Lecturer(s)
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Pátíková Zuzana, doc. 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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unspecified
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prerequisite |
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Knowledge |
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Středoškolská znalost předmětu matematika. |
Středoškolská znalost předmětu matematika. |
Středoškolská znalost předmětu matematika. Případně Seminář z matematiky TP1SM. |
Středoškolská znalost předmětu matematika. Případně Seminář z matematiky TP1SM. |
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. |
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 |
Practice exercises |
Lecturing |
Practice exercises |
Skills |
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Practice exercises |
Practice exercises |
assessment methods |
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Knowledge |
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Written examination |
Written examination |
Recommended literature
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Křenek, Josef. Diferenciální a integrální počet funkce jedné proměnné s aplikacemi v ekonomii. Vyd. 4. Zlín : Univerzita Tomáše Bati, Fakulta technologická, 2004. ISBN 8073181630.
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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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