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Last update: G_M (03.06.2004)
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Last update: T_KVOF (28.03.2008)
This one-semestral course is a continuation of the basic two year course on analysis and linear algebra for physicists. |
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Last update: prof. RNDr. Vladimír Souček, DrSc. (04.05.2005)
P. Čihák a kol.: Matematická analýza pro fyziky (V), Matfyzpress, Praha, 2001, 320 str. P. Čihák, J. Čerych, J. Kopáček: Příklady z matematiky pro fyziky V, Matfyzpress, Praha, 2002, 306 str. I. M. Gel'fand, G. E. Šilov: Obobščenyje funkcii i dejstvija nad nimi, Moskva, 1958, 439 str. L. Hormander: The analysis of linear partial differential operators I, Springer 1983,391 str. |
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Last update: T_KVOF (28.03.2008)
přednáška + cvičení |
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Last update: G_M (03.06.2004)
Special functions: Gamma and beta funcions, Bessel functions. Gauss integration, hypergeometrical series.
Fourier and Laplace transforms of functions. Definition and basic properties.
Theory of distributions:distributions, tempered distributions, (Dirac, vp and Pf distributions). Distributional calculus (multiplication by a smooth function, tensor product, convolution, differentiation, linear transformation).
Fourier transform of distributions and its applications: derivative, convolution, tensor product. Convolution equations, fundamental solution. Fourier transform of periodical functions and distributions, Fourier series of periodical distributions.
The wave equation: fundamental solutions, solutions with data, group of Lorentz transformations.
Laplace-Poisson equation:uniqueness, existence, Liouville theorem. Potential theory, jump of potentials. Theorem of three potentials. Dirichlet problem and its solution. Use of conformal mappings to obtain solution in two dimensional domain.
Heat equation: fundamental solutions, solutions with data. Heat waves, cooling of the ball.
Laplace transformation for distributions and its applications to the solution of electrical RLC-circuits. |