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Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}}],"gradeScaleId":"sis-0-5","outcomes":null,"tweetText":null,"content":{"fi":"Kursens innehåll: Vi introducerar begreppet Fourierserie av Lebesgueintegrerbara funktioner på intervallet [-\\pi,\\pi] , dvs. vi är speciellt intresserade av funktioner i L^1([-\\pi,\\pi]). Ett av huvudmålen är att bevisa Fejérs sats från år 1904 att aritmetiska medeltalet av symmetriska partialsummor av Fourierserien för en funktion i L^1([-\\pi,\\pi]) konvergerar mot funktionen i L^1-norm. Vidare undersöker vi punktvis konvergens för Fourierserier samt konvergensen av Fourierserier i L^2([-\\pi,\\pi]). Vi går också igenom ett exempel som visar att det är möjligt att Fourierserien till en kontinuerlig funktion divergerar. Kursen avslutas med en introduktion om diskreta Fouriertransformen samt den snabba Fouriertransformen.","sv":"Kursens innehåll: Vi introducerar begreppet Fourierserie av Lebesgueintegrerbara funktioner på intervallet [-\\pi,\\pi] , dvs. vi är speciellt intresserade av funktioner i L^1([-\\pi,\\pi]). Ett av huvudmålen är att bevisa Fejérs sats från år 1904 att aritmetiska medeltalet av symmetriska partialsummor av Fourierserien för en funktion i L^1([-\\pi,\\pi]) konvergerar mot funktionen i L^1-norm. Vidare undersöker vi punktvis konvergens för Fourierserier samt konvergensen av Fourierserier i L^2([-\\pi,\\pi]). Vi går också igenom ett exempel som visar att det är möjligt att Fourierserien till en kontinuerlig funktion divergerar. Kursen avslutas med en introduktion om diskreta Fouriertransformen samt den snabba Fouriertransformen."},"additional":{"sv":"Det är oklart när den här kursen erbjuds nästa gång, och hur den hålls. Informationen här har kopierats in från en gammal version av kursen, för att ge den studerande en indikation om ungefär hur kursen troligen skulle se ut."},"prerequisites":{"sv":"Analys och att känna till  Lebesgueintegralen är till nytta, men inget krav."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Fourier Series","id":"otm-4a2b7200-760d-3c07-a565-390d075d0a1e","code":"MA00BD21","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-5a6a3701-b188-3724-9476-784e433a4d92"],"organisations":[],"attainmentLanguages":[],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}