Universität Wien

250081 VO Real analysis (2025S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

This course takes place during the first half of the semester and may serve as preparation for the topics course that is to follow in the second half of the semester (Topics in Real Analysis)

  • Friday 07.03. 09:45 - 11:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.03. 09:45 - 11:15 Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 14.03. 09:45 - 11:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.03. 09:45 - 11:15 Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 21.03. 09:45 - 11:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.03. 09:45 - 11:15 Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 28.03. 09:45 - 11:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 01.04. 09:45 - 11:15 Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 04.04. 09:45 - 11:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.04. 09:45 - 11:15 Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 11.04. 09:45 - 11:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.04. 09:45 - 11:15 Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The course revisits the fundamental theorem of calculus from the point of view of modern measure theory.

Planned contents: differentiation theorem; absolutely continuous functions and functions of bounded variation; approximate identities, mollification.

Prerequisites: Lebesgue integration, convergence theorems, basics of L^p-spaces (as in the bachelor course at the University of Vienna)

Assessment and permitted materials

Oral exam at the end of the course, covering all topics of the lectures. No aids (lecture notes, internet access) are permitted during the exam.

Minimum requirements and assessment criteria

Minimum requirements: detailed knowledge of course material and its applications.

To pass, at least half of the questions need to be answered correctly. Illustrative list of grades: 88-100 sehr gut; 75-87 gut; 62-74 befriedigend; 50-61 genuegend; <50 nicht genuegend

Examination topics

Entire course material.

Reading list

* L. Grafakos, Fundamentals of Fourier Analysis - Grad. Texts in Math., Springer, 2024
* E. M. Stein und R. Shakarchi, Fourier Analysis, Princeton UP, Princeton, 2003.
* E. M. Stein und R. Shakarchi, Real Analysis, Princeton UP, Princeton, 2005.
* L. C. Evans and R. F. Gariepy. Measure theory and fine properties of functions. Studies in
Advanced Mathematics. CRC Press, Boca Raton, FL, 1992.

Association in the course directory

MANF

Last modified: We 30.04.2025 10:46