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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":{"sv":"Lärandemål:\r\n- känna till, förstå och kunna tillämpa resultat som garanterar existensen, entydigheten och stabiliteten av lösningen till ett differentialekvationsproblem\r\n- känna igen olika linjära problemtyper och, i mån av möjlighet, lösa dem i sluten form genom en lämplig lösningsmetod\r\n- förstå betydelsen av begreppen funktionsrum och integraltransformationer i dessa och fortsatta frågor gällande differentialekvationer"},"tweetText":null,"content":{"sv":"Kursen är en inledning till teorin om differentialekvationer för funktioner av en reell variabel. \r\n\r\nVi bevisar existensen, entydigheten och stabiliteten av lösningen till det allmänna begynnelsevärdesproblemet y&#39;(x)&#61;f(x,y(x)). Teorin om och lösningsmetoderna för linjära problem studeras mer ingående, och t.ex. matrisexponentialfunktionen och Laplacetransformationen införs som nya verktyg. \r\n\r\nDe underliggande matematiska strukturerna, såsom metriska rum, linjäritet samt begreppet integraltransformation, framhålls i presentationen."},"additional":{"sv":"Kursen undervisas ungefär vartannat år"},"prerequisites":{"sv":"Matematikens grunder I, Grundkurs i analys, Matriser och Differentialekvationer"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Advanced Course on Differential Equations","id":"otm-407f9307-d881-31ab-8a74-d886fb660b9e","code":"MA00BM91","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}}}