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Lecturer(s)
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Radová Jana, Mgr.
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Burkotová Jana, Mgr. Ph.D.
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Tomeček Jan, doc. RNDr. Ph.D.
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Ludvík Pavel, RNDr. Ph.D.
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Bebčáková Iveta, Mgr. Ph.D.
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Pavlačka Ondřej, RNDr. Ph.D.
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Course content
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1. Introduction: On the structure of mathematics, sets, basic logic. 2. Sequences: The notion of limits, theorems on limits, boundedness and convergence. 3. Functions: The notion of functions, continuity, properties of continuous functions, limits, limits of composite functions, elementary functions. 4. Differentiation: Relation to limits and continuity, the differential of a function, mean value theorems, Taylor's polynomials, L'Hospital's rule. 5. Integration: Motivation, Newton's formula and the relation to differentiation, primitive functions, integration by parts, integration by substitution, integration of rational functions, more on integration techniques, the Riemann integral and the proof of Newton's formula. 6. Applications: Length, surface, volume, center of gravity, moment of inertia, numerical methods.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 78 hours per semester
- Preparation for the Course Credit
- 40 hours per semester
- Preparation for the Exam
- 60 hours per semester
- Homework for Teaching
- 30 hours per semester
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Learning outcomes
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Understand differential calculus of functions of a single real variable
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a single variable.
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Prerequisites
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Grammar school mathematics
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation, the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test).
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Recommended literature
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J. Veselý. (2001). Matematická analýza pro učitele I. Matfyzpress.
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KOPÁČEK J. (2016). Matematická analýza nejen pro fyziky (I). Matfyzpress, Praha.
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KOPÁČEK J. (2005). Příklady z matematiky nejen pro fyziky (I). Matfyzpress, Praha.
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