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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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Course description: Elementary theory of transcendent functions, the integral calculus of a real function of one real variable and a theory of number series in the set of real numbers. Requirements on students: Mathematical analysis 1 Course program (syllabus): 1. Goniometric, cyklometric, exponencial and logaritmic function. Basic properties. 2. Primitive function (antiderivative) and indefinite integral. Basic rules. Basic substitutions. 3. Integration by parts. Integration by partial fractions. Substitution method. 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. Alternating series - the alternating series test, absolute convergence.
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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, transcendent functions of real variable.
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Prerequisites
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Analytic thinking. AN1.
KMA/AN1
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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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Bittnerová, D. - Plačková, G.:. Louskáček 2 - integrální počet funkce jedné proměnné.. TUL, liberec, 2008.
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