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These studies are available for the following degree students:</p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Master's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master's Degree Programme in Mathematics&nbsp;(Subject Teacher)</li><li>Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Doctoral Programme in Mathematics and Statistics</li><li>Doctoral Programme in Mathematics and Science (Specialication in Mathematics)</li><br></ul>","fi":"<p>Tämä opintojakso on tarjolla Matematiikan syventävät opinnot -ristiinopiskeluverkostossa. 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":{"en":"Upon successful completion of this course the students will be able to calculate the Fourier coefficients of a given integrable function, to check the conditions which guarantee pointwise and absolute convergence of Fourier series, and knows the basic concepts related to the continuous Fourier transform. In addition, the student will be able to calculate the discrete Fourier transform of a given function and has an idea of the wide range of possible applications of Fourier-Analysis.","fi":"Opintojakson suoritettuaan opiskelija osaa laskea annetun integroituvan funktion Fourier-kertoimet sekä tarkastaa ehdot, jotka takaavat Fourier-sarjan pisteittäisen ja tasaisen suppenemisen. Tämän lisäksi opiskelija hallitsee jatkuvan Fourier-muunnoksen perusominaisuudet ja osaa laskea annetun funktion diskreetin Fourier-muunnoksen. Opiskelijalla on käsitys Fourier-analyysin monipuolisista sovellusalueista."},"tweetText":null,"content":{"en":"The course covers basic properties of Fourier series and Fourier transforms, and of the discrete Fourier transform. In addition, some applications of Fourier Analysis are included in the course, including solution methods for partial differential equations.","fi":"Kurssilla perehdytään Fourier-sarjojen ja Fourier-muunnosten perusominaisuuksiin ja diskreettiin Fourier-muunnokseen, sekä Fourier-analyysin eräisiin sovelluksiin muun muassa osittaisdifferentiaaliyhtälöiden ratkaisussa."},"additional":{"en":"This course is open for everyone.\r\n\r\nThe course is held every other year during the autumn semester.","fi":"Tämä opintojakso on avoin kaikille.\r\n\r\nKurssi järjestetään syyslukukaudella joka toinen vuosi."},"prerequisites":{"en":"Basic understanding of series and integration theory.","fi":"Perustiedot sarja- ja integrointiteoriasta"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Introduction to Fourier Analysis","id":"otm-7343bae3-f398-3779-a47a-19525c60f1a6","code":"LF00CS59","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-42edd1ec-1dc5-35c1-b11f-d74a959e96c9"],"organisations":[],"attainmentLanguages":["en","fi"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}