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Lecturer(s)
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Pátíková Zuzana, doc. Mgr. Ph.D.
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Fiľo Jaroslav, Mgr.
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Sousedíková Lucie, Ing.
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Janíková Miriam, Mgr. Ph.D.
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Martinek Pavel, Ing. Ph.D.
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Course content
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unspecified
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Learning activities and teaching methods
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Lecturing, Practice exercises
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| prerequisite |
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| Knowledge |
|---|
| Středoškolská znalost předmětu matematika. Případně Seminář z matematiky TP1SM. |
| Středoškolská znalost předmětu matematika. Případně Seminář z matematiky TP1SM. |
| learning outcomes |
|---|
| Verbally define the term function (a real function of one real variable) and the related terms domain of definition and range of values. |
| Verbally define the term function (a real function of one real variable) and the related terms domain of definition and range of values. |
| Describe what is true for a pair of mutually inverse functions, and when the inverse function can be constructed. |
| Describe what is true for a pair of mutually inverse functions, and when the inverse function can be constructed. |
| Define cyclometric functions. |
| Define cyclometric functions. |
| Explain the geometric meaning of the derivative of a function at a point. |
| Explain the geometric meaning of the derivative of a function at a point. |
| Explain when a set of vectors is linearly dependent/independent. |
| Explain when a set of vectors is linearly dependent/independent. |
| Describe what a unit, regular, inverse matrix is. |
| Describe what a unit, regular, inverse matrix is. |
| Skills |
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| Determine and set the domain of definition of the function. |
| Determine and set the domain of definition of the function. |
| From the graph of the function, recognize the intervals on which the function is increasing, decreasing, simple, convex, concave. |
| From the graph of the function, recognize the intervals on which the function is increasing, decreasing, simple, convex, concave. |
| Illustrate with a sketch the nature of the behavior of the function at the given limit. |
| Illustrate with a sketch the nature of the behavior of the function at the given limit. |
| Calculate limits using algebraic adjustments and using L'Hospital's rule. |
| Calculate limits using algebraic adjustments and using L'Hospital's rule. |
| Differentiate elementary, composite, product and quotient functions. |
| Differentiate elementary, composite, product and quotient functions. |
| Calculate the stationary points of the function and decide on the types of possible extremes. |
| Calculate the stationary points of the function and decide on the types of possible extremes. |
| Find the inflection points of a function and the intervals on which the function is convex/concave. |
| Find the inflection points of a function and the intervals on which the function is convex/concave. |
| Find the equation of the asymptote of a function with and without a slope. |
| Find the equation of the asymptote of a function with and without a slope. |
| Find the equation of the tangent to the graph of the function and sketch it. |
| Find the equation of the tangent to the graph of the function and sketch it. |
| Draw a vector in a Cartesian coordinate system. |
| Draw a vector in a Cartesian coordinate system. |
| Add vectors, subtract them, multiply them by a scalar and multiply each other by a scalar product. |
| Add vectors, subtract them, multiply them by a scalar and multiply each other by a scalar product. |
| Add, subtract and multiply number matrices. |
| Add, subtract and multiply number matrices. |
| Calculate the determinant of a square matrix of the 2nd and 3rd order. |
| Calculate the determinant of a square matrix of the 2nd and 3rd order. |
| Use the Gaussian elimination method to calculate the solution to a system of linear equations. |
| Use the Gaussian elimination method to calculate the solution to a system of linear equations. |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Lecturing |
| Practice exercises |
| Practice exercises |
| assessment methods |
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| Written examination |
| Written examination |
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Recommended literature
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Croft. A., Davidson, R. Foundation Math. Pearson, 2020. ISBN 1292289686.
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Ostravský, Jan, Křenek, Josef. Diferenciální a integrální počet funkce jedné proměnné s aplikacemi v ekonomii. Zlín : UTB, 2004. ISBN 80-7318-163-0.
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Riley, K.F. a kol. Mathematical Methods for Physics and Engineering. Cambridge University Press, 2015. ISBN 100521679710.
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