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Lecturer(s)
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Hrabáček Vítězslav, Ing. Ph.D.
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Kučera Vilém, RNDr. Ph.D.
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Lysák Jaroslav, Ing. Ph.D.
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Brada Pavel, Ing. Ph.D.
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Pech Ondřej, Ing. Ph.D.
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Breitfelder Ondřej, Mgr.
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Vrbková Marie, Ing. Ph.D.
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Lášek António, prof. RNDr. Ph.D.
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Siahkamari Josef, Mgr. Ph.D.
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Course content
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Week 1: sets and operations on them; bounded number set; maximum, minimum, supremum and infimum of a number set; Week 2: sequences of real numbers; bounded and monotone sequences; convergent and divergent sequences; Week 3: methods for computing limits of sequences; Cauchy sequences; Week 4: infinite number series; necessary condition and criteria for convergence of number series; Week 5: absolute and relative convergence of number series; alternating series; Week 6: real functions of one real variable; properties of functions; composite and inverse functions; Week 7: limits of a function; one-sided limits; calculating limits; Week 8: continuity of a function at a point and points of discontinuity; continuity on an interval; Week 9: derivative of a function; rules for calculating the derivative; geometric meaning of the derivative; differential of a function; Week 10: mean value theorems; stationary points of a function; l'Hospital's rule; Week 11: primitive functions; calculating the indefinite integral; integration by parts; integration by substitution; Week 12: definite integral; calculating the definite integral; the mean value theorem; Week 13: improper integrals; Taylor's polynomial; Taylor's theorem.
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Learning activities and teaching methods
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Seminar
- Contact hours
- 26 hours per semester
- Preparation for comprehensive test (10-40)
- 26 hours per semester
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| prerequisite |
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| Knowledge |
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| recognise direct and inverse proportion problems |
| describe the rules for modifying numerical and algebraic expressions |
| describe basic functions (polynomials, goniometric functions, exponential, logarithmic functions) |
| recognise arithmetic and geometric sequences |
| identify quadratic, exponential, logarithmic and goniometric equations |
| Skills |
|---|
| solve quadratic, exponential, logarithmic and goniometric equations |
| modify numerical and algebraic expressions |
| sketch graphs of basic functions |
| calculate the partial sum of an arithmetic and geometric sequence |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| recognise logical symbols, statements and quantifiers |
| describe continuous and inverse functions |
| describe a sequence and series of real numbers |
| describe the derivative and integral of a function of one real variable |
| Skills |
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| draw the graph of the inverse function; algebraic, goniometric, exponential and hyperbolic |
| differentiate and integrate functions of one real variable |
| solve optimization problems for functions of one real variable |
| decide on the convergence and divergence of a sequence, a series and an improper integral |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Seminar |
| Skills |
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| Seminar |
| Competences |
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| Seminar |
| assessment methods |
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| Knowledge |
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| Test |
| Skills |
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| Test |
| Competences |
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| Test |
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Recommended literature
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Canuto, Claudio. Mathematical analysis I. New York : Springer, 2008. ISBN 978-88-470-0875-5.
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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.. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-978-8.
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Fonda, Alessandro. A Modern Introduction to Mathematical Analysis. Cham : Birkhäuser, 2023. ISBN 978-3-031-23712-6.
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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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