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250062 VO Applied analysis (2019W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Tuesday 01.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 04.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 08.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 11.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 15.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 18.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 22.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 25.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 29.10. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 05.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 08.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 12.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 15.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 19.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 22.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 26.11. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 29.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 03.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 06.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 10.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 13.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 17.12. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 07.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 10.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 14.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 17.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 21.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 24.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
Tuesday 28.01. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Friday 31.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

We present some aspects of modern 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.
In a second part we present basic aspects of harmonic analysis and sampling theory and applications in imaging.
We also present the basics of harmonic analysis and 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 examples that the students work out and present on the blackboard.

Assessment and permitted materials

an oral presentation is strongly desired

Minimum requirements and assessment criteria

Examination topics

Reading list

C. Schmeiser, "Angewandte Mathematik", lecture notes
P. Grohs, "Time frequency analysis", lecture notes
D. Kammler, "A First Course in Fourier Analysis", Cambridge University Press, revised edition, 2008.
J. W. Goodman, "Introduction to Fourier Optics", Roberts and Company Publishers, 2005.

Association in the course directory

MAMA

Last modified: We 03.02.2021 00:24