{"componentChunkName":"component---src-templates-course-unit-page-tsx","path":"/en/courseunit/ls00ek98/","result":{"data":{"translations":{"edges":[{"node":{"context":{"locale":"fi","code":"LS00EK98","title":"Käänteisongelmat"},"path":"/fi/opintojakso/ls00ek98/"}},{"node":{"context":{"locale":"en","code":"LS00EK98","title":"Inverse Problems"},"path":"/en/courseunit/ls00ek98/"}}]},"SISU":{"courseUnit":[{"id":"otm-4fd178a0-be8c-3d09-9243-8b2f3f14eb83","code":"LS00EK98","name":{"en":"Inverse Problems","fi":"Käänteisongelmat","sv":"Käänteisongelmat"},"credits":{"max":5,"min":5},"studyLevel":null,"possibleAttainmentLanguages":[{"name":{"en":"English","fi":"englanti","sv":"engelska"}}],"responsibleOrganisations":[],"coordinatingOrganisations":[],"curriculumPeriods":[],"cooperationNetworkDirection":"INBOUND","cooperationNetworks":[{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-15471","jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280","jy-DP-30241"],"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","jy-DP-30241"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"<p>This course is offered through the Network for Inverse Problems. These studies are available for the following degree students:<br><br></p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master’s Degree Programme in Mathematics</li><li>Master's degree Programme in Mathematics (Subject Teacher)</li><li>Doctoral Degree Programme in Mathematics and Statistics</li></ul>","fi":"<p>Tämä opintojakso on tarjolla Inversio-ongelmien verkostossa. Verkoston opinnot ovat tarjolla seuraavien tutkinto-ohjelmien opiskelijoille:<br><br></p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan aineenopettajan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajan&nbsp;maisteriohjelma</li><li>Matematiikan\nja tilastotieteen tohtoriohjelma</li></ul>"},"cooperationNetwork":{"abbreviation":"inversio","name":{"en":"Education network on Inverse Problems","fi":"Inversio-ongelmien koulutusverkosto"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"The student will gain understanding of basics of the theory of linear inverse problems and will be able to utilize the theory in computational inverse problems in practical applications. The course develops the following generic skills: digitalization, critical thinking, identification and development of one&#39;s own expertise, and interaction and communication.","fi":"Opintojakson suoritettuaan opiskelija hallitsee lineaaristen inversio-ongelmien teorian perusteet ja kykenee soveltamaan teoriaa käytännön sovelluksissa esiintyvien numeeristen ongelmien ratkaisemiseen. Opintojakso kehittää seuraavia geneerisiä taitoja: digitalisaatio, kriittinen ajattelu, oman asiantuntijuuden tunnistaminen ja kehittäminen ja vuorovaikutus ja viestintä."},"tweetText":null,"content":{"en":"- Introduction. - Basics of linear functional analysis - Singular value decomposition and pseudoinverse. - Tikhonov regularization. - Non-linear inverse problems. - Statistical interpretation of Tikhonov regularization. - Iterative methods.","fi":"- Johdanto. - Lineaarisen funktioanalyysin perusteet. - Singulaariarvohajotelma ja pseudoinverssi. - Tikhonov-regularisointi. - Epälineaariset käänteisongelmat. - Sivurajoitteet ja tilastollisen tulkinnan perusteet. - Iteratiiviset menetelmät."},"additional":{"en":"Time: The course will be held only every second academic year. You can see the course implementations in Study guide, under &#34;Course Units&#34; or &#34;Show past courses&#34;. This course is intended for the following student groups: - Undergraduate students in Technical Physics (MSc) - Undergraduate students in Applied Physics (MSc) - Graduate students in technology, physics and mathematics.","fi":"Ajankohta: Opintojakso luennoidaan joka toinen vuosi. Tarkista seuraavan toteutuksen ajankohta opinto-oppaasta kohdasta &#34;Toteutukset&#34; tai &#34;Näytä menneet toteutukset&#34;. Tämä opintojakso on tarkoitettu seuraaville opiskelijaryhmille: - Teknillisen fysiikan tutkinto-opiskelijat (diplomi-insinööri) - Sovelletun fysiikan tutkinto-opiskelijat (filosofian maisteri) - Tekniikan, fysiikan ja matematiikan jatko-opiskelijat"},"prerequisites":{"en":"Recommendations of the prior learning: differential calculus, matrix calculus and linear algebra, Matlab programming","fi":"Suositeltava edeltävä osaaminen: differentiaalilaskenta, matriisilaskenta ja lineaarialgebra, Matlab-ohjelman käyttötaidot"},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Inverse Problems","id":"otm-4fd178a0-be8c-3d09-9243-8b2f3f14eb83","code":"LS00EK98","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"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}