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Lecturer(s)
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Daněk Josef, Doc. Ing. Ph.D.
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Holubová Gabriela, Doc. Ing. Ph.D.
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Formánková Levá Hana, RNDr.
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Benedikt Jiří, Doc. RNDr. Ph.D.
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Švígler Vladimír, RNDr. Ph.D.
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Course content
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Week 1: Mathematical statements, sets and elementary operations. Week 2: Sequences of real numbers, boundedness, monotonicity, supremum and infimum. Week 3: Limit of a sequence. Methods of calculating a limit, properties of convergent sequences. Week 4: Euler number. Series of real numbers, sum of series, geometric series, harmonic series. Week 5: Functions of one real variable, their domain, restriction, equality of functions. Week 6: Properties of functions. Inverse and composed functions. Week 7: Limits of functions. Continuity of a function at a point. Week 8: Points of discontinuity. Derivative of a function, their geometrical and the physical meaning. Rules of differentiation. Week 9: Tangent and normal lines. Higher order derivatives. Extrema and optimization. Week 10: l'Hospital's rule. Analysing graphs of functions. Solvability of nonlinear equations. Week 11: Taylor's polynomial. Primitive function and indefinite integral. Week 12: Integration by parts and integration by substitution. Definite integral. Week 13: Improper integrals. Integrals with variable bounds.
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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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| be familiar with high school knowledges |
| to explain basic methods of solving simple mathematical problems |
| to understand a simple mathematical text |
| Skills |
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| to solve linear and kvadratic equalities and inequalities and their systems |
| to work with absolute values, powers and manipulate with mathematical expressions |
| to sketch graphs of elementary functions |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| understand logical constructions and to be able to read mathematical text |
| use rigorous arguments in calculus and ability to apply them in solving problems on the topics in the syllabus |
| demonstrate knowledge of the definitions and the elementary properties of sequences, series and continuous and differentiable functions of one real variable |
| Skills |
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| use the rules of differentiation to differentiate functions |
| sketch the graph of a function using critical points, and the derivative test for increasing/decreasing and concavity properties |
| set up max/min problems and use differentiation to solve them |
| use l'Hospital's rule |
| evaluate integrals using techniques of integration, such as substitution and integration by parts |
| use developed theory in solving problems on physical systems |
| to work with sequences and series of real numbers |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Interactive lecture |
| Practicum |
| Skills |
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| Practicum |
| Task-based study method |
| Competences |
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| Lecture |
| Practicum |
| 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 |
| Skills demonstration during practicum |
| Competences |
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| Oral 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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Thomson, Bruckner, Bruckner. Elementary real analysis. 2008.
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Zorich, Vladimir A. Mathematical Analysis I. Berlin, 2004. ISBN 3-540-40386-8.
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