Analysis 3

This course requires the knowledge on Analysis 1, Analysis 2 and Linear Algebra.

The course starts with the regularization, approximation by convolution and partition of unity. Then, we continue by the transformation formula of the multidimensional integral together with its application. The third part of the lecture focuses on the concept of real submanifolds on which we want to develop an integration theory. Here we also see a crucial theorem: the Gauss integral theorem, which has many applications in many fields of mathematics.  Fourier analysis will be introduced at the end of the course.

Betreuung

Dozent: Prof. Dr. Friedmar Schulz
Übungsleiter: Dr. Kim-Hang Le

Umfang

  • ECTS credits: 4
  • 2+1 SWS

Termine und Räume

  • Vorlesung
    • Tuesday 14:0016:00:         N24, H12
  • Übung (Erste Übungsstunde am 06.11.17, jede zweite Woche)
    • Monday 10:0012:00:          N24, H12

Please enroll in Moodle!

Prüfung

Voraussetzung zur Zulassung zur Prüfung sind das Erreichen von 50% der Summe aller Punkte auf den Übungsblättern.

Übungblätter

Literatur

  • Forster - Analysis 3
  • Hildebrand - Analysis 2
  • Reed, Simon - Fourier Analysis, selfadjointness
  • Sauvigny - Partielle Differentialgleichungen der Geometrie und der Physik
  • Stein, Shakarchi - Fourier Analysis
  • Walter - Analysis 2