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Lecturer(s)
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Bílek Jiřina, doc. RNDr. CSc.
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Bůžek Pavel, Ing. Mgr.
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Course content
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1. Sequences of real numbers 2. Series 3. Limits and continuity of a function. Points of discontinuity 4. Derivation of a function, calculation, meaning of derivation 5. Calculations of limits. L'Hôpital's rule 6. Examination of the function graph 7. Fundaments of integral calculus 8. General theory of probability 9. Random variables and their characteristics
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, E-learning, Collaborative instruction, Cooperative instruction, Seminar classes
- unspecified
- 15 hours per semester
- Contact hours
- 52 hours per semester
- Preparation for comprehensive test (10-40)
- 40 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| achieve a high school level of mathematical knowledge |
| Skills |
|---|
| achieve a high school level of mathematical skills |
| Competences |
|---|
| N/A |
| learning outcomes |
|---|
| Knowledge |
|---|
| define the concept of sequences of real numbers |
| define the concept of number series |
| understand the meaning of the first and second derivatives of a function |
| understand the meaning of L'Hospital's rule |
| explain the concept of asymptote |
| understand the meaning of integral |
| explain the concepts of random phenomenon, probability |
| explain the concept of random variable |
| Skills |
|---|
| determine the first and second derivatives of functions of one real variable |
| apply l'Hospital's rule |
| determine asymptotes of functions of one real variable |
| investigate the progression of functions of one real variable |
| determine the integral of simple functions of one real variable |
| determine the probability of a random phenomenon in simple cases |
| Competences |
|---|
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Lecture supplemented with a discussion |
| Interactive lecture |
| Collaborative instruction |
| Practicum |
| Skills |
|---|
| Practicum |
| Skills demonstration |
| Collaborative instruction |
| Competences |
|---|
| Task-based study method |
| assessment methods |
|---|
| Knowledge |
|---|
| Test |
| Continuous assessment |
| Skills demonstration during practicum |
| Self-evaluation |
| Skills |
|---|
| Test |
| Skills demonstration during practicum |
| Continuous assessment |
| Self-evaluation |
| Competences |
|---|
| Continuous assessment |
| Test |
|
Recommended literature
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učebnice pro gymnázia např. vydavatelství Prometheus.
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Delventhal, Katka Maria; Kissner, Alfred; Kulick, Malte. Kompendium matematiky : vzorce a pravidla : četné příklady včetně řešení : od základních operací po vyšší matematiku. V Praze : Euromedia Group - Knižní klub, 2004. ISBN 80-242-1227-7.
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Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Polák, J. Středoškolská matematika v úlohách II.. Praha, 2011. ISBN 978-80-7196-419-.
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Polák, J. Středoškolská matematika v úlohách I.. Praha, 2006. ISBN 978-80-7196-337-0.
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