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Lecturer(s)
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Šimůnková Martina, RNDr. Ph.D.
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Course content
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1. Primitive function (antiderivative) and indefinite integral. Basic rules. Basic substitutions. 2. Integration by parts. Integration by partial fractions. 3. Special substitutions. 4. Riemann integral. Definition and basic properties. 5. Newton-Leibniz theorem (fundamental theorem of calculus). Substitutions and integration by parts for definite integrals. 6. Newton integral. Improper integral 7. Geometric applications of Riemann integral. Using symmetry. 8. Physical applications of Riemann integral. 9. Numerical methods for Riemann integral (approximate integration) - midpoint rule, trapezoidal rule, Simpson´s rule. 10. Infinite series - partial sum, sum of series, convergence and divergence. Geometric series, harmonic series. Series with positive terms.Tests of convergence. 11. Alternating series - the alternating series test, absolute convergence. 12. Series of functions - interval of convergence. Conditional convergence. Power series, radius of convergence. 13. Differentiation and integration of power series. Taylor and Maclaurin Series. 14. Reserve.
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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 the integral calculus of a real fuction of one real variable and a theory of number series and series of functions in the set of real numbers.
Integral calculus, series.
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Prerequisites
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Analytic thinking. AN1M.
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Assessment methods and criteria
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Oral exam, Written exam
Credit - see syllabus.
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Recommended literature
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Veselý, J. Matematická analýza pro učitele, 1.díl.. Praha, Matfyzpress, 1997.
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Veselý, J. Matematická analýza pro učitele, 2. díl.. Praha, Matfyzpress.
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