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Lecturer(s)
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Petrášková Vladimíra, doc. RNDr. Ph.D.
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Course content
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Topics of lectures and seminars: 1. The concept of function. Examples of some important functions. (linear function, quadratic function, absolute value function,) 2. Operations with functions: arithmetic, composition of functions, restriction of functions. 3. Polynomials. Their special cases (direct ratio, power function,...) 4. Rational functions and their special cases. 5. Basic properties of real functions of one real variable: parity, periodicity, injectivity, bijectivity, bounded function. 6. Properties of functions: maximum / minimum, supremum / infimum, monotonicity of a function. 7. Inverse function and its basic properties. 8. Function of the n-th root. Power with rational exponent. 9. Exponential function (natural exponential, general exponential). General power. 10. Logarithmic function (natural logarithm, common logarithm, a logarithm to the base a). 11. Trigonometric functions: a) in a right triangle (degrees), b) on a unit circle (radians). 12. Editing expressions with elementary functions. 13. Equations and inequalities with elementary functions - graphical solution, algebraic solution. 14. Cyclometric functions.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
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Learning outcomes
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The aim of the course is to acquaint students with the concept of function, basic properties of functions and known functions.
The student will be familiar with the basic concepts related to the real function of one real variable, will be able to apply the acquired knowledge in practical tasks.
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Prerequisites
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none
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Assessment methods and criteria
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Student performance assessment, Combined exam
During the semester, completion of two written tests and elaboration of assigned tasks. Exam test + oral exam.
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Recommended literature
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Odvárko, O. Matematika pro gymnázia: goniometrie. Praha: Prometheus, 1994.
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Odvárko, O. Matematika pro gymnázia:funkce. Praha: Prometheus, 2011.
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Petrášková, V., Štěpánková, H. Algebraické funkce a diferenciální počet funkce jedné proměnné. České Budějovice: Jihočeská univerzita, 2014. ISBN 978-80-7394473-5.
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Petrášková, V., Zmeškalová, E. Algebraické funkce. České Budějovice: Jihočeská univerzita, 2005. ISBN 978-80-7040-825-1.
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