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Lecturer(s)
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Lysák Jaroslav, Ing. Ph.D.
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Zedníková Jana, Mgr.
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Štětina Petr, RNDr.
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Course content
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1. Vectors. 2. Determinants. 3. Inverse matrix and applications of matrix calculus. 4. Methods for integration (per partes, basic substitutions). Improper integrals. 5. The ideas of integral calculus in numerical mathematics. Applications in math. statistics and economy. 6. Differencial equations - basic methods. 7. Linear differencial equation of the first order and its applications in economy. 8. Sequences. 9. Difference of a sequence, difference of higher orders. Difference equation. 10. Linear difference equation and its applications in economy. 11. Partial derivation and gradient, extremes of functions of multiple variables. 12. Applications of functions of multiple variables in economy. 13. Resume. Examples. Conclusion.
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Learning activities and teaching methods
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Lecture with practical applications, Collaborative instruction, Seminar classes, Individual study, Practicum
- Preparation for formative assessments (2-20)
- 6 hours per semester
- Preparation for comprehensive test (10-40)
- 9 hours per semester
- Contact hours
- 39 hours per semester
- Preparation for an examination (30-60)
- 24 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| prepare model tasks of simpler type for application of matrix calculus |
| recognize basic continuous and inverse functions of one real variable |
| describe the derivative of a function and the integral of a function of one real variable |
| Skills |
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| to solve systems of linear equations by suitable application of matrix calculus |
| draw graph of algebraic, trigonometric, exponential and logarithmic functions |
| differentiate and integrate functions of one real variable |
| solve optimization problems for functions of one real variable |
| Competences |
|---|
| bc. study: recognizes a problem, clarifies its nature, divides it into parts |
| N/A |
| learning outcomes |
|---|
| Knowledge |
|---|
| describe the basic properties of the sequence |
| to construct a linear difference equation with constant coefficients |
| describe graph and contour lines of real functions of two variables |
| introduce derivative of partial derivative and gradient |
| formulate the problem of finding the extreme of the function of two variables |
| Skills |
|---|
| find an inverse matrix |
| compute the value of the determinant of a matrix |
| find an antiderivate and to compute an integral of certain functions of one variable |
| use integral calculus in its applications (geometry, math.statistics, ecomomy) |
| use a differencial or difference equation for describing a simple economic model, to solve it and to interpretate results |
| determine extremes of a function of multiple variables |
| Competences |
|---|
| bc. study: they decide independently and responsibly on the basis of a framework assignment in the context only partially known bc. study: independently gain further professional knowledge, skills and competences based on practical experience and its evaluation, but also by independent study of theoretical knowledge of the field |
| teaching methods |
|---|
| Knowledge |
|---|
| Practicum |
| Collaborative instruction |
| Individual study |
| Interactive lecture |
| Seminar classes |
| Skills |
|---|
| Seminar |
| Practicum |
| Competences |
|---|
| Practicum |
| Interactive lecture |
| assessment methods |
|---|
| Knowledge |
|---|
| Combined exam |
| Test |
| Skills demonstration during practicum |
| Skills |
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| Test |
| Skills demonstration during practicum |
| Competences |
|---|
| Combined exam |
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Recommended literature
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Dolanský, Petr; Tuchanová, Milena. Matematika pro ekonomy 1.,2.,3.část : pro distanční studium. 1.vyd. Plzeň : ZČU, 1995.
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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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Kaňka M., Henzler J. Matematika pro ekonomy. Ekopress Praha, 1997.
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Kaňka, Miloš; Henzler, Jiří. Matematika pro ekonomy 2. 1. vyd. Praha : Ekopress, 1997. ISBN 80-86119-01-7.
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Mašek, Josef. Základy matematiky II : cvičení. 1. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-507-3.
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P. Drábek, S. Míka. Matematická analýza II. Plzeň, 2010. ISBN 978-80-7082-977-6.
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P. Drábek, S. Míka. Matematická analýza I. Plzeň, 2003. ISBN 80-7082-978-8.
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