250009 VO Applied Analysis (2025W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Moodle

We 10.12. 13:15-14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

First lecture = "organisational meeting" with all 3 teachers on friday 3 Oct at 9h45 in HS13.

In this meeting we present the format of the 2 parts of the course: "lecture" (250009 VO) and "exercises" (250048 PS).

Then the first half of the course (5th of October - 21st of November) is dedicated to "harmonic analysis",
followed by "asymptotic analysis".

Friday 03.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 08.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 10.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 17.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 22.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 24.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.10. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 31.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 05.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 07.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 14.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 21.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.11. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 28.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 05.12. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
N Wednesday 10.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 12.12. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.12. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 19.12. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 07.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 09.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 14.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 16.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 21.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 23.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 28.01. 13:15 - 14:45 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Friday 30.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course (VO+PS, 4h+2h, 6+4 ECTS) is designed for master and PhD students in mathematics, computational sciences, physics,...

The "lecture course" (250009 VO) where theory is presented is intertwined with an "exercise course" (250048 PS) where problems are solved by the students. Both courses should be enrolled ! (Note that the problems of the exercise classes of the PS are the written part of the asymptotic analyis exam of the VO)

Prerequisites : basic linear algebra and analysis, also basic knowledge of complex analysis and functional analysis;
for the harmonic analyis part programming experience (e.g., Python or MATLAB) is recommended but not required.

We present some aspects of modern "Applied Analysis", in particular aspects in "harmonic analysis" and in "asymptotic analysis" .

The first part of this course offers a rigorous and computational introduction to applied harmonic analysis, a core mathematical framework behind many modern technologies that comprises Fourier analysis, time-frequency techniques, and wavelet transforms.
Possible applications range from classical signal and image processing to fields such as data science and quantum signal representations. The course emphasizes both theoretical foundations and practical implementation, combining mathematical rigor with coding assignments and real-world examples.

The second part of the course presents key concepts of "asymptotic analysis": first we deal with the "scaling" of model equations (i.e the adimensionalization by dividing by reference quantities of the same physical dimension that also yields "small" dimensionless parameters.
Then the concept of regular perturbation theory is worked out, as a tool for (formal) asymptotic expansions in the context of "model hierarchies".
For singular perturbations we work out the concept of boundary layers and multi-scale expansions.
Our examples are mainly ODE, PDE including fluid dynamics - like the transition from Burgers to Hopf equation or Boltzmann to Navier-Stokes to Euler equation.
Emphasis is on methods, not on rigorous proofs.

Assessment and permitted materials

Written and oral exam consisting of two parts corresponding to the two parts of the course.
Examination dates will be offered regularly from end of January 2026 on.

Minimum requirements and assessment criteria

The minimal requirement is an understanding of the basics of the theory and the capacity to solve basic problems.
In the written part of the exam, 50% of possible points must be achieved for the harmonic analysis part.

Examination topics

Content of the two parts of the course as well as theory of the problems of the exercise classes.

Reading list

M. Dörfler and N.J. Mauser, H.P. Stimming: "Applied Analysis" (lecture notes in English)
---
T. Olson: Applied Fourier Analysis
I. Daubechies: Ten lectures on Wavelets
L. Grafakos: Classical Fourier Analysis
K. Gröchenig: Foundations of Time-Frequency Analysis

N.J. Mauser, H.P. Stimming, D. Bäumer "Mathematische Modellierung" (lecture notes in German)
C. Kuttler: "Mathematische Modellbildung" (lecture notes in German)

Association in the course directory

MAMA; ML1; MEL

Last modified: Tu 21.10.2025 13:47