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Lecturer(s)
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Černá Dana, doc. RNDr. Ph.D.
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Hozman Jiří, RNDr. Mgr. Ph.D.
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Course content
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Lectures: 1. Laplace transform of continuous functions. Properties of Laplace transform. 2. Laplace transform of discontinuous functions. Solution of differential equations using the Laplace transform. 3. Geometric shapes in the plane, surfaces in space, definition od double and triple integral. 4. Properties of multidimensional integrals. Fubini theorem. 5. Substitution in double and triple integral. Polar, cylindric, and spheric coordinates. 6. Applications: area of a figure, volume of a solid, mass, moment, center of gravity. 7. Oriented curve. Curve integral of the 1st and 2nd kind, calculation. Applications: work of a force, circulation. 8. Potential of a vector field. Independence of a curve integral of the integration path. Green theorem. 9. Oriented surface. Surface integral of the 1st and 2nd kind, calculation. Applications: mass, center of gravity of a figure, flux of a field through a figure. 10. Gradient, divergence, curl. Potential, sourceless, irrotational fields. Stokes theorem, Gauss theorem. 11. Function series, domain of convergence. 12. Power series. Abel convergence theorem, radius of convergence. 13. Differentiation and integration of power series. 14. Taylor series, expansion of some elementary functions. Practice: The material explained at the previous week lecture is practised.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
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Learning outcomes
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Laplace transform, double and triple integrals, curve and surface integrals, function series, in particular power and Fourier series.
Basic principles and practices of Laplace transform, integral calculus, and function series.
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Prerequisites
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Condition of registration: subjects Mathematics 1 and Mathematics 2.
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Assessment methods and criteria
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Combined examination
Credit: Active participation on practice. Tests successfully written during the semestr, semestral work. Exam: Written and oral, composed of the theoretical and computational part.
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Recommended literature
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Brabec, J. - Hrůza, B. Matematická analýza 2.. Praha, SNTL, 1986.
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Brabec, J. - Martan, F. - Rozenský Z. Matematická analýza 1. Praha, SNTL, 1985.
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Brožíková, E. - Kittlerová, M. Sbírka příkladů z matematiky 2.. Praha, Vydavatelství ČVUT, 2002.
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Černý, I. Úvod do inteligentního kalkulu.. Praha, Academia, 2002.
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Jarník, V. Diferenciální počet II.
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Jirásek, F. - Čipera, S. - Vacek, M. Sbírka řešených příkladů z matematiky 2.. Praha, SNTL, 1989.
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Mezník, I. - Karásek, J. - Miklíček, J. Matematika 1 pro strojní fakulty. Praha, SNTL, 1992.
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Nekvinda, M. - Říhová, H. - Vild, J. Matematické oříšky 2 (cvičení).. Liberec, TUL, 1999.
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Pírko, Z. - Veit, J. Laplaceova transformace.. Praha, SNTL, 1972.
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Rektorys, K. a další. Přehled užité matematiky.. Praha, Prometheus, 2000.
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Strang, G. Calculus.. Cambridge, MA, Welesley-Cambridge Press, 1990.
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