250062 VO Applied analysis (2023W)
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Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
This lecture with integrated exercises is designed for master and PhD students in mathematics, computational sciences, physics.
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 ODE, PDE and 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.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. Some key proofs are part of the lecture.Examples and applications are an intrinsic part, also exercise problems for individual homework that are presented in class.
Thursday
05.10.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
09.10.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
12.10.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
16.10.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
19.10.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
23.10.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday
30.10.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday
06.11.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
09.11.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
13.11.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
16.11.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
20.11.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
23.11.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
27.11.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
30.11.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
04.12.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
07.12.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
11.12.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
14.12.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
08.01.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
11.01.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
15.01.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
18.01.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
22.01.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
25.01.
15:00 - 16:30
Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
Monday
29.01.
13:15 - 14:45
Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
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 consisting of two parts (asymptotic and harmonic analysis). Examination dates will be offered regularly from end of January 2024 to October 2024.
Minimum requirements and assessment criteria
Understanding of the key theory presented in the course and workout of the exercise problems.
Examination topics
Content of the two parts of the course as well as principles of the discussed exercises.
Reading list
N.J. Mauser, H.P. Stimming and M. Dörfler, M. Ehler: "Applied Analysis" (lecture notes in English)---
N.J. Mauser, H.P. Stimming, D. Bäumer "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"
N.J. Mauser, H.P. Stimming, D. Bäumer "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"
Association in the course directory
MAMA
Last modified: Th 11.04.2024 11:26