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.

Lecture Team

Lecturer: Prof. Dr. Friedmar Schulz
Exercise instructor: Dr. Kim-Hang Le

Extent

  • ECTS credits: 4
  • Hours per week: 2+1

Exam

We offer two writting examinations (schriftliche prüfung), the first at the end of this winter semester and the second before the beginning of the next summer semester:

  • Thursday, 01.03.2018         9:30-11:30      H12
  • Thursday, 12.04.2018         9:30-11:30      H15

In order to be admitted to the final examination, you have to reach 50% of the points in the homeworks.

Times and rooms

  • Lecture (starting on 17.10.17)
    • Tuesday 14:0016:00:         N24, H12
  • Exercises (starting on 06.11.17, every two weeks)
    • Monday 10:0012:00:          N24, H12

Please enroll in Moodle!

References

  • 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