Universität Wien
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250062 VO Applied analysis (2023W)

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

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)

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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: Mo 28.10.2024 12:26