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58950-01 - Vorlesung: Differential equations and Sobolev spaces (8 KP)
| Semester | Herbstsemester 2020 |
| Weitere Semesterveranstaltungen zu diesen KP |
58950-01 (Vorlesung) 58950-02 (Übung) |
| Angebotsmuster | unregelmässig |
| Dozierende | Gianluca Crippa (gianluca.crippa@unibas.ch, BeurteilerIn) |
| Inhalt | Brief introduction to partial differential equations. The ordinary differential equation and the transport equation. Theory of characteristics. Energy methods. Sobolev spaces. Elliptic regularity theory. DiPerna-Lions theory for the transport equation. Quantitative estimates for the ordinary differential equation. Applications to mixing of fluids. |
| Literatur | Lawrence C. Evans, "Partial Differential Equations", AMS. Haim Brezis, "Functional Analysis, Sobolev Spaces and Partial Differential Equations", Springer. Further literature will be communicated during the course. |
| Bemerkungen | The Zoom-links of the lectures and the exercises will be made available via the ADAM-webpage of the course. Both lectures and exercises will be held "live" at the given times in order to allow for interaction. In addition, both lectures and exercises will be recorded and made available in the Zoom-cloud (the link will be posted on the ADAM-webpage as well). There will also be the possibility of some optional office hours or discussion meetings to be held in physical presence. |
| Teilnahmevoraussetzungen | Analysis I & II. Lineare Algebra I & II. Reelle Analysis. Some background on PDEs and functional analysis will be useful (from instance, from previous analysis or numerics courses, or from mathematical methods). |
| Unterrichtssprache | Englisch |
| Einsatz digitaler Medien | kein spezifischer Einsatz |
| HörerInnen willkommen |
| Intervall | Wochentag | Zeit | Raum |
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Keine Einzeltermine verfügbar, bitte informieren Sie sich direkt bei den Dozierenden.
| Module |
Vertiefungsmodul: Analysis (Masterstudium: Mathematik) |
| Prüfung | Lehrveranst.-begleitend |
| Hinweise zur Prüfung | Lecture: Oral Exam after the two semesters (mündliche Masterprüfung Vertiefungsmodul Analysis). Exercises: Credit Points will be assigned under the following conditions: (1) Active participation to the lecture and to the exercise session. (2) 66% of the points from the weekly exercise series (points are given for meaningful attempts of solution — “sinvolle Bearbeitung"). (3) Written or oral discussion on the exercises at the end of the semester (exact rules will be defined depending on the Corona-situation). |
| An-/Abmeldung zur Prüfung | Anm.: Belegen Lehrveranstaltung; Abm.: stornieren |
| Wiederholungsprüfung | keine Wiederholungsprüfung |
| Skala | Pass / Fail |
| Belegen bei Nichtbestehen | beliebig wiederholbar |
| Zuständige Fakultät | Philosophisch-Naturwissenschaftliche Fakultät, studiendekanat-philnat@unibas.ch |
| Anbietende Organisationseinheit | Fachbereich Mathematik |