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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":"After completing the course, the student knows how to develop, analyze, and apply computational methods applicable to solving systems of conservation laws. We discuss the fundamental properties of conservation laws, and from the wide variety of numerical methods, we focus on finite difference, finite volume, and discontinuous Galerkin methods. Throughout the course, the emphasis will be on understanding both mathematical and computational aspects of the selected numerical methods. The course develops the following generic skills: critical thinking, identification and development of one&#39;s own expertise, and interaction and communication.","fi":"Opintojakson suoritettuaan opiskelija osaa kehittää, analysoida ja soveltaa laskennallisia menetelmiä, jotka soveltuvat säilymislakien ratkaisemiseen. Opintojaksolla käsitellään säilymislakien perusominaisuuksia ja lukuisista numeerisista menetelmistä keskittymme differenssi, äärellisten tilavuuksien ja epäjatkuvaan Galerkin menetelmiin. Valittuja numeerisia menetelmiä tarkastellaan sekä matemaattisista että laskennallista lähtökohdista. Opintojakso kehittää seuraavia geneerisiä taitoja: kriittinen ajattelu, oman asiantuntijuuden tunnistaminen ja kehittäminen ja vuorovaikutus ja viestintä."},"tweetText":null,"content":{"en":"Conservation laws. Linear systems. Non-linear systems. Riemann problems. Finite difference method. Finite volume method. Discontinuous Galerkin method.","fi":"Säilymislait. Lineaariset systeemit. Epälineaariset systeemit. Riemann ongelma. Differenssimenetelmä. Äärellisten tilavuuksien menetelmä. Epäjatkuva Galerkin menetelmä."},"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) - Other undergraduate or graduate students in technology, physics and mathematics, or equivalent international students, lifelong learners and Open University students provided that the pre-requisites are met.","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) - Muut tekniikan, fysiikan ja matematiikan tutkinto-opiskelijat tai vastaavat kv-opiskelijat, jatkuvat oppijat sekä avoimen yliopiston opiskelijat edellyttäen, että esitietovaatimukset täyttyvät."},"prerequisites":{"en":"Recommended: Finite Element Methods (LS00EN04), Numerical Methods (LS00DB67), Partial Differential Equations (LS00EO63) or equivalent knowledge.","fi":"Suositellaan: Finite Element Methods (LS00EN04), Numerical Methods (LS00DB67), Osittaisdifferentiaaliyhtälöt (LS00EO63) tai vastaavat tiedot."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Numerical&nbsp;Approximations of Conservation Laws","id":"otm-e01a08e3-2344-32f5-b21c-f12883c7d3c4","code":"LS00DE09","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}}}