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Mathematics for Physicists III - NMAF005
Title: Matematika pro fyziky III
Guaranteed by: Laboratory of General Physics Education (32-KVOF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2008
Semester: winter
E-Credits: 7
Hours per week, examination: winter s.:3/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Class: Fyzika
Classification: Physics > Mathematics for Physicists
Co-requisite : NMAF004
Annotation -
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)
Literature - Czech

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)
Syllabus -

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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