{"componentChunkName":"component---src-templates-course-unit-page-tsx","path":"/en/courseunit/lf00cp21/","result":{"data":{"translations":{"edges":[{"node":{"context":{"locale":"fi","code":"LF00CP21","title":"Kokonaiset funktiot"},"path":"/fi/opintojakso/lf00cp21/"}},{"node":{"context":{"locale":"en","code":"LF00CP21","title":"Entire Functions"},"path":"/en/courseunit/lf00cp21/"}}]},"SISU":{"courseUnit":[{"id":"otm-850e1c09-a812-3386-b0d1-0e48f4b58903","code":"LF00CP21","name":{"en":"Entire Functions","fi":"Kokonaiset funktiot","sv":"Kokonaiset funktiot"},"credits":{"max":8,"min":8},"studyLevel":null,"possibleAttainmentLanguages":[{"name":{"en":"English","fi":"englanti","sv":"engelska"}},{"name":{"en":"Finnish","fi":"suomi","sv":"finska"}}],"responsibleOrganisations":[],"coordinatingOrganisations":[],"curriculumPeriods":[],"cooperationNetworkDirection":"INBOUND","cooperationNetworks":[{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["jy-DP-15471","jy-DP-13215"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-af81f116-e2c7-4ddd-a995-b5a3f769efd0"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-7115fcfa-a836-4071-87dd-12907142ff6e"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-d4ca8e88-2100-4732-9b27-613c74807e98"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-56907236-443b-46cc-82cd-4f5f900be109"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-141caed2-2906-4382-8115-8a32f8aea2d9"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-a1152c89-5848-4824-b84c-d9b9366c8de3"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["otm-141caed2-2906-4382-8115-8a32f8aea2d9"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":["otm-a1152c89-5848-4824-b84c-d9b9366c8de3"],"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"<p>This course is offered through the Network for Advanced Studies in Mathematics. 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":"After completing the course, the student will be able to\r\n•\tunderstand why growth and zeros are among the most important properties of entire functions\r\n•\tknow a collection of classical results, for example, theorems by Hadamard and Phragmén-Lindelöf\r\n•\tknow a collection of special functions and their fundamental properties","fi":"Opintojakson suoritettuaan opiskelija\r\n•\tymmärtää miksi kasvu ja nollakohdat ovat kokonaisten funktioiden tärkeimpiä ominaisuuksia\r\n•\ttuntee joukon klassisia tuloksia, esimerkiksi Hadamardin ja Phragmén-Lindelöfin lauseet\r\n•\ttuntee joukon erikoisfunktioita sekä niiden perusominaisuudet"},"tweetText":null,"content":{"en":"Growth and zeros of entire functions, order of growth and exponent of convergence, canonical products, Hadamard factorization theorem, Phragmén-Lindelöf theorems, complex interpolation, linear fractional transformations, special functions.","fi":"Kokonaisten funktioiden kasvu ja nollakohdat, kasvun kertaluku ja konvergenssieksponentti, kanoniset tulot, Hadamardin faktorisointilause, Phragmén-Lindelöfin lauseet, kompleksinen interpolointi, lineaarikuvaukset, erikoisfunktiot."},"additional":{"en":"This course is open for everyone, including exchange students. All the course material is in English. Homework, turn-in homework and exams can be written in Finnish or in English. If there are exchange students present, the lectures will be in English, otherwise the lectures will be in Finnish.\r\n\r\nThis course can be included in the MSc advanced studies. \r\n\r\nLectured every two years in periods 3-4. Joensuu campus.","fi":"Tämä opintojakso on avoin kaikille, mukaan lukien vaihto-opiskelijat. Kaikki kurssimateriaali on englanniksi. Kotitehtävät, kirjallisesti palautettavat tehtävät ja tentit voi tehdä joko suomeksi tai englanniksi. Jos paikalla on vaihto-opiskelijoita, niin luennot pidetään englanniksi, muussa tapauksessa luennot pidetään suomeksi. \r\n\r\nTämän kurssin voi sisällyttää maisteriopintojen syventäviin opintoihin.\r\n\r\nLuennoidaan joka toinen lukuvuosi, periodeissa 3-4. Joensuun kampus."},"prerequisites":{"en":"Real analysis (8 cr), Series (5 cr), Integrals and function sequences (4 cr), Complex analysis a (4 cr) and Complex analysis b (4 cr).","fi":"Reaalianalyysi (8 op), Sarjat (5 op), Integraalit ja funktiojonot (4 op), Kompleksianalyysi a (4 op) ja Kompleksianalyysi b (4 op)."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Entire Functions","id":"otm-850e1c09-a812-3386-b0d1-0e48f4b58903","code":"LF00CP21","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}}}