19212801 Lecture

Theory of Functions

Alexander Schmitt

Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

Schedule: Mo 08:00-10:00, Mi 08:00-10:00

Class starts on: 2024-04-15

Course language: German/English

Contact hours: 4

Number of participants: 80

Limited attendance: Yes

Attendance required: Yes

Relevant semester: 4

Modules where this course belongs: 0084cB2.3 0084dB2.3 E17oA1.1

Comments

Function theory is a classical field of mathematics, which deals with the properties of complex-differentiable functions on the complex number plane and has connections to algebra, analysis, number theory and geometry.

The concept of complex differentiability restricts real-differentiable functions from R2 to R2 to angle-preserving images. We will discover that complex-differentiable functions are quite rigid objects, but they are endowed with many amazing analytical, geometric, and visual properties.

A major result discussed in this lecture is Cauchy's integral theorem which states that the integral of any complexly differentiable function along a closed path in the complex plane is zero. We will see many nice consequences of this result, e.g. Cauchy's integral formula, the residual theorem and a proof of the fundamental theorem of algebra, as well as modern graphical representation methods.

Suggested reading

Literatur:

E. Freitag and R. Busam 'Complex analysis', (Springer) 2nd Edition 2009 (the original German version is called 'Funktionentheorie')

26 Class schedule

Regular appointments

Mon, 2024-04-15 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-04-22 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-04-29 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-05-06 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-05-13 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-05-27 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-06-03 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-06-10 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-06-17 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-06-24 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-07-01 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-07-08 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Mon, 2024-07-15 08:00 - 10:00
Funktionentheorie (Serientermin 1)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-04-17 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-04-24 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-05-08 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-05-15 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-05-22 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-05-29 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-06-05 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-06-12 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-06-19 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-06-26 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-07-03 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-07-10 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)

Wed, 2024-07-17 08:00 - 10:00
Funktionentheorie (Serientermin 2)

Lecturers:
Univ.-Prof. Dr. Alexander Schmitt

Location:
A3/Hs 001 Hörsaal (Arnimallee 3-5)