diplomsko delo
Tina Jarc (Author), Joso Vukman (Mentor)

Abstract

V diplomskem delu 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.

Keywords

matematika;Fourierove vrste;enačbe;diferencialne enačbe;konvergenca;robni pogoji;lastne vrednosti;lastne funkcije;valovna enačba;toplota;prevajanje;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Source: Maribor
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [T. Jarc]
UDC: 51(043.2)
COBISS: 18219016 Link will open in a new window
Views: 3262
Downloads: 326
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Other data

Secondary language: English
Secondary title: Fourier series and some partial differential equations
Secondary abstract: 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.
Secondary keywords: Fourier series;Fourier coefficients;convergence;boundary conditions;eigenvalues;eigenfunctions;differential equations;wave equation;heat equation.;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in fiziko
Pages: 30 f.
Keywords (UDC): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID: 19130