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Lecturer(s)
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Nosková Lucie, Mgr. Ph.D.
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Course content
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1st Functions of one real variable. Properties of functions - D(f), H(f), graph, function simple, monotone, periodic, inverse, composite function. 2nd Basic functions and their properties - constant, linear, power, exponential, logarithmic, goniometrical. 3rd Continous function. Limit functions - definitions, limit theorems, one-sided limits (limit on the right/on the left), infinite limits. 4th Derivate of function - definition, geometrical meaning of derivation of function. Derivate of selected functions. The rules for calculating the derivative, derivate theorems. 5th Derivates of grander orders. The importance of derivations in chemistry - the instantaneous velocity of chemical reactions. 6th Course of functions - functions monotone, extremes, convex and concave functions, inflection points. Examination of the function. 7th Integral and its properties. The introduction of indefinite and definite integral. Integration of selected functions. Properties of integrals. Geometrical meaning of definite integral. 8th Calculating methods of indefinite integrals - the appropriate modification, integration by parts, substitution method. Calculation methods of definite integrals. 9th Functions of several real variables - basic concepts, graph. 10th Partial derivate of functions of two real variables. 11th Differential equations - basic concepts, solving simple differential equations.
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Learning activities and teaching methods
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Skills demonstration, Students' self-study, Lecture with visual aids, Seminar
- Preparation for comprehensive test (10-40)
- 40 hours per semester
- Contact hours
- 39 hours per semester
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| prerequisite |
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| Knowledge |
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| describe elementary functions, their properties, course |
| Skills |
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| edit algebraic expressions |
| solve equations and inequalities |
| learning outcomes |
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| Knowledge |
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| to describe properties and the course of elementary functions of one real variable |
| define derivative function |
| to clarify the meaning of the derivation of the function for its course |
| Skills |
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| to specify the function limit |
| to derive the function of one real variable |
| určit parciální derivace funkce dvou reálných proměnných |
| Competences |
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| to derive the functions of two real variables |
| teaching methods |
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| Knowledge |
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| Lecture with visual aids |
| Seminar |
| Skills demonstration |
| Self-study of literature |
| assessment methods |
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| Test |
| Skills demonstration during practicum |
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Recommended literature
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HEŘMÁNEK L. a kol. Sbírka příkladů z Matematiky I ve strukturovaném studiu. VŠCHT, Praha, 2008. ISBN 978-80-7080-688-3.
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KLÍČ, Alois. Matematika I ve strukturovaném studiu. Praha, VŠCHT. 2007.
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Míčka, Jiří. Sbírka příkladů z matematiky. Vyd. 4., přeprac. Praha : Vysoká škola chemicko-technologická, 2002. ISBN 80-7080-484-X.
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PAVLÍKOVÁ P., SCHMIDT O.. Základy matematiky. VŠCHT, Praha, 2006. ISBN 978-80-7080-615-9.
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TURZÍK D., DUBCOVÁ M., PAVLÍKOVÁ P. Základy matematiky pro bakaláře. VŠCHT, Praha, 2011. ISBN 978-80-7080-787-3.
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