Analysis 3 (HS 2017)

Dozent

  • Prof. Dr. Zoltan Balogh

Assistierende

  • De Vito Giorgio
  • Sipos Kinga
  • Züst Roger

Zeit und Ort

  • Montag, 10 - 12 Uhr, B7 (ExWi)
  • Donnerstag, 08 - 10 Uhr, B7 (ExWi)
  • Beginn: Montag, 18. September 2017

Details

  • 6 ECTS-Punkte
  • Anmeldung zur schriftlichen Prüfung bis spätestens am vorletzten Freitag der Vorlesungszeit via KSL

Contents

Fourier Series:

  • Fourier series of periodic functions.
  • Convergence theorems of Dirichlet and Fejér.
  • Relations of Bessel and Parseval.
  • Applications of Fourier series in solving partial differential equations.

 

Lebesgue Integral:

  • Properties of sigma algebras and outer measures.
  • Definition of the Lebesgue measure and integral.
  • Lebesgue dominated convergence and monotone convergence theorems.
  • Theorems of Fubini and Tonelli and transformation formula.
  • L^p spaces and integral inequalities.

 

Fourier Transform:

  • Definition and properties of the Fourier transform of L1 and 2 functions.
  • The theorem of Rieman-Lebesgue and the theorem of Plancherel.
  • Applications of the Fourier transform in solving partial differential equations and the Heisenberg uncertainty principle.