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Lecturer(s)
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Kotrla Lukáš, Ing. Ph.D.
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Stehlík Petr, Doc. RNDr. Ph.D.
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Hesoun Jakub, Mgr.
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Švígler Vladimír, RNDr. Ph.D.
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Zahradníková Michaela, RNDr.
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Volek Jonáš, RNDr. Ph.D.
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Course content
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Week 1: Sets and elementary operations; subsets of real numbers; absolute value; maximum, minimum, least upper bound, and greatest lower bound of a subset of real numbers; Week 2: Sequences of real numbers; subsequences; bounded and monotone sequences; recursively defined sequences; convergent and divergent sequences; Week 3: Algebra of limits and fundamental theorems concerning the properties of a limit; Week 4: Conditions ensuring the convergence of infinite sequences and series; Week 5: Absolute and relative convergence, alternating series; Week 6: Functions of one real variable; graphical representation; inverse functions; composition of functions; Week 7: Local and global behaviour of a function; limits; one-sided limits; algebra of limits; Week 8: Continuity of a function at a point; points of discontinuity; continuity in a closed interval; Week 9: Derivative and differential of a function - definition and both the geometrical and the physical meaning; differentiability and continuity of a function; Week 10: Differentiation from first principles, product rule and chain rule, Rolle's theorem, Langrange's and Cauchy's mean value theorems; stationary points of a function; l'Hospital's rule; Week 11: Indefinite integral; fundamental theorem of calculus; integration by parts and integration by substitution; Week 12: Definite integral and its applications; mean value theorem inequalities for integrals; Week 13: Improper integrals; higher order derivatives and differentials; Taylor's theorem;
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Learning activities and teaching methods
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Lecture supplemented with a discussion
- Contact hours
- 78 hours per semester
- Preparation for comprehensive test (10-40)
- 24 hours per semester
- Preparation for an examination (30-60)
- 56 hours per semester
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| prerequisite |
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| Knowledge |
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| be familiar with high school mathematics |
| explain basic methods of solving simple mathematical problems |
| understand a simple mathematical text |
| Skills |
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| solve linear and quadratic equations and inequalities as well as their systems |
| work with absolute values, powers and simplify mathematical expressions |
| sketch the graphs of elementary functions and their simple modifications |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| demonstrate knowledge of definitions and elementary properties of sequences, series, and differentiable functions of one real variable |
| be able to read and understand mathematical text |
| use logical constructions in formulating basic definitions and theorems |
| Skills |
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| use the calculus rules to differentiate functions |
| sketch the graph of a function using critical points, derivative tests for monotonicity and concavity properties |
| set up max/min problems and use differentiation techniques to solve them |
| evaluate integrals using basic integration techniques, such as substitution and integration by parts |
| work with sequences and series of real numbers |
| use developed theory in solving problems on physical systems |
| use l'Hospital's rule |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| Skills |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| Competences |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| assessment methods |
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| Knowledge |
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| Continuous assessment |
| Test |
| Combined exam |
| Skills |
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| Continuous assessment |
| Test |
| Combined exam |
| Competences |
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| Continuous assessment |
| Test |
| Combined exam |
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Recommended literature
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Děmidovič, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod : Fragment, 2003. ISBN 80-7200-587-1.
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Drábek, Pavel; Míka, Stanislav. Matematická analýza I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-558-8.
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Míková, Marta; Kubr, Milan; Čížek, Jiří. Sbírka příkladů z matematické analýzy I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-568-5.
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Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Pultr, Aleš. Matematická analýza I. Praha : Matfyzpress, 1995. ISBN 80-8586-3-09-X.
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