Universität Wien
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250062 VO Applied analysis (2024W)

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

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

First lecture = "organisational meeting" with all 3 teachers on friday 4 Oct in HS11.
Precise time can be slightly shifted (15 minutes) according to students' wishes.

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.

  • Friday 04.10. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.10. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 11.10. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.10. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 18.10. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.10. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 25.10. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.10. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Tuesday 05.11. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 08.11. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.11. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 15.11. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.11. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 22.11. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.11. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 29.11. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.12. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 06.12. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.12. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 13.12. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.12. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Tuesday 07.01. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 10.01. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.01. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 17.01. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.01. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Friday 24.01. 11:30 - 13:00 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.01. 15:00 - 16:30 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.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

(Written +) oral exam consisting of two parts (asymptotic and harmonic analysis).
Examination dates will be offered regularly from end of January 2025 on.

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, D. Bäumer and M. Dörfler, M. Ehler: "Applied Analysis" (lecture notes in English)
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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: Fr 17.01.2025 13:26