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Lecturer(s)
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Finěk Václav, doc. RNDr. Ph.D.
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Šimůnková Martina, RNDr. Ph.D.
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Course content
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1. Review and extension of knowledge of differential calculus (comprehensive investigation of function behavior). 2. Riemann integral I (definition and basic properties of the definite integral). 3. Riemann integral II (linearity, integral as a function of its upper limit, and existence of antiderivative). 4. Antiderivatives and basic integration methods (indefinite integral, integration by parts, basic substitutions). 5. Special integration techniques (partial fractions decomposition and selected advanced substitutions). 6. Geometric applications of the definite integral (area of a planar region, arc length). 7. Introduction to numerical integration (basic approximation methods). 8. Improper integrals (generalization of the Riemann integral), mean value theorems for integrals, and selected topics. 9. Infinite series I (basic concepts, convergence and divergence, series with non-negative terms). 10. Infinite series II (alternating series, selected convergence tests, absolute and conditional convergence). 11. Introduction to functions of two variables (basic concepts, limits and continuity of functions of two variables). 12. Differential calculus of functions of two variables (partial derivatives, total differential and its applications). 13. Taylor polynomial and Taylor series (local approximation of functions of one and two variables). 14. Implicit functions (basic implicit function theorem and its geometric interpretation).
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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
Course requirements (Assessment): Active participation in seminars and successful completion of tests. Final examination: Written examination.
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Recommended literature
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