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Mathematics A

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code151-0300/04
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English, German, Spanish
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
ARE30Ing. Orlando Arencibia Montero, Ph.D.
S1A20prof. RNDr. Dana Šalounová, Ph.D.
FUN01Mgr. Taťána Funioková, Ph.D.
RUC05RNDr. Pavel Rucki, Ph.D.
KOZ214Ing. Mgr. Petr Kozel, Ph.D.
ZAH0001Marek Zahradníček
GEN02Mgr. Marian Genčev, Ph.D.
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.
Learning Outcomes of the Course Unit
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.
• Order knowledge about vectors in the plain.
• Identify the types of matrices.
• Solve the system of linear equations.

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.
• Express knowledge of vectors to the space.

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.
• Apply knowledge of linear algebra in economics, e.g. traffic problems, structural analysis.
• Solve basic problems of linear programming.
Course Contents
1. Real sequences - definition, properties, arithmetic sequence, geometric sequence, limit of a sequence.
2. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions, composition of functions.
3. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval.
4. An introduction to the derivate – slope of a tangent line at a point, derivative, equation of a tangent line and normal line to a curve at a point, techniques of differentiation, higher order derivations, l´Hospital´s rule.
5. Linear algebra – matrices, addition and multiplication of matrices, rank of a matrix, determinant, the inverse of the matrix, matrix equations.
Recommended or Required Reading
Required Reading:
[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.
[1] GENČEV, M., HRUBÁ, J., PULCEROVÁ, S., RUCKI, P. Matematika A. SOT, vol. 5, Ostrava: VŠB-TU Ostrava, 2013. ISBN 978-80-248-3154-1.
[2] GENČEV, M., RUCKI, P. Cvičebnice z matematiky nejen pro ekonomy I. SOT, vol. 32, Ostrava: VŠB-TU Ostrava, 2017, ISBN 978-80-248-4100-7.
[3] Studijní opory s převažujícími distančními prvky pro předměty teoretického základu studia, http://www.studopory.vsb.cz
Recommended Reading:
[1] LARSON, R. Elementary Linear Algebra. Brooks/Cole Cengage Learning, Belmont, 8th edition, 2016, ISBN 978-1305658004.
[2] LUDERER, B., NOLLAU, V., VETTERS, K. Mathematical Formulas for Economists. Springer Verlag, 3rd edition, 2006, ISBN 978-3540469018.
[3] 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.
[1] POLOUČKOVÁ, A., ŠALOUNOVÁ, D. Diferenciální počet I. VŠB–TU Ostrava, 2003, ISBN 80-7078-904-2.
[2] POLOUČKOVÁ, A., ŠALOUNOVÁ, D. Úvod do lineární algebry. VŠB-TU Ostrava, 2002, ISBN 80-248-0199-X.
[3] COUFAL, J., KLŮFA, J. Matematika pro ekonomické fakulty 1. 1. Vydání Ekopress, Praha 2000. ISBN 80-86119-30-0.
[4] KAŇKA, M., HENZLER, J. Matematika pro ekonomické fakulty 2. 1. Vydání Ekopress, Praha 2000. ISBN 80-86119-31-9.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Graded creditGraded credit100 (100)51
        Zápočtová písemkaWritten test100 51