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undergraduate thesis
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Fourier Series
Keti Martinić (2017)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Applied Mathematics Research Group
Metadata
TitleFourierovi redovi
AuthorKeti Martinić
Mentor(s)Krešimir Burazin (thesis advisor)
Abstract
U ovom radu ćemo proučiti pojam Fourierovog reda i Fourierovih koeficijenata. Potom ćemo analizirati vrste konvergencija Fourierovog reda ( Konvergencija po točkama, uniformna konvergencija, konvergencija u smislu \(L^{2}\) -norme) te definirati kompleksni oblik Fourierovog reda i Fourierovih koeficijenata. Takoder ćemo definirati i Fourierovu transformaciju koja se koristi za procesiranje signala te je pružila veliki doprinos u tehničkim znanostima i medicini. U zadnjem poglavlju ćemo navesti dva primjera primjene Fourierovog reda, provodenje topline i valna jednadžba.
Keywordstrigonometric function Fourier series Fourier coefficients convergence Fourier integral Fourier transform partial differential equations
Parallel title (English)Fourier Series
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Lower level organizational unitsChair of Applied Mathematics
Applied Mathematics Research Group
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Mathematical Analysis
Study programme typeuniversity
Study levelundergraduate
Study programmeUniversity undergraduate study programme in mathematics
Academic title abbreviationuniv.bacc.math.
Genreundergraduate thesis
Language Croatian
Defense date2017-09-29
Parallel abstract (English)
In this paper we will study the terms Fourier series and Fourier coefficients. Then we will analyze the types of convergence of Fourier series (pointwise convergence, uniform convergence, convergence in \(L^{2}\) -norm) and define the complex form of Fouriers series. We will also define Fourier transform which is used to process the signal and has contributed greatly to technical sciences and medicine. In the last section, there are two examples of the application of the Fourier series, heat conduction and wave equation.
Parallel keywords (Croatian)trigonometrijska funkcija Fourierov red Fourierovi koeficijenti konvergencija Fourierov integral Fourierova transformacija parcijalne diferencijalne jednadžbe
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:768487