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Lecturer(s)
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Lacková Veronika, RNDr. Ph.D.
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Eisenmann Petr, doc. PaedDr. CSc.
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Loukotová Lucie, Mgr.
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Course content
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Real numbers and their properties, suprema and infima, sequences Limits of sequences, their basic properties Calculus of limits of sequences Series of real numbers, their convergence, criteria of series of positive numbers Series of sign changing numbers, absolute and non-absolute convergence Continuity of functione and its properties Basic theorems on continuous functions Limits of functions Derivative of functions and its properties Mean value theorem and its consequences Derivatives versus monotonicity, convex functions Applications of derivatives, graphing functions Aproximation by polynomial functions, Taylor polynoms
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Students will learn basic concepts of mathematical analysis, mainly precise definitions of continuity, limits and derivatives. They will also learn how to use those tools in other fields, as physics, economy, and in mathematics (graphing functions, approzimation by polynomial functions).
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Prerequisites
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Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.
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Assessment methods and criteria
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unspecified
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Recommended literature
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ČERNÝ, Ilja. Inteligentní kalkulus.
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ČERNÝ, Ilja. Matematická analýza II. Liberec: Technická univerzita, 1996. ISBN 80-7083-188-X.
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ČERNÝ, Ilja. Matematická analýza I. Liberec: Technická univerzita, 1995. ISBN 80-7083-188-X.
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JARNÍK, Vojtěch. Integrální počet I. Praha: Academia, 1984.
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KOPÁČEK, Jiří. Matematická analýza pro fyziky I. Praha: Matfyzpress, 1997. ISBN 80-85863-74-X.
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VESELÝ, Jiří. Matematická analýza pro učitele. Praha: Matfyzpress, 1997. ISBN 80-85863-23-5.
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