GREEN'S FUNCTION OF THE LAPLACE OPERATOR FOR A BALL

Anna  Bogdan

doi:10.5281/zenodo.12069780

Authors

Anna Bogdan Fergana State University, faculty of mathematics and informatics, area of mathematics, student of the third course

Abstract

This material examines the key concepts of mathematical physics - the Green's function and the Laplace operator, and their application for solving problems related to the distribution of potentials and fields in various physical systems. Particular attention is paid to the study of the properties of the Green's function of the Laplace operator for a sphere and its use in solving practical problems.

Keywords:

Green's function, Laplace operator, mathematical physics, potential theory, potential distribution, spherical geometry, Laplace equation, Poisson equation, Dirichlet problem, method of separation of variables, Fourier transform, convolution, boundary conditions, asymptotics, numerical methods.

References

Sveshnikov, A.N. Bogolyubov, V.V. Kravtsov Lectures on mathematics physics. M: Moscow University Publishing House, 2004.

A.N. Bogolyubov, V.V. Kravtsov Problems in mathematical physics. M: Moscow University Publishing House, Science Publishing House, 1998.

Vladimirov V. V., Zharinov V. V. Equations of mathematical physics. M.:FISMATLITU, 2004.

Vladimirov BC Equations of mathematical physics. M.: Nauka, 1986.

N. S. Koshlyakov, E. B. Gliner, M. M. Smirnov Partial equations derivatives of mathematical physics. M.: “Higher School”, 1970.

B.M. Budak, A.A. Samarsky, A.N. Tikhonov, Collection of problems in mathematical physics, M.: FIZMATLIT, 2004

A.N. Tikhonov, A.A. Samarsky, Equations of mathematical physics, M.: Moscow State University Publishing House, 1998

N.N. Mirolyubov, M.V. Kostenko, M.L. Levinshtein, N.N. Tikhodeev, Methods for calculating electrostatic fields, M.: “Higher School”, 1963

F.M. Morse, G. Feshbach, Methods of Theoretical Physics, vol.1

A.G. Sveshnikov, A.N. Tikhonov, Theory of functions of a complex variable. M.: FIZMATLIT, 2001.

M.A. Lavrentiev, B.V. Shabat, Methods of the theory of complex functions variable variable. Gostekhizdat, 1951

E.V. Zakharov, I.V. Dmitrieva, S.I. Orlik, Mathematical equations physics. Collection of problems. Moscow State University named after M.V. Lomonosov, Faculty of Computational Mathematics and Cybernetics. Moscow, 2009

S.G. Kalashnikov, Electricity. M.: Fizmatlit, 2003.

Readership

4 Views

0 PDF downloads

4 Countries

GREEN'S FUNCTION OF THE LAPLACE OPERATOR FOR A BALL

Authors

Abstract

Keywords:

References

Readership

Downloads

Published

Issue

Section

How to Cite

Publisher

Contact

Links