# 151-0500/03 – Mathematics A (Math 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 English Year of introduction 2018/2019 Year of cancellation Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
RUC05 RNDr. Pavel Rucki, 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

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] CARVAJAL, Andrés M., HAMMOND, Peter J., STRØM, Arne, SYDSAETER, Knut. Essential mathematics for economic analysis. Pearson, 5th edition, 2016, ISBN 978-1-292-07461-0. [2] STOCKER, Christopher J., ZIEGLER, Michael R., BYLEEN, Karl E., BARNETT, Raymond A. College mathematics for business, economics, life sciences, and social sciences. Pearson, 14th edition, 2019, ISBN 978-0-13-467414-8.

### 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.

### E-learning

https://lms.vsb.cz/course/view.php?id=88522

### 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: Attendance at lectures is recommended, at least 90% attendance is required (1 absence without excuse at most).

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Conditions for subject completion and attendance at the exercises within ISP: Attendance at lectures and seminars is recommended. Successful passing of the credit examination is required.

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2020/2021 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
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2020/2021 (B6208) Economics and Management (6208R174) European Business Studies P English Ostrava 1 Compulsory study plan
2019/2020 (B6208) Economics and Management (6208R174) European Business Studies P English Ostrava 1 Compulsory study plan
2019/2020 (B0311A050005) Applied Economics (S02) International Economic Relations P English Ostrava 1 Compulsory study plan
2019/2020 (B0311A050005) Applied Economics (S01) Economic Development P English Ostrava 1 Compulsory study plan
2019/2020 (B0412A050006) Finance P English Ostrava 1 Compulsory study plan
2018/2019 (B6208) Economics and Management (6208R174) European Business Studies P English Ostrava 1 Compulsory study plan
2018/2019 (B6202) Economic Policy and Administration (6202R010) Finance P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

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### Assessment of instruction

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