151-0801/03 – Mathematics A (MA Cžv)
Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |
Subject guarantor | Ing. Orlando Arencibia Montero, Ph.D. | Subject version guarantor | Ing. Orlando Arencibia Montero, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | winter |
| | Study language | Czech |
Year of introduction | 1999/2000 | Year of cancellation | 2022/2023 |
Intended for the faculties | EKF | Intended for study types | Bachelor |
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.
• 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.
Teaching methods
Lectures
Individual consultations
Other activities
Summary
Taught in Czech only. It contains the following topics:
1. Linear algebra – Euclidean space, matrices, determinant.
2. Linear algebra – the inverse of the matrix, linear equations.
3. Functions of one real variable – definition, properties, graphs, inverse
functions.
4. The limit of function – properties of limits, limits to infinity, one sided
limits, definition of continuit, sequences, limits
of sequences.
5. An introduction to the derivation – slope of a tangent line at a point,
6. Higher order derivations, l´Hospital´s rule.
7. Additional applications of derivation.
Compulsory literature:
[4] Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011.
[5] Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.
Recommended literature:
[4] Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008.
[5] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007.
[6] Simon C.P., Blume L. Mathematics for Economists. W.W. Norton & Company, New York-London, 2005.
Way of continuous check of knowledge in the course of semester
Kontrolní úkoly v prostředí LMS MOODLE na EkF VŠB-TUO
Požadavky na ukončení (zápočet):
Splnění zápočtových prácí. Z maximálního počtu bodů je nutno získat alespoň 50%.
E-learning
Other requirements
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Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Eliaš, J., Horváth, J., Kajan, J.: Zbierka úloh z vyššej matematiky 1. časť. Alfa Bratislava, 6. vydání 1985.
2. Eliaš, J., Horváth, J., Kajan, J.: Zbierka úloh z vyššej matematiky 2. časť. Alfa Bratislava, 6. vydání, 1986.
3. Göhler, W., Ralle, B.: Lexikón vyššej matematiky. Alfa Bratislava, 1992, ISBN 80-05-00531-8.
4. Horský, Z.: Učebnice matematiky pro posluchače VŠE I. SNTL, Praha 1980
5. Kaňka, M., Coufal, J., Klůfa, J., Henzler, J.: Učebnice matematiky pro ekonomické fakulty. Victoria Publishing Praha, 1996, ISBN 80-7187-148-6.
6. Kaňka, M., Hanzler, J.,: Matematika pro ekonomy 2, EKOPRESS, Praha, 1997
7. Klůfa, J., Coufal, J.: Matematika pro ekonomy 1, EKOPRESS, Praha, 1997
8. Kolektiv autorů: Cvičení z matematiky I, II. Vysoká škola báňská, Ostrava.
9. Krajňáková, D., Míčka, J., Machačová, L.: Zbierka úloh z matematiky. Alfa Bratislava a SNTL Praha, 1988.
10. Poloučková, Šalounová: Diferenciální počet I, VŠB-TU, Ostrava, 2001. ISBN 80-7078-904-2.
11. Sydsaeter, K., Hammond, P.J.: Mathematics for Economic Analysis. Prentice-Hall, Inc., 1995, ISBN 0-13-583600-X.
12. Šalounová,D., Poloučková,A. Úvod do lineární algebry. VŠB-Technická univerzita, Ostrava 2003. ISBN 80-248-0199-x.
13. Škrášek, J., Tichý, Z.: Základy aplikované matematiky I. SNTL – Nakladatelství technické literatury, Praha, 2. vydání, 1989.
14. Šmakal, S., Prágerová, A., Voříšek, J.: Učebnice matematiky pro posluchače VŠE II. SNTL, Praha 1984
15. Vrbický, J., Šalounová, D.: Lineární algebra. VŠB -- Technická univerzita Ostrava, 2000, ISBN 80-7078-960-3.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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