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Lecturer(s)
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Finěk Václav, doc. RNDr. Ph.D.
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Šimůnková Martina, RNDr. Ph.D.
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Course content
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1. Sets, number sets, inequalities, supremum and infimum, logic, proofs in mathematics, mappings and functions. 2. Compositions of functions, inverse functions, basic real functions and their properties, plane curves. 3. Sequences of real numbers, limits. 4. Continuity and limits of functions. 5. Derivatives and differentials. 6. Theorems about continuous functions, the mean value theorems, l´Hospital rule. 7. Monotone functions, convex and concave functions, meaning of the first and second derivative, inflexion, relative and absolute extrema, asymptotes, analysis of function behavior. 8. Numerical methods for nonlinear equations and numerical quadratures. 9. The principle of nested intervals. Cantor's theorem on nested intervals. 10. Taylor polynomial 11. Implicit function
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
- Preparation for credit
- 28 hours per semester
- Preparation for exam
- 28 hours per semester
- Home preparation for classes
- 38 hours per semester
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Learning outcomes
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Elementary theory of a real function of one real variable and the differential calculus of a real fuction of one real variable.
Functions of one variables, differential calculus.
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Prerequisites
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Secondary school mathematics.
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Assessment methods and criteria
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Oral exam, Written exam
Exam: Written and/or oral form.
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Recommended literature
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Bittnerová, D., Plačková, G. Louskáček 1 - diferenciální počet funkcí jedné reálné proměnn. Liberec, 2007.
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Černý, I. Matematická analýza, 1. část. [Skripta TU v Liberci.]. TUL, Liberec, 1995.
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Černý, I. Matematická analýza, 2. část. [Skripta TU v Liberci.]. TUL, Liberec, 1996.
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Jarník, V. Diferenciální počet I. Praha 1963..
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Jirásek, F., Kriegelstein, E., Tichý, Z. Sbírka řešených příkladů z matematiky. Praha, 1982.
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