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Last update: T_KMA (13.05.2008)
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Last update: T_KMA (13.05.2008)
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. Mgr. Milan Pokorný, Ph.D., DSc. (28.09.2020)
Credits for tutorials, including those for written tests and active participation, are a necessary prerequisite in order to take the exam. Credits are given by the tutor. The exam consists of a written part and oral examination.
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Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (28.09.2020)
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. J. Kopáček a kol.: Příklady z matematiky pro fyziky IV, Matfyzpress, 2003, 159 str. R. Strichartz: A guide to distribution theory and Fourier transform, 2015, 218 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. R. Černý, M. Pokorný: Matematika pro fyziky V,
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Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (28.09.2020)
lectures and tutorials, starts online, further according the situation |
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Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (28.09.2020)
The exam consists of a written part and oral examination. To pass the written part, at least 40% of the points are necessary.
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Last update: T_KMA (13.05.2008)
1. Laplace transform of functions Definition and basic properties. Inversion theorems, application to intial promblems in ODEs.
2. Special functions Gamma and beta funcions, Bessel functions. Gauss integration, hypergeometrical series.
3. Theory of distributions Distributions, tempered distributions, (Dirac, vp and Pf distributions). Distributional calculus (multiplication by a smooth function, tensor product, convolution, differentiation, linear transformation). Convergence of distributions, distributions with parameter, Fourier and Laplace 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.
4. Applications of theory of distributions Laplace-Poisson equation:uniqueness, existence, Liouville theorem. 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. The wave equation: fundamental solutions, solutions with data.
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Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (22.06.2021)
Knowledge of differential and integral calculus of one and several real variables, one complex variable. |