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This one semestral course is a continuation of the basic
two year course on analysis and linear algebra.
Last update: G_M (03.06.2004)
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Čihák P., Rokyta M. a kolektiv: Matematická analýza pro fyziky V. (skripta)
Čihák P., Kopáček J.: Příklady z matematiky pro fyziky V. (skripta)
Schwartz L.: Matematické metody ve fyzice. SNTL
Vladimirov V.S.: Uravnenija matematičeskoj fiziki Last update: Zakouřil Pavel, RNDr., Ph.D. (05.08.2002)
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Special functions: Gamma and beta funcions, Bessel functions. Gauss integration, hypergeometrical series.
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. Fourier transform of radial functions, application of Bessel functions.
The wave equation: fundamental solutions, solutions with data, group of Lorentz transformations. Maxwell equations.
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. Last update: T_KVOF (13.05.2003)
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