20.500.12556/DKUM-17450 Fourierove vrste in nekatere parcialne diferencialne enačbe Fourier series and some partial differential equations V diplomski nalogi obravnavamo Fourierove vrste. V prvem poglavju analiziramo zgodovinski razvoj Fourierovih vrst ter predstavimo postopek za iskanje Fourierovih koeficientov na način, kot je to počel Leonhard Euler (1707—1783). Zanima nas tudi konvergenca Fourierovih vrst in računanje vsote vrst. S pomočjo Fourierovih vrst smo izračunali vsoto znane vrste . V drugem poglavju se ukvarjamo z robnimi pogoji, z lastnimi vrednostmi in lastnimi funkcijami. V tretjem poglavju obravnavamo valovno enačbo. Predstavimo metodo za reševanje te enačbe na način, kot je to počel Daniel Bernoulli (1700—1782). V zadnjem poglavju obravnavamo enačbo za prevajanje toplote. In diploma paper we study Fourier series. In the first chapter we analyze the historic development of Fourier series and show Leonhard Euler’s (1707–1783) method for searching Fourier coefficients. We are interested in the convergence of Fourier series and the sum of the series. With the help of Fourier series we calculated the sum of the series . In the second chapter we study boundary conditions, eigenvalues and eigenfunctions. In the third chapter we present the wave equation. We show the method for solving this kind of equation, which was developed by Daniel Bernoulli (1700–1782). In the last chapter we present the heat equation. Fourierove vrste Fourierovi koeficienti konvergenca robni pogoji lastne vrednosti lastne funkcije diferencialne enačbe valovna enačba enačba za prevajanje toplote. Fourier series Fourier coefficients convergence boundary conditions eigenvalues eigenfunctions differential equations wave equation heat equation. true true false [T. Jarc] Slovenski jezik Angleški jezik Diplomsko delo 2011-02-07 16:08:57 2011-03-17 13:34:12 2022-04-13 09:30:46 2023-12-22 03:28:16 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18219016 URN:SI:UM:DK:50WUNUSZ UNI_Jarc_Tina_2011.pdf UNI_Jarc_Tina_2011.pdf 1 05E9DF3A4C161C98B37C7BEFA328F350 2f5e28713107b182d1a84e43edbfab29e2e3ff3822b71e793dbbb91e2a6899d4 e504218e-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/8c54a0c4-049c-496f-9d4f-a830f2064215 https://dk.um.si/Dokument.php?lang=slv&id=20728 Fakulteta za naravoslovje in matematiko 0 0 0