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| Semester | fall semester 2020 |
| Course frequency | Irregular |
| Lecturers | Gianluca Crippa (gianluca.crippa@unibas.ch, Assessor) |
| Content | 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. |
| Bibliography | 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. |
| Comments | 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. |
| Admission requirements | 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). |
| Language of instruction | English |
| Use of digital media | No specific media used |
| Course auditors welcome |
| Interval | Weekday | Time | Room |
|---|
No dates available. Please contact the lecturer.
| Modules |
Module Specialisation: Analysis (Master's Studies: Mathematics) |
| Assessment format | continuous assessment |
| Assessment details | 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). |
| Assessment registration/deregistration | Reg.: course registration, dereg: cancel course registration |
| Repeat examination | no repeat examination |
| Scale | Pass / Fail |
| Repeated registration | as often as necessary |
| Responsible faculty | Faculty of Science, studiendekanat-philnat@unibas.ch |
| Offered by | Fachbereich Mathematik |