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Lecturer(s)
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Cvrček Milan, PhDr. Ph.D.
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Slámová Tereza, Mgr. Ph.D.
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Bittner Václav, Mgr. Ph.D.
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Tuček Richard, Mgr.
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Course content
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I.Functions 1. Introduction: terminology, notation. Sets od numbers. 2. Function. Graphs. Explicit, implicit and parametric functions. The definition, domain of the function. Function properties 3. Operations with functions. Inverse function. Linear, quadratic functions. 4. Further elementary functions. II. Introduction to differential calculus 5. Sequence, limit of sequences. Calculation of the limit. 6. Limit of a function. 5. Continuity. Continuous function, asymptotic behavior of functions. 7. Derivative of function. Geometric meaning of the definition. Derivatives of elementary functions. Derivative of sum and product functions. Derivative of inverse function. 8. Application of differential calculus:l'Hospitalovo rule. Extreme of function. 9. Points of inflection. Applications of derivatives to studying of graph of a function.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Preparation for exam
- 125 hours per semester
- Class attendance
- 56 hours per semester
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Learning outcomes
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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
Basic knowledge of differential calculus.
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Prerequisites
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Mathematics -- the secondary level
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Assessment methods and criteria
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Oral exam, Written exam
Requirements on credit: two tests of the subject matter. The date of each test will be announced in advance by teacher. It is necessary to get score at least 50% for each test. Requirements on exam: Knowledge of problem solving, concepts and basic ideas.
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Recommended literature
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Bittnerová, D., Plačková G. Louskáček. Část 1, Diferenciální počet funkcí jedné reálné proměnné. Liberec : Technická univerzita v Liberci, 2005. ISBN 80-7083-984-8.
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Hrubý D., Kubát J. Matematika pro gymnázia : diferenciální a integrální počet. Praha : Prometheus, 2004. ISBN 80-7196-210-4.
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Kadeřábek J. Základy matematiky : Studijní texty pro distanční bakalářské studium - textilní marketing. Liberec : Technická univerzita v Liberci, 1999. ISBN 80-7083-367-X.
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Nekvinda M., Vild J. Matematické oříšky 1.. Liberec : Technická univerzita v Liberc, 2006. ISBN 80-7372-017-5.
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Nekvinda, M. Matematika. Část 1.. Liberec : Technická univerzita v Liberci, 2001. ISBN 80-7083-447-1.
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Rektorys K. Přehled užité matematiky.. Praha : Prometheus, 2000. ISBN 80-7196-179-5.
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