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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Fürst Tomáš, RNDr. Ph.D.
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Burkotová Jana, Mgr. Ph.D.
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Ludvík Pavel, RNDr. Ph.D.
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Bebčáková Iveta, Mgr. Ph.D.
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Course content
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1. Euclid space, scalar product, euclid metric and norm, topology, convergence, norm equivalence in Rn. 2. Functions of several real variables: limit and continuity, directional and partial derivatives, differential and relations among them. 3. Vector functions: directional and partial derivatives, differential, potential, divergence, rotation, physical interpretation and applications. 4. Extremal values of functions of several variables: local and global extrema, conditional extrema. 5. Series: convergence criteria for series with nonnegative and general values, absolute and relative convergence. 6. Sequences and series of functions, uniform convergence. 7. Taylor series. 8. Fourier series and their applications, introduction to complex analysis.
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Learning activities and teaching methods
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Lecture, Monologic Lecture(Interpretation, Training), Work with Text (with Book, Textbook)
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Learning outcomes
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To understand the basics of differential calculus of functions of more variables.
Comprehension Understand the mathematical tools of diferential calculus of functions of a single variable, theory of number and functional series (Taylor and Fourier series).
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Prerequisites
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Differential and integral calculus of functions of one real variable.
KMA/MA1
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Assessment methods and criteria
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Oral exam, Written exam
Credits: active attendance, passing written tests Exam: written and oral
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Recommended literature
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Online přednáška.
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Online přednáška.
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Došlá, Z., Novák, V. (2007). Nekonečné řady. MU PřF, Brno.
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Kopáček, J. (2007). Matematická analýza nejen pro fyziky (III). Matfyzpress, Praha.
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Kopáček, J. (2015). Matematická analýza nejen pro fyziky (II). Matfyzpress, Praha.
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Kopáček, J. (2006). Příklady z matematiky nejen pro fyziky III. Matfyzpress, Praha.
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Kopáček, J. (2006). Příklady z matematiky nejen pro fyziky II. Matfyzpress, Praha.
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Rachůnek, L., Rachůnková, I. (2004). Diferenciální počet funkcí více proměnných. UP Olomouc.
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Rachůnková, I., Kojecká, J. (1998). Řešené příklady z matematické analýzy III. Univerzita Palackého v Olomouci, Olomouc.
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Veselý, J. (2001). Matematická analýza pro učitele II. Matfyzpress, Praha.
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