151-0801/03 – Mathematics A (MA Cžv)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits5
Subject guarantorIng. Orlando Arencibia Montero, Ph.D.Subject version guarantorIng. Orlando Arencibia Montero, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction1999/2000Year of cancellation2022/2023
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
POL95 RNDr. Alena Poloučková
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Lifelong Credit 1+0

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

Lifelong form (validity from: 1960/1961 Summer semester, validity until: 2010/2011 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Exercises evaluation Credit 85  85 3
        Written exam Written test   3
Mandatory attendence participation:

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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
2014/2015 (B6208) Economics and Management (6208R037) Management C Czech Ostrava 1 Compulsory study plan
2014/2015 (B6208) Economics and Management (6208R020) Business Economics C Czech Ostrava 1 Compulsory study plan
2013/2014 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2013/2014 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2012/2013 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2011/2012 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (02) Public Economics and Administration C Czech Ostrava 1 Compulsory study plan
2010/2011 (B6202) Economic Policy and Administration (6202R040) Regional Development C Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6202R049) Accounting and Taxes (02) Accounting and Taxes C Czech Ostrava 1 Compulsory study plan
2010/2011 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics C Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R037) Management (02) Management C Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

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Assessment of instruction

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