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Last update: G_M (16.05.2012)
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Last update: doc. RNDr. Pavel Pyrih, CSc. (28.10.2019)
Conditions for semester 2019/20
Elaboration of all Sandboxes and Tracks is a necessary condition for the course completion
Detailed explained here:
http://matematika.cuni.cz/pyrih-kalkulus.html |
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Last update: doc. RNDr. Pavel Pyrih, CSc. (28.10.2019)
J. Kopáček: Matematika pro fyziky III, IV
S. Fučík, J. Milota: Matematická analýza II |
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Last update: doc. RNDr. Pavel Pyrih, CSc. (28.10.2019)
see
http://matematika.cuni.cz/pyrih-kalkulus.html |
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Last update: doc. RNDr. Pavel Pyrih, CSc. (28.10.2019)
see Course completion requirements |
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Last update: G_M (27.04.2012)
Basic properties, Fubini theorem, substitutions, polar and spherical coordinates, volumes. Measure theory. basic properties of measure, construction of measure from outer measure, measurable functions, integral based on measure, Jordan and Lebesgue measures. Function sequences and series. Pointwise and uniform convergence (Weierstrass test), commutation of convergence and limits, derivatives and integrals. Power series and their convergence radius, derivatives and integrals. Integrals with parameters. Commutation of integral with limits, series and derivatives, Gamma and Beta functions, application to more complicated integrals. Fourier series. Trigonometric series, Fourier coeficients, Parseval equation, convergence of Fourier series, application to series of numbers. |
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Last update: doc. RNDr. Pavel Pyrih, CSc. (28.10.2019)
Previous knowledge of Kalkulus 1 and 2 will be useful. |