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Mathematical Fluid Mechanics

Courses

Current Semester (winter semester 24/25)

For more recent information on the courses, see here

All teaching activities take place in presence in the corresponding lecture halls. 

Lecture: Wed., Thu. 10:15 - 11:45 in SE 40, Kathin Hellmuth & Christian Klingenberg

Exercises: Fr., 14:15 - 15:45 in S0.102, Daniel Weggenmann

This class focuses on the mathematics behind many algorithms and techniques used in machine learning. Besides mathematical theory, we will also look at applied machine learning. - After successfully completing this course the student will be able to find and implement the machine learning technique appropriate for a given applied problem at hand.

This course addresses master students of mathematics / mathematical physics / computational mathematics.
The lecture requires knowledge from the courses Analysis 1,2 and 3 from the Bachelor studies as well as basic knowledge in stochastics.

Wed. 16:15 - 17:45 in SE 40

First meeting on Wed., Oct. 16. at 16:15 in SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

Wed. 16:15 - 17:45 in SE 40

First meeting on Wed., Oct.16. at 16:15 in SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Master thesis.

Wed. 10:15 - 11:45,  seminar room SE 22.02.008 (Physik West)

jointly with mit Thorsten Ohl,

First meeting: Wed., Oct. 16. at 10:15 in SE 22.02.008 (Physik West)

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

irregularily, compare the calender of the work group.

Previous Semesters

For further information on previous courses see here

Summer semester 2024

Lecture:  Wed 8:30 -10:00, Thu 16:15 -17:45 in SE 30 (Emil Fischer Str. 30)

Exercises (held by Kathrin Hellmuth):  Fr. 10:15 - 11:45 in SE 30 (Emil Fischer Str. 30), first exercise class in the second week of classes, on Friday, April 26

This course is open for all students of Master Mathemastics / Mathematical Physics / Computational Mathematics. The lecture introduces to theory and numerics of nonlinear partial differential equations and their applications.

Knowledge from analysis 1 & 2 & 3 from the Bachelor is required. 

Di 14:15 -15:45,  im Raum 40.03.003 (Emil Fischer Str. 40)

jointly with Leon Bungert.

In this course we will hand you some literature to the topic "Mathematics of Machine Learning". The material will be discussed in meetings with both lecturers. 

Knowledge from the lecture "Mathematics of Machine Learning" is required in principle, otherwise it has to be obtained in personal studies in order to understand the literature.

It is possible to get aquainted to topics that might lead to a Master thesis.

Wed. 10:15 - 11:45 in SE 40 (Emil Fischer Str. 40)

Within the scope of this seminar it is possible to read up on a topic for a bachelor thesis.

First meeting: Wed. 17. April at 10:15 in SE 40 (Emil Fischer Str. 40)

 

Wed. 10:15 - 11:45 in SE 40 (Emil Fischer Str. 40)

First meeting on Wed., April 17 at 10:15 Uhr in SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Master thesis.

irregularily, compare the calender of the work group.

Winter semester 2023/24

Lecture: Mathematics of Machine Learning: Tues. 14:15 -15:45,  Thurs. 10:00 -11:30 in SE 40 (Emil Fischer Str. 40)

Exercises (held by Kathrin Hellmuth): Fr. 14:00 -15:30  in SE 40, first exercise class in the second week of classes, on Friday, Oct. 27

Final Exam on Tue. Feb. 6, 2024 at 14:15 am

This class focuses on the mathematics behind many algorithms and techniques used in machine learning. Besides mathematical theory, we will also look at applied machine learning. - After successfully completing this course the student will be able to find and implement the machine learning technique appropriate for a given applied problem at hand.

This course addresses master students of mathematics / mathematical physics / computational mathematics.

The lecture requires knowledge from the courses Analysis 1,2 and 3 from the Bachelor studies as well as basic knowledge in stochastics.

 

Wed. 16:15 - 17:45 in SE 40

First meeting on Wed., Oct. 18 at 16:15 in SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

Wed. 16:15 - 17:45 in SE 40

First meeting on Wed., Oct. 18 at 16:15 Uhr in SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Master thesis.

Wed. 10:15 - 11:45, seminar room SE 22.02.008 (Physik West),

joint with Thorsten Ohl,

first meeting: Wednesday, Oct. 18 in SE 22.02.008 (Physik West)

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

irregularily, compare the calender of the work group.

 

Summer semester 2023

lecture:  Mo. 14:15 -15:45,  Tue. 12:15 -13:00 in SE 30 (Emil Fischer Str. 30)

exercise section: Tue. 13:00 -13:45  in SE 30

first exercise class in the second week of classes, on Tue. Apr. 25

In this class we will cover a range of topics pertaining to an important system of partial differential equations of continuum mechanics, the compressible Euler equations: derivation of the equations, questions of exsitence and uniqueness and numerical methods. The class will be taught by Simon Markfelder (following his book, see here) and myself.

This course addresses master students of mathematics / mathematical physics / computational mathematics.

The lecture requires knowledge from the courses Analysis 1,2 and 3 from the Bachelor studies. No worries if you have not taken a course in PDE before.

 Wed. 10:15 - 11:45 in SE 40 (Emil Fischer Str. 40)

Within the scope of this seminar it is possible to read up on a topic for a bachelor thesis.

First meeting: Wed. 19. April at 10:15 in SE 40 (Emil Fischer Str. 40)  

Wed. 10:15 - 11:45 in SE 40

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

First meeting for this seminar: 19. April at 10:15 in SE 40.

The first meeting and the lectures will be hold in the above mentioned lecture hall. 

more Information on the Research Seminar.

 

 

 

Winter semester 2022/23

Lecture: Tue. 10:15 -11:45,  Thurs. 10:15 -11:45 in SE 40 (Emil Fischer Str. 40)

Exercises (held by Kathrin Hellmuth): Fr. 14:15 -15:45  in SE 40

This class focuses on the mathematics behind many algorithms and techniques used in machine learning. Besides mathematical theory, we will also look at applied machine learning. - After successfully completing this course the student will be able to find and implement the machine learning technique appropriate for a given applied problem at hand.

This course addresses master students of mathematics / mathematical physics / computational mathematics.

The lecture requires knowledge from the courses Analysis 1,2 and 3 from the Bachelor studies as well as basic knowledge in stochastics.

 

Wed. 16:15 - 17:45, SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

 

Wed. 16:15 - 17:45 in SE 40

Within the scope of this seminar, it is possible to work on a topic that might lead to a Master thesis.

Wed. 10:15 - 11:45, class room SE 22.02.008 (Physik West), joint with Thorsten Ohl,

First meeting: Wednesday Oct. 18. Okt. at 10:15 in SE 22.02.008 (Physik West)

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

Lectures take place in the class room SE 22.02.008 (Physik West)

further information

irregularily, compare the calender of the work group.

 

Summer semester 2022

Lecture: Tue 10:15 -11:45, Wed 14:15 -15:45 in room SE 30 (Emil Fischer Str. 30)

Exercises: Thu. 12:15 - 13:45 in room SE 40 (Emil Fischer Str. 40)

This course adresses master students of mathematics / mathematical physics / computational mathematics. It introduces theory (and numerics) for non-linear partial differential equations and their applications. 

The lecture requires knowledge from teh courses analysis 1,2 and 3 from the bachelor studies.

Wed. 10:15 - 11:45

Within the scope of this seminar it is possible to read up on a topic for a bachelor thesis.

First meeting: Wed. 27. April at 10:15 in SE 40 (Emil Fischer Str. 40)

Wed. 10:15 - 11:45

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

First meeting: Wed. 27. April at 10:15 in SE 40 (Emil Fischer Str. 40)

Wed. 10:15 - 11:45

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

First meeting: Wed. 27. April at 10:15 in SE 40 (Emil Fischer Str. 40)

more Information on the Research Seminar.

Winter Semester 2021/22

Lecture: Wed 14:15 -15:45; Thu. 10:15 -11:45 in HS 2 in SE 30

Exercises: Thu. 8:30 - 10:00 in SE 40

This course is open for all Students of Master Mathemastics / Mathematical Physics / Computational Mathematics. The lecture introduces to theory and numerics of nonlinear partial differential equations and their applications.

Knowledge from analysis 1 & 2 & 3 from the Bachelor is required. 

The lecture and exercises will be hold in presence in the above mentioned lecture halls.

Tue 16:15 - 17:45, Seminar room SE 22.00.017 (Physics building West), together with Thorsten Ohl,

Within the scope of this seminar it is possible to get aquainted to topics that might lead to a Bachelor thesis. 

First meeting for this seminar: in the first week of the semester on October 19 at 16:15 in Seminar room 22.00.017 (Physics building West).

The first meeting and the lectures will be hold in the above mentioned lecture hall. 

Mo. 10:15 - 11:45 in SE 40

Within the scope of this seminar, it is possible to get aquainted to topics that might lead to a Bachelor thesis. 

First meeting for this seminar: in the first week of the semester on October 18 at 10:15 in SE 40.

The first meeting and the lectures will be hold in the above mentioned lecture hall. 

Mo. 10:15 - 11:45 in SE 40

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

First meeting for this seminar: 18. Okt. 2021 at 10:15 in SE 40.

The first meeting and the lectures will be hold in the above mentioned lecture hall. 

Mo. 10:15 - 11:45 in SE 40

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

First meeting for this seminar: 8. Okt. 2021 at 10:15 in SE 40

The first meeting and lectures will be hold in the  above mentioned lecture hall.

more Information on the Research Seminar.

 

Summer Semester 2021

Lecture: Tu10:15 -11:45, Wed14:15 -15:45 online

Exercises (by Marlies Pirner): Th. 12:15 - 13:45 online

The lecture is suitable for students of the master programs of mathematics, mathematical physics, computational mathematics. I tgives an introduction to theory and numerics of non-linear partial differential equations and their application.

Knowledge of the Bachelor courses Aanalysis 1-3 is required.

The lecture will be given via Zoom. The access data can be found on the WueCampus course after inscribing for this course.

Alternatively, you can ask for it via Email.

 

Wed. 10:15 - 11:45, online

first meeting: 14. April at 10:15 , online

Within the scope of this seminar, it is possible to work on a topic that might lead to a Bachelor thesis.

The first meeting and the talks will be given on Zoom.

The access data can be found on the  WueCampus course after inscribing for this course.

Alternatively, you can ask for it via Email.

Wed. 10:15 - 11:45, online

first meeting: 14. April at 10:15 , online

Within the scope of this seminar, it is possible to work on a topic that might lead to a Master thesis.

The first meeting and the talks will be given on Zoom.

The access data can be found on the WueCampuscourse after inscribing for this course.

Alternatively, you can ask for it via Email.

Wed. 10:15 - 11:45, online

First meeting: 14. April at 10:15, online

Within the scope of this seminar, it is possible to work on a topic that might lead to a Master thesis.

The first meeting and the talks will be given on Zoom.

The access data can be found on the WueCampus course after inscribing for this course.

Alternatively, you can ask for it via Email.

irregularily, compare the calender of the work group.

 

Winter Semester 2020/21

Lecture: Tu. 08:15 - 9:45 online  und Th. 16:15 - 17:45 online , 

Exerciese: Th 12:15-13:45 online 

This course is also for Students of Master Mathemastics/Computational Mathematics. The lecture introduces to partial differential equation of fluid dynamics.

Lecture and exercises are done via Zoom. Futher Information is provided later, see up-to-date information.

 

Th. 10:15-11:45 online 

First meeting:  We,  03. Nov at 10:15

Lectures are done via Zoom.

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

The lectures can be found online.

Di. 10:15-11:45 am online 

 

First meeting for this seminar: in the first week of the semester on Wednesday, 03. Nov. at 10:15 am online or by individual agreement.

Lectures are done via Zoom.

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

The lectures can be found online.

Th. 10:15-11:45 online 

First meeting:  We,  03. Nov at 10:15

Lectures are done via Zoom.

Within the scope of this seminar it is possible to read up on a topic for a bachelor thesis.

The lectures  can be found online.

Di. 16:15 - 17:45, online, together with Thorsten Ohl,

First meeting:  We,  03. Nov at 16:15, online

Lectures are done via Zoom.

Within the scope of this seminar it is possible to read up on a topic for a bachelor thesis.

The lectures can be found online.

more Information on the Research Seminar.

 

Summer Semester 2020

Lecture: Tu. 10:15 - 11:45 Uhr und We. 14:15 - 15:45 Uhr,  Room SE 30

Exercise: Th 12:15-13:45, SE40

This course is also for Students of Master Mathemastics/Computational Mathematics. The lecture introduces to partial differential equation of fluid dynamics.

We. 10:15-11:45, Raum SE 40

First meeting:  We,  29.04 at 10:15 Uhr in SE 40.

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

We. 10:15-11:45, Room SE 40

First meeting:  We,  29.04 at 10:15 Uhr in SE 40.

Within the scope of this seminar it is possible to read up on a topic for a Bachelor thesis.

Lecture: Tu 12:15 -13:45 & We 17:15 -18:45 online - later SO.108

Exercises: jointly with Jan Scherz Th. 12:15 - 13:45 & 14:15 - 15:45 online - later SE 8

 

 

 

Winter Semester 2019/20

Vorlesung: Tu. 12:15 - 13:45 Uhr und We. 8:15 - 9:45 Uhr,  Raum SE 40

Übung: Th 16:15-17:45, S0.101 (Tutor Claudius Birke)

Theory and numerics of nonlinear partial differential equations

We. 10:15-11:45, Raum SE 40

First meeting:  Tu,  15.10 at 10:15 Uhr in SE 40.

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

We. 10:15-11:45, Raum SE 40

First meeting:  Tu,  15.10. at 10:15 Uhr in SE 40.

Within the scope of this seminar it is possible to read up on a topic for a Bachelor thesis.

First meeting Tu, 15.10., 16.15 , Room SE 22.00.017, Emil Hilb Weg 22

 

Summer Semester 2019

Prof. Dr. Christian Klingenberg

Lecture: Tu. 10:15 - 11:45 Uhr und We. 14:15 - 15:45 Uhr,  Room SE 30

Exercise: Th 12:15-13:45, S0.101 (By Farah Kanbar)

This course is also for Students of Master Mathemastics/Computational Mathematics (As the Module: "Zurzeitnochnichtbekannt"). The lecture introduces to partial differential equation of fluid dynamics.

We. 10:15-11:45, Raum SE 40

First meeting:  We,  24.05 at 10:15 Uhr in SE 40.

Within the scope of this seminar it is possible to read up on a topic for a master thesis.

 

Tuesday, June 4

 

4:00 - 4:35 pm: Maximilian Lorenz: On modeling American options

4:40 - 5:15 pm: Kathrin Hellmuth: Volatility models in stochastic financial mathematics

5:20 - 5:55 pm: Matthias Pascal Clad: On the wave equation

 

Tuesday, June 11

 

4:00 - 4:35 pm: Stefan Pfeuffer: Well-posedness for scalar conseravation laws

4:40 - 5:15 pm: Kardelen Koc: On well-balanced schemes for Friedrichs Systems

 

Tuesday June 25

 

4:00 - 4:35 pm: Julian Meusel: On a strongly hyperbolic formulation of the Einstein equations

4:40 - 5:15 pm: Sarah Winkelmann: Numerics for conservation laws: finite volume methods

5:20 - 5:55 pm: Sarah Winkelmann: Numerics for conservation laws: high order methods

6:00 - 6:30 pm Mattis Vogelsang: On the equations of magnetohydrodynamics

 

Tuesday July 9

 

4:00 - 4:35 pm: Winnie Hartwig: An introduction to the discontinuous Galerkin method, part 1

4:40 - 5:15 pm: Winnie Hartwig: An introduction to the discontinuous Galerkin method, part 2

5:20 - 5:55 pm: Felix Weiß: On the discontinuous Galerkin method, part 1

6:00 - 6:35 pm: Felix Weiß: On the discontinuous Galerkin method, part 2

 

additional participants in this seminar:

- Lukas Baumgärtner: Machine learning and numerical simulations of partial differential equations

We. 10:15-11:45, Raum SE 40

First meeting:  We,  24.04 at 10:15 Uhr in SE 40.

Within the scope of this seminar it is possible to read up on a topic for a Bachelor thesis.

 

Mi. 12. Juni

8:00 - 8:35 Uhr: Jonas Dornbusch: Numerische Methoden zur Lösung der Wärmeleitungsgleichung

8:40 - 9:15 Uhr: Maximilian Schemel: Über die Modellierung von Öl-lagerstätten mit der Buckley-Leverett Gleichung

9:20 - 9:55 Uhr: Maximilian Schell: Wohlgestelltheit für skalare Erhaltungsgleichungen

 

Mi. 26. Juni

8:00 - 8:35 Uhr: Till Düsberg: Räuber-Beute Modelle in der mathematischen Biologie

8:40 - 9:15 Uhr: Fridolin Popov: Über ein Modell über die Bewegung von Zellen

9:20 - 9:55 Uhr: Moritz Beck: Über stochastische Differentialgleichungen I

 

Mi. 10. Juli

8:00 - 8:35 Uhr: Moritz Beck: Über stochastische Differentialgleichungen II

8:40 - 9:15 Uhr: Marius Volpert: Numerische Lösungen für Erhaltungsgleichungen: der Godunov-Löser

9:20 - 9:55 Uhr: Jonas Schlecht: Numerische Lösungen für Erhaltungsgleichungen: approximativer Godunov-löser

Dr. Stephan Schmidt

Lecture: Tu. 12:15 - 13:45, S0.108 and We. 16:00 - 17:00 Uhr,  Turing-Hörsaal

Exercises: Th. 12:15-13:45, 14:15-15:45, 16:15-17:45, SE 8

Winter Semester 2018/19

Prof. Dr. Christian Klingenberg

Lecture: Tu. 10:15 - 11:45 and We. 10:15 - 11:45,  Room SE 40

Exercise: We 8:30-10:00, S0.101 (By Simon Markfeder)

This is a first course on partial differential equations. 

Mo. 8-10, Raum SE 40

 

Mo. 3. Dez.

8:00 - 8:30 Uhr: Tsu-Peng Hsu: “Gas flow in one space dimension, part 1”

8:40 - 9:10 Uhr: Steffen Krannich: "Gas flow in one space dimension, part 2”

9:20 - 9:50 Uhr: Kardelen Koc: "Gas flow in one space dimension, part 3”

 

Mo. 10. Dez.

8:00 - 8:30 Uhr: Sarah Winkelmann: “Numerics of hyperbolic equations part 1"

8:40 - 9:10 Uhr: Alexander Bayer: "“Numerics of hyperbolic equations part 2"

9:20 - 9:50 Uhr: Stefan Zips: “Numerics of hyperbolic equations part 3"

 

Mo. 17. Dez.

8:00 - 8:30 Uhr, Julian Meusel: “A covariant alternative to the Einstein equations: deriving the second-order CCZ4 system”

8:40 - 9:10 Uhr, Tobias Herzing: “Introduction to stochastic differential equations”

9:20 - 9:50 Uhr, Tobias Herzing: "Numerics of stochastic differential equations”

 

Mo. 7. Jan.

8:00 - 8:30 Uhr: Nadja Henning: “Godunov’s method for linear system of hyperbolic partial differential equations”

8:40 - 9:10 Uhr: Stephan Pfeuffer: “Finite volume method for scalar conservation laws”

9:20 - 9:50 Uhr: Winnie Hartwig: “Godunov’s method for systems of conservation laws using approximate Riemann solvers”

 

Mo. 21. Jan.

8:00 - 8:30 Uhr: Siqi Wang: Computing financial derivatives

8:40 - 9:10 Uhr: Jonas Jackwirth: “Finite volume methods for multi-dimensional systems of conservation laws”

9:20 - 9:50 Uhr: Tahamina Akter: “An introduction to to the Boltzmann equation”

 

Mo. 28. Jan.

8:00 - 8:30 Uhr: Katharina Bernard: “On reconstruction of dynamic objects in computerized tomography”

8:40 - 9:10 Uhr: Kathrin Hellmuth: “Derivation of the Black Scholes equation”

9:20 - 9:50 Uhr: Steffen Hennig: “On numerical conformal mappings”

Do. 12-14, Raum 40.03.003

 

Do. 10. Jan. 2019

12:15 - 12:50 Uhr, Moritz Beck: Über Zwei Punkt Randwertprobleme

13:00 - 13:35 Uhr, Tillman Schmucker: Die Wärmeleitungsgleichung

 

Do. 24. Jan. 2019

12:15 - 12:50 Uhr, Jonas Schlecht: Numerik zur Wärmeleitungsgleichung, erster Teil

13:00 - 13:35 Uhr, Fridolin Popov: Numerik zur Wärmeleitungsgleichung, zweiter Teil

 

Do. 31. Jan. 2019

12:15 - 12:50 Uhr, Stefan Pfeuffer: Finite Differenzen Verfahren zur Lösung schalerer Erhaltungsgleichungen

13:00 - 13:35 Uhr, Lukas Baumgärtner: ClawPack, ein Programmpaket zur Lösung von hyperbolischen Erhaltungsgleichungen

Di. 16:15 - 17:45, Physik West SE 22.00.017 

 

08.01.2019  Luca Umminger: “Einführung, stochastische Prozesse, Brownsche Bewegung”

 

08.01.2019  Solveig Wittig: Itô Integral

 

15.01.2019  Maureen Krumtünger, Itô Formel

 

15.01.2019  Kaja Jurak, Stochastiche Differentialgleichungen

 

22.01.2019  Caecilia Hepperle, Diffusion 1

 

22.01.2019  Bastian Dittrich. Diffusion 2

 

29.01.2019, Nicole Dannenberg, Diffusion 3

 

29.01.2019  Anton Söllner,  Black-Scholes oder Feynman-Kac

Dr. Stephan Schmidt

Lecture : Tu. 16:15 - 17:45 Uhr, Room S0.103 und We 14:15 - 15:45 Uhr,  Room S0.103

Exercises: We 16:15-17:45, S0.102