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Lecturer(s)
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Hylasová Karolína, Mgr.
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Krejčíková Kateřina, Bc.
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Egermaier Jiří, Ing. Ph.D.
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Ťoupal Tomáš, Ing. Ph.D.
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Marek Patrice, Ing. Ph.D.
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Štauberová Zuzana, Mgr.
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Kobeda Zdeněk, RNDr.
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Tomiczková Světlana, RNDr. Ph.D.
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Course content
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1. Mathematical reasoning - open statements and quantifiers, sets and elementary operations, subsets of real numbers. Vectors and its interpretation and using. 2. Matrix calculus and applications of matrix calculus in economics. 3. Systems of linear equations and methods of solution. 4. Real functions of one real variable - properties of functions. 5. Real functions of one real variable - operations with functions, composition of functions, overview of elementary functions. 6. Limits and continuity of functions - limit definition and definition of one-sided limit. 7. Limits and continuity of functions - algebra of limits. Continuity of a function, points of discontinuity. 8. Derivative of a function - definitions and their geometrical and economical meaning. Differentiation from first principles, product rule and chain rule. Application of differential calculus in economics. 9. Applications of differential calculus - tangent, Taylor polynomial, limit computation, solving optimization problems. 10. Applications of differential calculus - sketching graphs. 11. Integral calculus - indefinite integral and basic calculation methods. 12. Integral calculus - definite integral and applications of integral calculus in economics. 13. Final summary.
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Learning activities and teaching methods
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Interactive lecture, Task-based study method, Students' self-study, Practicum
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Contact hours
- 52 hours per semester
- Preparation for comprehensive test (10-40)
- 32 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| know mathematical concepts and procedures in the range of secondary school curricula |
| to think logically and not to have negative prejudices about mathematics |
| recognise basic types of functions, their most important properties and can draw graphs of these functions (linear, quadratic, exponential, logarithmic, linear-to-linear) |
| Skills |
|---|
| has no negative relation to abstract thinking |
| can solve linear and quadratic equations and inequalities |
| has experience in calculating algebraic expressions |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| selected possibilities of using mathematical methods and approaches in modeling economic phenomena |
| mathematical terms and procedures from the areas of mathematics listed in the syllabus of the subject |
| Skills |
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| can correctly apply formal and content aspect in mathematical expression, both written and oral |
| is able to apply the principles of matrix calculus to simple model problems |
| is able to apply the principles of differential and integral calculus to simple model problems |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Interactive lecture |
| Practicum |
| Self-study of literature |
| Skills |
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| Interactive lecture |
| Practicum |
| Self-study of literature |
| Competences |
|---|
| Interactive lecture |
| Practicum |
| Self-study of literature |
| assessment methods |
|---|
| Knowledge |
|---|
| Combined exam |
| Skills demonstration during practicum |
| Skills |
|---|
| Combined exam |
| Skills demonstration during practicum |
| Competences |
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| Combined exam |
| Skills demonstration during practicum |
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Recommended literature
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Bauer, Luboš; Lipovská, Hana; Mikulík, Miloslav,; Mikulík, Vít. Matematika v ekonomii a ekonomice. První vydání. 2015. ISBN 978-80-247-4419-3.
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Čížek, Jiří; Kubr, Milan; Míková, Marta. Sbírka příkladů z matematické analýzy I. 1. vyd. Plzeň : ZČU, 1995. ISBN 80-7082-216-3.
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Dolanský, P., Tuchanová, M. Příklady z matematiky pro ekonomy II.
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Dolanský, Petr. Matematika pro distanční studium. 1. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-643-6.
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Dolanský, Petr; Tuchanová, Milena. Matematika pro ekonomy II. 1. část, distanční studium. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-656-8.
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Dolanský, Petr; Tuchanová, Milena. Matematika pro ekonomy 1 : pro distanční studium. Plzeň : ZČU, 1995. ISBN 80-7082-183-3.
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Dolanský, Petr; Tuchanová, Milena. Příklady z matematiky pro ekonomy I : distanční studium. 1. vyd. Plzeň : ZČU, 1995. ISBN 80-7082-184-1.
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Drábek, Pavel; Míka, Stanislav. Matematická analýza I.. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-978-8.
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Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnné. 2. nezměn. vyd. Praha : SNTL, 1981.
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Mašek, Josef. Základy matematiky I : cvičení. 1. vyd. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-567-7.
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Tesková, Libuše. Lineární algebra. 2. vyd. Plzeň : Západočeská univerzita, 2005. ISBN 80-7043-413-9.
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Tesková, Libuše. Sbírka příkladů z lineární algebry. 4. vyd. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-552-9.
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