Calculus of Variations
Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Die Anforderungen an Studien- und Prüfungsleistungen werden in den aktuellen Ergänzungen der Modulhandbücher beschrieben, die ab Ende Oktober 2025 als Teil des Kommentierten Vorlesungsverzeichnisses veröffentlicht werden.
Teacher: Guofang Wang
Assistant: Florian Johne
Language: in German
The aim of the calculus of variations is to minimise or maximise certain mathematically treatable quantities. More precisely, we consider \(\Omega \subset {\mathbb R}^n\) functionals or variation integrals of the form \[F (u) = \int_\Omega f(x,u (x ),Du (x))dx, \quad \hbox{ f\"ur } u : \Omega\to {\mathbb R}\] on \(\Omega \subset {\mathbb R}^n\).
Examples are arc length and area, as well as energies of fields in physics. The central question is the existence of minimisers. After a brief introduction to the functional analysis tools, we will first familiarise ourselves with some necessary and sufficient conditions for the existence of minimisers. We will see that compactness plays a very important role. We will then introduce some techniques that help us to get by without compactness in special cases: The so-called compensated compactness and the concentrated compactness.
necessary: Functional Analysis \
useful: PDE, numerical PDE
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 04.02., 12:15, SR 218, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Ernst Kuwert
Assistant: Florian Johne
Language: Talk/participation possible in German and English
Analysis I–III
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Mathematics I for Engineering Students
Lecture: Mo, Mi, 16-18h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Ernst Kuwert
Assistant: Florian Johne
Lecture: Mo, Mi, 16-18h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Ernst Kuwert
Assistant: Florian Johne
Language: in German
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Teacher: Ernst Kuwert
Assistant: Florian Johne
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Applied Mathematics (MSc14)
Lecture: Do, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Florian Johne
Seminar: Minimalflächen
Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Guofang Wang
Assistant: Florian Johne
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)