[{"metadata":{"revision":77,"createdBy":"a385877@tuni.fi","createdOn":"2019-12-01T22:26:47.751578","lastModifiedBy":"tuni-prod2.i","lastModifiedOn":"2026-08-14T14:50:13.501694","modificationOrdinal":255138927},"documentState":"ACTIVE","id":"otm-94ffcfc5-0db4-4507-b475-63f290639e04","universityOrgIds":["tuni-university-root-id"],"groupId":"uta-ykoodi-47926","approvalState":"urn:code:approval-state-type:approved","credits":{"min":5,"max":5},"completionMethods":[{"localId":"4d6459bf-7dd9-43cd-be8c-30d54c663c0a","description":null,"studyType":"DEGREE_STUDIES","assessmentItemOptionalityDescription":null,"automaticEvaluation":true,"require":null,"typeOfRequire":"ALL_SELECTED_REQUIRED","assessmentItemIds":["otm-d877cdc4-926a-4dea-8ff6-4016074ac27d","otm-a681e95e-4085-442d-9d2e-9f80a4170b9f"],"repeats":[{"studyYearRange":{"start":2020,"end":2021},"yearInterval":null,"repeatPossibility":["tuni-university-root-id/2006/0/1"]}],"evaluationCriteria":null,"prerequisites":null},{"localId":"483703ec-9270-46e9-91e3-879efd63f39c","description":null,"studyType":"DEGREE_STUDIES","assessmentItemOptionalityDescription":null,"automaticEvaluation":true,"require":null,"typeOfRequire":"ALL_SELECTED_REQUIRED","assessmentItemIds":["otm-e69f0ad4-f4f0-4df8-8754-3777346fefcb"],"repeats":[],"evaluationCriteria":null,"prerequisites":null}],"assessmentItemOrder":["otm-d877cdc4-926a-4dea-8ff6-4016074ac27d","otm-a681e95e-4085-442d-9d2e-9f80a4170b9f","otm-e69f0ad4-f4f0-4df8-8754-3777346fefcb"],"substitutions":[[{"courseUnitGroupId":"tut-cu-g-35897","credits":null}],[{"courseUnitGroupId":"tut-cu-g-35891","credits":null}]],"name":{"en":"Introduction to Analysis","fi":"Johdatus analyysiin"},"code":"MATH.MA.110","abbreviation":"MTTMP1A","validityPeriod":{"startDate":"2020-08-01","endDate":"2024-08-01"},"gradeScaleId":"sis-0-5","tweetText":null,"outcomes":{"fi":"Opiskelijan koulusta peräisin oleva laskurutiini vahvistuu sille tasolle, jota varsinaisten analyysin opintojaksojen suorittaminen edellyttää. Erityisesti opiskelija hallitsee itseisarvoja sisältävien epäyhtälöiden käsittelyn. Opiskelija hallitsee perustiedot alkeisfunktioista. Opiskelija osaa laskea raja-arvoja, derivaattoja ja integraaleja. Hän ymmärtää derivaatan muutosvoimakkuutena ja integraalin pinta-alana. Hän pystyy käsittelemään sekä vektoriarvoisia että usean muuttujan funktioita."},"prerequisites":{"fi":"<p>Lukion pitkän matematiikan pakolliset kurssit<br /></p>"},"content":{"fi":"<p>·       Yhtälöiden ratkaiseminen (Epäyhtälöt ja itseisarvo)</p><p>· Funktion käsite ja alkeisfunktiot</p><p>. trigonometrian kertausta<br /></p><p>·       Kompleksiluvut. perusasiat<br /></p><p>·       Raja-arvot</p><p>·       Derivaatta erotusosamäärän raja-arvona. Alkeisfunktioiden derivaatat</p><p>·       Taso ja avaruuskäyrät</p><p>·       Usean muuttujan funktion derivaatta ja gradientti</p><p>·       Integraalifunktio  ja määrätty integraali </p><p>·       Osittaisintegrointi, sijoitusmenetelmä ja rationaalifunktioiden integrointi <br /></p>"},"additional":null,"learningMaterial":{"fi":"<p>Luentomoniste tai luennolla jaettava materiaali.</p>"},"literature":[],"searchTags":["Matematiikka, Mathematics"],"categoryTags":[],"recommendedFormalPrerequisites":[{"prerequisites":[{"courseUnitGroupId":"uta-ykoodi-38874","type":"CourseUnit"}]}],"compulsoryFormalPrerequisites":[],"studyFields":["urn:code:study-field:okm-6"],"studyLevel":"urn:code:study-level:basic-studies","courseUnitType":"urn:code:course-unit-type:regular","subject":null,"cefrLevel":null,"responsibilityInfos":[{"text":null,"personId":"otm-db36a5ca-5e83-4d78-b13b-c31efd32ad37","roleUrn":"urn:code:module-responsibility-info-type:administrative-person","validityPeriod":{"endDate":"2024-04-30"}},{"text":null,"personId":"tuni-person-as99553","roleUrn":"urn:code:module-responsibility-info-type:administrative-person","validityPeriod":{"endDate":"2022-02-01"}},{"text":null,"personId":"tuni-person-funktio","roleUrn":"urn:code:module-responsibility-info-type:responsible-teacher","validityPeriod":{"endDate":"2024-08-01"}},{"text":null,"personId":"tuni-person-maarvi","roleUrn":"urn:code:module-responsibility-info-type:responsible-teacher","validityPeriod":{"endDate":"2024-08-01"}},{"text":null,"personId":"tuni-person-tt428140","roleUrn":"urn:code:module-responsibility-info-type:administrative-person","validityPeriod":{"startDate":"2024-04-29","endDate":"2024-08-01"}},{"text":null,"personId":"otm-db36a5ca-5e83-4d78-b13b-c31efd32ad37","roleUrn":"urn:code:module-responsibility-info-type:administrative-person","validityPeriod":{"startDate":"2025-08-06"}}],"organisations":[{"organisationId":"tuni-org-1010000001","educationalInstitutionUrn":null,"roleUrn":"urn:code:organisation-role:responsible-organisation","share":1,"validityPeriod":{}}],"possibleAttainmentLanguages":["urn:code:language:fi"],"equivalentCoursesInfo":null,"curriculumPeriodIds":["uta-lvv-2020"],"customCodeUrns":{"urn:code:custom:tuni-university-root-id:tentit":["urn:code:custom:tuni-university-root-id:tentit:k_massa"],"urn:code:custom:tuni-university-root-id:strategic-themes":[],"urn:code:custom:tuni-university-root-id:degree-programmes":["urn:code:custom:tuni-university-root-id:degree-programmes:mtta"],"urn:code:custom:tuni-university-root-id:offering-location":["urn:code:custom:tuni-university-root-id:offering-location:keskusta"],"urn:code:custom:tuni-university-root-id:offering-information":["urn:code:custom:tuni-university-root-id:offering-information:degree-students","urn:code:custom:tuni-university-root-id:offering-information:elective-studies","urn:code:custom:tuni-university-root-id:offering-information:open-university-students","urn:code:custom:tuni-university-root-id:offering-information:tampere3-cross-institutional-studies"]},"classificationCodeUrns":null,"inclusionApplicationInstruction":null,"cooperationNetworkDetails":null,"s2r2Classification":null,"partOfDegree":null,"rdiCreditsEnabled":"DISABLED"}]