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250062 VO Applied analysis (2022W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Briefing meeting on 6. Oct,
precise time of lecture somewhat flexibel

Thursday 06.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 11.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 13.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 18.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 20.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 25.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 27.10. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 03.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 08.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 10.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 15.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 17.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 22.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 24.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 29.11. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 01.12. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 06.12. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 13.12. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 15.12. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 10.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 12.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 17.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 19.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 24.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Thursday 26.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 31.01. 14:00 - 15:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

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

Starting with the "scaling" of model equations, we introduce regular and singular perturbation theory as a tool for asymptotic expansions in the context of "model hierarchies", with emphasis on PDE and fluid dynamics - like the transition from Burgers to Hopf equation or Boltzmann to Navier-Stokes to Euler equation.

The second part of the course is on Fourier methods in applied harmonic analysis. We investigate approximation rates via Fourier methods, and discuss other important transforms such as the Wavelet or Radon transform etc.

Examples and applications are presented, also exercises for individual homework.

Assessment and permitted materials

Oral exam (presence on the blackboard or distance by zoom) where the presentation of exercises enters the grade.

Minimum requirements and assessment criteria

Understanding of the key theory presented in the course and the key exercises.

Examination topics

What has been presented in the course and the exercises.

Reading list

N.J. Mauser, C. Schmeiser and H.P. Stimming - M. Dörfler and M. Ehler: "Applied Analysis" (lecture notes in English)

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S. Hittmeir, N.J. Mauser and H.P. Stimming "Mathematische Modellierung" (lecture notes in German)

C. Kuttler: "Mathematische Modellbildung" (lecture notes in German)

T. Olson: Applied Fourier Analysis
I. Daubechies: Ten lectures on Wavelets
L. Grafakos: "Classical Fourier Analysis"
S. Helgason: "The Radon Transform"

Association in the course directory

MAMA

Last modified: We 26.07.2023 16:08