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Lecturer(s)
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Hozman Jiří, RNDr. Mgr. Ph.D.
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Salač Petr, doc. RNDr. CSc.
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Course content
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1. Introduction - used symbols, notations. Basic terms of sententional calculus. Number sets. 2. The least upper bounds and greatest lower bounds. Sequences and limit of sequences (finite, infinite), 3. Accumulation point of sequence. Theorems about limit, calculation of limit, number e. 4. Real function of one real variable. Basic characteristic of function. Composite function and inverse function. 5. Review of elementary functions. 6. Limits and continuity - limits of functions, asymptotic behavior of functions 7. Differentiation - differentiable functions, rules for differentiation 8. Rolle's Theorem, the mean value theorem, L' Hospital's rule, Taylor polynomial and Taylor series 9. Extreme of function and points of inflection. Applications of derivatives to studying of graph of a function. 10. Primitive function and indefinite integral. Basic rules, method per partes, substitution method. 11. Integration by partial fractions. 12. Riemann definite integral. Method per partes and substitution method for Riemann definite integral. Newton-Leibniz's theorem. 13. Applications of Riemann definite integral. Infinite integral. 14. Reserve. Practice: The material explained at the previous week lecture is practised.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
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Learning outcomes
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In subject there are explained the basic issues of mathematical analysis. Function, graph of a function, operations with functions. Survey of elementary functions of one real variable. Sequences. Limits of functions. Differentation, technique of derivation, applications. Antiderivative, integration. Riemann integral, applications.
Calculus (differential and integral) of function of one real variable.
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Prerequisites
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Knowledge of mathematics at the high school level.
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Assessment methods and criteria
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Combined examination
Presence in seminars, pass 3 tests, knowledge of secondary school mathematics. Exam: The prerequisites for passing an exam are credits from subjects KMD/M1A-P a KAP/SEM-P. The exam has written and oral parts.
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Recommended literature
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Budinský, B., Charvát, J.:. Matematika 1 [skriptum ČVUT fakulta stavební]. Praha, 2000.
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Děmidovič, B. P.:. Sbírka úloh a cvičení z matematické analýzy. FRAGMENT, 2003.
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Mezník, I. - Karásek, J. - Miklíček, J. Matematika 1 pro strojní fakulty. Praha, SNTL, 1992.
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Nekvinda, M. - Vild, J. Matematické oříšky I. Liberec, 2001. ISBN 80-7083-262-2.
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Nekvinda, M. Matematika I. Liberec, 2000.
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Rektorys, K. a další:. Přehled užité matematiky.. Praha, Prometheus, 2000. ISBN 80-85849-92-5.
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Vild, J. - Říhová, H.:. Diferenciální kalkul F1.. Liberec, 2002. ISBN 80-7083-552-4.
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Vild, J. - Říhová, H.:. Integrální kalkul F1.. Liberec, 2005. ISBN 80-7083-587-7.
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