Universität Wien

250062 VO Applied analysis (2021W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
MIXED
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

We hope that the covid-situation will allow "presence teaching" in the class room, according to the rules in vigour in october 2021 ("3G" and less dense packing of classroom).

We prepare for "distance teaching", too - i.e. classes via zoom.

Or a combination: one day per week presence, one day zoom.

In any case, all "blackboard lectures" will be "streamed" and made available for watching later.

  • Tuesday 05.10. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.10. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.10. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.10. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.10. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.10. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.11. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.11. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.11. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.11. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.11. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.11. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.11. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.11. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.12. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.12. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.12. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.12. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.01. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.01. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.01. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.01. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.01. 15:00 - 16:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.01. 12:30 - 14:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.01. 15:00 - 16:30 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 (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: Tu 04.10.2022 08:28