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Lecturer(s)
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Ježek Vladimír, doc. Ing. Ph.D.
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Lysák Jaroslav, Ing. Ph.D.
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Pekarovič Václav, Mgr.
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Brada Pavel, Ing. Ph.D.
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Siahkamari Josef, Mgr. Ph.D.
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Course content
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Week 1: Mathematical reasoning; sets and elementary operations; Week 2: Sequences of real numbers and their properties; Week 3: Methods of calculating a limit of a sequence; Week 4: Series of real numbers; convergence criteria; Week 5: Functions of one real variable and their properties; Week 6: Local and global behaviour of a function; limits; algebra of limits; Week 7: Continuity of a function at a point; points of discontinuity; continuity in a closed interval; Week 8: Derivative and differential of a function, their geometrical and the physical meaning; differentiability and continuity of a function; Week 9: Differentiation, product rule and chain rule; stationary points of a function; l'Hospital's rule; Week 10: Higher order derivatives and differentials; Taylor's theorem; Week 11: Indefinite integral; integration by parts and integration by substitution; Week 12: Applications of differential and integral calculus in solving optimization and physical problems. Week 13: Recapitulation
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Learning activities and teaching methods
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Interactive lecture, Lecture with practical applications, Practicum
- Contact hours
- 52 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Preparation for an examination (30-60)
- 32 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with a high school algebra and trigonometry. |
| 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 the definitions and the elementary properties of sequences, series, and differentiable functions of one real variable |
| structure and character of mathematical text |
| logical constructions in formulating basic definitions and theorems |
| Skills |
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| ability to read and understand mathematical text |
| use the calculus rules to differentiate functions |
| sketch the graph of a function using critical points, the derivative tests for monotonicity and concavity properties |
| set up max/min problems and use differentiation techniques to solve them |
| evaluate integrals using techniques of integration, such as substitution and integration by parts |
| to work with sequences and series of real numbers |
| use developed theory in solving problems on physical systems |
| use l'Hospital's rule |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Interactive lecture |
| Practicum |
| Task-based study method |
| Skills |
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| Interactive lecture |
| Practicum |
| Task-based study method |
| Competences |
|---|
| Interactive lecture |
| Practicum |
| Task-based study method |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Test |
| Skills demonstration during practicum |
| Skills |
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| Oral exam |
| Written exam |
| Test |
| Competences |
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| Oral exam |
| Written exam |
| Test |
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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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