulsory literature:

[1] SYDSAETER, K., HAMMOND, P. J. Mathematics for Economics Analysis. Pearson, 2002, ISBN 978-81-7758104-1. [2] HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. The MIT Press, London, 3rd edition, 2011, ISBN 978-0-262-01507-3. [3] TAN, T.S. Single variable calculus: early transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011, ISBN 978-1-4390-4600-5.

### Recommended literature:

[1] LUDERER, B., NOLLAU, V., VETTERS, K. Mathematical Formulas for Economists. Springer Verlag, 3rd edition, 2006, ISBN 978-3540469018. [2] HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. The MIT Press, London, 3rd edition, 2011, ISBN 978-0-262-01507-3.

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

Credit requirements: 1. Passing the credit test (succes rate - at least 50%) 2. Active participation at seminars - at most one absence without leave 3. Familiarity with lecture topics and ability to solve assigned problems Credit requirements in case of individual study: It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.

### Other requirements

Credit requirements: 1. Passing the credit test (succes rate - at least 50%) 2. Active participation at seminars - at most one absence without leave 3. Familiarity with lecture topics and ability to solve assigned problems Credit requirements in case of individual study: It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Introduction - number sets, intervals, solving of elementary equations and relations, simplifying powers and roots. 2. - 3. Sequences – basic concepts, arithmetic and geometric sequence and their application, summation, limit of a sequence, definition of Euler's number e. 4. - 6. Function of a single real variable – definition, domain and range, classification, elementary functions, graph of a function, inverse functions. 7. - 8. Limit of a function - limit of a function at a point, improper limit of a function, limit of a funciton at infinity. 9. - 10. Derivative of a function - equation of a tangent line and normal line to a curve at a point, differentiation techniques, higher order derivatives, differential of a function, l'Hospital's Theorem. 11. - 12. Application of the derivative - monotonoic function, local and global extrema of a function, convex and concave function, inflexion points, asymptotes. 13. - 14. Revision.

### Conditions for subject completion

Full-time form (validity from: 2018/2019 Winter semester)
Min. number of pointsMax. počet pokusů
Zápočtová písemka Written test 100  51 2
Mandatory attendence participation: Na cvičeních je povolena max. 1 absence bez omluvy.

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

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### Occurrence in study plans

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2023/2024 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
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2023/2024 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
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2023/2024 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2023/2024 (B0414A050001) Marketing (S02) Marketing and business P Czech Šumperk 1 Compulsory study plan
2023/2024 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2023/2024 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0311A050015) Informatics in Economy P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0411A050001) Accounting and Taxes P Czech Valašské Meziříčí 1 Compulsory study plan
2022/2023 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2022/2023 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2022/2023 (B0414A050001) Marketing (S02) Marketing and business P Czech Šumperk 1 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0311A050015) Informatics in Economy P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0411A050001) Accounting and Taxes P Czech Valašské Meziříčí 1 Compulsory study plan
2021/2022 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0411A050001) Accounting and Taxes P Czech Valašské Meziříčí 1 Compulsory study plan
2020/2021 (B0311A050015) Informatics in Economy P Czech Ostrava 1 Compulsory study plan
2020/2021 (B6209) Systems Engineering and Informatics (6209R017) Informatics in Economics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0414A050001) Marketing (S02) Marketing and business P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0414A050001) Marketing (S01) Marketing Communication P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S01) International Economic Relations P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S05) Sports management P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S04) Economics and Law in Business P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S03) Management P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0312A050001) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S02) Business Administration P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0413A050012) Economics and Management (S02) Business Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2019/2020 (B0311A050004) Applied Economics (S02) Economic Development P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0412A050005) Finance P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0411A050001) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2019/2020 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2018/2019 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2018/2019 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2018/2019 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

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