Universität Wien

250062 VO Applied analysis (2023W)

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

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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.

  • Donnerstag 05.10. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 09.10. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 12.10. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 16.10. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 19.10. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 23.10. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 30.10. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 06.11. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 09.11. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 13.11. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 16.11. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 20.11. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 23.11. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 27.11. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 30.11. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 04.12. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 07.12. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 11.12. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 14.12. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 08.01. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 11.01. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 15.01. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 18.01. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 22.01. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Donnerstag 25.01. 15:00 - 16:30 Hörsaal 16 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 29.01. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Oral exam consisting of two parts (asymptotic and harmonic analysis). Examination dates will be offered regularly from end of January 2024 to October 2024.

Mindestanforderungen und Beurteilungsmaßstab

Understanding of the key theory presented in the course and workout of the exercise problems.

Prüfungsstoff

Content of the two parts of the course as well as principles of the discussed exercises.

Literatur

N.J. Mauser, H.P. Stimming 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"

Zuordnung im Vorlesungsverzeichnis

MAMA

Letzte Änderung: Mo 28.10.2024 12:26