Universität Wien

250062 VO Applied analysis (2017W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

First course : 4 Oct 2017, 16h30

  • Wednesday 04.10. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.10. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.10. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.10. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.10. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.10. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.10. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.11. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.11. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.11. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.11. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.11. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.11. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.11. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.11. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.12. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.12. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.12. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.12. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.01. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.01. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.01. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.01. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.01. 15:00 - 17:30 Seminarraum 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.01. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.01. 16:15 - 17:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 31.01. 16:30 - 18:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

We present some aspects of modern "Applied Analysis" : "Asymptotic Analysis" and "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", like the transition from Burgers to Hopf equation or Boltzmann to Navier-Stokes to Euler equation.

We also present basic aspects of harmonic analysis, approximation theory; sampling theory and applications in imaging.

Methods: Dimensionless variables, scaling, perturbations; continuum mechanics; multi-scale problems; Fourier transform; Radon transform; mathematical foundations of imaging.

Part of the course consists of exercises ("homework") to illustrate the theory, that the students work out and present on the blackboard.

Assessment and permitted materials

Exam: oral exam with blackboard.
Presentation of the exercises during the semester is strongly desired and improves grade of the exam.

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.

Reading list

C. Schmeiser, "Angewandte Mathematik",
C. Kuttler, "Mathematische Modellbildung";

T. Sauer: Approximationstheorie (Vorlesungsskript), Universität Gießen, https://www.fim.uni-passau.de/fileadmin/files/lehrstuhl/sauer/geyer/Approx.pdf
E. W. Cheney: Introduction to Approximation Theory, 2nd edition, Chelsea, New York, 1982.
N. Trefethen, Approximation Theory and Approximation Practice, SIAM.

Association in the course directory

MAMA

Last modified: Tu 03.08.2021 00:23