F3363 Physical proseminar 3

Faculty of Science
Autumn 2001
Extent and Intensity
0/2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Václav Holý, CSc. (seminar tutor)
Guaranteed by
prof. RNDr. Josef Humlíček, CSc.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: prof. RNDr. Václav Holý, CSc.
Prerequisites
A good knowledge of basic mathematical analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The seminar is devoted to mathematical methods useful in solving physical problems that are often neglected in the basic mathematical course. An emphasis is given to practical applications in physics.
Syllabus
1. Elements of the theory of distributions. Distributions as a functionals, properties. Dirac distribution. Application - electric field of a point charge and elementary dipole. 2. Cnovolution algebra Convolution of distributions, inverse distribution. Methods of calculation of ionverse distributions. The Heaviside calculus 3. Fourier series of a periodical function of one and many variables. Direct and reciprocal lattice, expansion of crystal potential energy. Fourier series of convolution of periodical functions. 4. Fourier transformation of a function of one variable A function of many variables, convolution of functions, periodical functions. Wave packets, Fraunhofer diffraction, space filtration, the sampling theorem. 5. Laplace transformation Definition of the Laplace transformation of functions and distributions, inverse laplace transformation, connection of the Laplace and Fourier transformations. 6. Response of the physical system on external stimulation. Symmetry of physical system. Response function. Response function of the free and elastically bounded particle, response function of an electrical circuit, generalized permitivity. 7. Some special functions. The Sturm-Liouville problem. Cylindrical functions (the Bessel functions, Neumann functions, Hankel functions). Spherical functions (the Legendre polynomials, adjoint Legendre functions, spherical functions). Application of the special functions in solving physical problems
Literature
  • SCHWARTZ, Laurent. Matematické metody ve fyzice. 1. vyd. Praha, 1972, 357 s. info
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • TICHONOV, Aleksandr Nikolajevič and Aleksandr Andrejevič SAMARSKIJ. Uravnenija matematičeskoj fiziki. 2. ispr. i dop. izd. Moskva: Gosudarstvennoje izdatel'stvo techniko-teoretičeskoj literatury, 1953, 679 s. info
  • BATEMAN, Harry and Arthur ERDÉLYI. Vysšije transcendentnyje funkcii. Translated by Naum Jakovlevič Vilenkin. Izd. 2-oe stereotipnoe. Moskva: Nauka. Glavnaja redakcija fiziko-matematičeskoj literatury, 1974, 295 s. info
  • Spravočnik po special'nym funkcijam s formulami, grafikami i matematičeskimi tablicami. Edited by Milton Abramowitz - Irene A. Stegun. Moskva: Nauka. Glavnaja redakcija fiziko-matematičeskoj literatury, 1979, 830 s. info
Assessment methods (in Czech)
proseminář ukončený zápočtem.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught every week.
The course is also listed under the following terms Autumn 1999, Autumn 2000.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2001/F3363