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Lecturer(s)
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Dofková Radka, doc. PhDr. Ph.D.
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Laitochová Jitka, doc. RNDr. CSc.
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Course content
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The subject studies the calculus of functions of one variable and its application. It clarifies basic terminology of the theory (real function of a real variable, limit and continuity, derivatives) and the development of functions. 1. Real functions of a real variable, graphs, a limit of a function and its geometric interpretation, infinite limits, limits at infinity, continuous functions. Calculating limits. Derivative of a function, differentiation rules, importance of the sign of first derivative, higher-order derivatives. 2. Local and global extreme values of a function, course of a function. Differential of a function, Taylor's theorem. Indefinite number sequence, limit of a sequence.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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Differential calculus of functions of one variable and its applications. Limits. Continuous functions. Derivatives. Determining the shape of a function.
Know how to use calculus to study functions (sketch the graph), to find maxima and minima and to approximate functions.
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Prerequisites
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Knowledge of secondary school mathematics, especially functions.
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Assessment methods and criteria
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Mark
Passing tests, elaboration of homeworks.
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Recommended literature
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Jarník, V. (1955). Diferenciální počet I.. Praha.
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Laitochová, J. (2010). Functions and Graphs. Olomouc.
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Laitochová, J. (2007). Matematická analýza 1. Diferenciální počet - 1. část. Olomouc : Univerzita Palackého.
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Laitochová, J. (2004). Matematická analýza 1. Diferenciální počet - 2. část. Olomouc : Univerzita Palackého.
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Škrášek, J. Tichý, Z. (1983). Základy aplikované matematiky. Praha: SNTL.
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Thomas, G.,B. (2008). Thomas' Calculus. Pearson Addison Wesley.
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