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Lecturer(s)
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Pitrová Veronika, RNDr. PhD., Ph.D.
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Eisenmann Petr, doc. PaedDr. CSc.
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Course content
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1. Real numbers and their properties 2. Suprema and infima, sequences of real numbers 3. Limits of sequences and their calculation 4. Real-valued functions of real variable 5. Continuous functions and their properties 6. Limits of functions (proper) 7. Improper limits and limits in infinity 8. Derivative of a function and its properties 9. Application of derivatives to finding roots 10. Mean value theorem and its corollaries 11. Monotonicity and convexity by means of derivatives 12. Graphing 13. Approximation of functions by polynomials, Taylor polynomials 14. Trigonometric functions by means of Taylor polynomials 15. Summary
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Basics of calculus, mainly continuity of real functions of real variable, their limits and derivatives, applications of derivatives to optimization, graphing and approximating functions by polynomials).
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Prerequisites
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Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.
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Assessment methods and criteria
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unspecified
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Recommended literature
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ČERNÝ, Ilja. Inteligentní kalkulus.
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ČERNÝ, Ilja. Matematická analýza II. Liberec: Technická univerzita, 1996. ISBN 80-7083-188-X.
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ČERNÝ, Ilja. Matematická analýza I. Liberec: Technická univerzita, 1995. ISBN 80-7083-188-X.
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JARNÍK, Vojtěch. Integrální počet I. Praha: Academia, 1984.
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KOPÁČEK, Jiří. Matematická analýza pro fyziky I. Praha: Matfyzpress, 1997. ISBN 80-85863-74-X.
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VESELÝ, Jiří. Matematická analýza pro učitele. Praha: Matfyzpress, 1997. ISBN 80-85863-23-5.
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