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Lecturer(s)
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Polášek Vladimír, Mgr. Ph.D.
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Course content
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1. Basics of mathematical logic. 2. Sets and set operations. Number sets. 3. Simple functions and their transformations. Graph function. 4. Functions and their properties, operations with functions. Compound function. Inverse function. 5. Limits of functions. Continuity of a function. 6. Asymptotes of a graph of a function. One sided limits. 7. Derivative of a function. Basic rules and properties. 8. Tangent and normal lines of a function. Derivatives of Composite functions. 9. Derivatives of higher order. L'Hospital's rule. Local Extrema of a function. 10. Behavior of a funcion. 11. Primitive function. 12. Integration for parties. Substitution method. 13. Integration of rational functions. 14. Definite integral. Application of a definite integral.
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Learning activities and teaching methods
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Lecturing, Practice exercises, Individual work of students
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| prerequisite |
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| Knowledge |
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| Basic initial knowledge and skills of secondary school mathematics are assumed. |
| Basic initial knowledge and skills of secondary school mathematics are assumed. |
| learning outcomes |
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| 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. |
| Identify the elementary functions from the graphs. |
| Identify the elementary functions from the graphs. |
| 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 what a primitive function is to a given function. |
| Explain what a primitive function is to a given function. |
| Formulate the Newton-Leibniz formula. |
| Formulate the Newton-Leibniz formula. |
| Clarify the geometric meaning of a definite integral. |
| Clarify the geometric meaning of a definite integral. |
| 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. |
| Sketch the graphs of elementary functions and describe their properties. |
| Sketch the graphs of elementary functions and describe their properties. |
| 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 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. |
| Compute simple indefinite integrals. |
| Compute simple indefinite integrals. |
| Using a definite integral, calculate the area content of bounded graphs of elementary functions. |
| Using a definite integral, calculate the area content of bounded graphs of elementary functions. |
| teaching methods |
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| Knowledge |
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| Practice exercises |
| Practice exercises |
| Individual work of students |
| Individual work of students |
| Lecturing |
| Lecturing |
| assessment methods |
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| Written examination |
| Written examination |
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Recommended literature
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Matejdes, M. Aplikovaná matematika. Matcentrum-Zvolen, 2005.
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Ostravský J., Polášek V. Diferenciální a integrální počet funkce jedné proměnné: vybrané statě. Zlín, 2011. ISBN 978-80-7454-124-7.
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Polášek, V., Sedláček, l. & Kozáková, L. Matematický seminář. Zlín: Nakladatelství UTB., 2018.
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