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Lecturer(s)
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Hozman Jiří, RNDr. Mgr. Ph.D.
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Černá Dana, doc. RNDr. Ph.D.
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Course content
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Lectures: 1. Fourier transform, Laplace transform. 2. Double and triple integral. Calculation by successive integration. 3. Substitution in double and triple integral. Polar, cylindric, and spheric coordinates. Applications: area of a figure, volume of a solid, mass, moment, center of gravity. 4. Oriented curve. Curve integral of the 1st and 2nd kind, calculation. Applications: work of a force, circulation. 5. Potential of a vector field. Independence of a curve integral of the integration path. Green theorem. 6. 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. 7. Gradient, divergence, curl. Potential, sourceless, irrotational fields. Stokes theorem, Gauss theorem. 8. Function series, domain of convergence, power series. Abel convergence theorem, radius of convergence. Differentiation and integration of power series. 9. Taylor series, expansion of some elementary functions. 10. Periodic functions. Fourier trigonometric series, convergence. Expansion of some functions. Parseval equality. 11. Functions of complex variable. Cauchy-Riemann conditions, Cauchy theorem. 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)
- Class attendance
- 70 hours per semester
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Learning outcomes
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Fourier and Laplace transform. Double and triple integrals, curve and surface integrals. Function series, in particular power and Fourier series. Functions of complex variable.
Fundaments of integral calculus. Function series.
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Prerequisites
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Condition of registration: subjects Calculus 1, Calculus 2.
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Assessment methods and criteria
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Written exam
Credit: Active participation on practice. Tests successfully written during the semestr, semestral work. Exam: Written, 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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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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