On July 30th, 2024, due to an important database update, there will be service interruptions in the Student Self-Service and Workforce Management areas between 8 AM and 11 AM. Thank you for your understanding.

# 102.114 Revision course for Mathematics III 2023W 2022W 2019W 2018W 2017W 2016W 2015W 2014W 2013W 2012W 2011W 2010W 2009W 2008W 2007W

2023W, RE, 1.0h, 1.0EC

## Properties

• Semester hours: 1.0
• Credits: 1.0
• Type: RE Revision Course
• Format: Online

## Learning outcomes

After successful completion of the course, students are able to...

• ... in the theory of complex functions ...
• ... investigate the complex differentiability of a given function via the Cauchy--Riemann differential equations and calculate conjugate harmonic functions.
• ... calculate complex integrals over a parametrized curve or via the antiderivative.
• ... identify and classify the pols of a complex function and calculate the residuum at a pole.
• ... solve complex integrals via the Residue Theorem.
• ... in the vector space theory of a system of functions ...
• ... calculate the orthogonal projection of a given function onto the linear span of a given system of functions.
• ... calculate the coefficiets of the Fourier series of a given function.
• ... determine the limit of the Fourier series of a given function at a specified point using the Dirichlet Theorem.
• ... in the theory of integral-transformations...
• ... calculate the Laplace tranform of a given function, via the definition and the elementary properties (linearity, similarity, differential, integration, shift, ...) of the Laplace transform.
• ... dertermine the inverse of the Laplace transform of a function using the complex inversion-formula and the residue theorem.
• ... solve initial value problems using the Lapace transform.
• ... calculate the Fourier transform and inverse Fourier transform, via the definition and the elementary properties (linearity, similarity, differential, shift, ...) of the Fourier transform.
• ... in the theory of linear partial differential equations ...
• ... classify a given linear partial differential equation (order, coefficients, homogen or inhomogen, type,...).
• ... determine a general solution of a given linear partial differential equation of first order via the method of characteristics.
• ... determine a general solution of classical homgeneous linear partial differential equations  of second order (potential equation, heat equation, wave equation,...) by method of seperation of variables and fit the general solution to a given set of boundary conditions via application of the theory of Fourierseries.

## Subject of course

Complex analysis, integral transforms, PDEs

## Teaching methods

Discussion of case studies

Immanent

## Course dates

DayTimeDateLocationDescription
Tue14:00 - 15:0031.10.2023 Zoom-MeetingRepetitorium Math 3 zu den Inhalten der 1. Übung
Tue14:00 - 16:0007.11.2023 Zoom-MeetingRepetitorium Math 3 zu den Inhalten der 2. Übung und Vorbereitung zum 1. Zwischentest
Tue14:00 - 15:0021.11.2023 Zoom-MeetingRepetitorium Math 3 zu den Inhalten der 3. Übung
Tue14:00 - 16:0028.11.2023 Zoom-MeetingRepetitorium Math 3 zu den Inhalten der 4. Übung und Vorbereitung zum 2. Zwischentest
Tue14:00 - 15:0012.12.2023 Zoom-MeetingRepetitorium Math 3 zu den Inhalten der 5. Übung
Tue14:00 - 16:0009.01.2024 Zoom-MeetingRepetitorium Math 3 zu den Inhalten der 6. Übung und Vorbereitung zum 3. Zwischentest

## Examination modalities

Die Beurteilung des Repetitorium wird anhand der insgesamt 3 Online-Quiz erfolgen (jeweils vor dem Test im TUWEL verfügbar).

Sie werden nur dann eine Note für das Repetitorium bekommen, wenn Sie an zumindest 2 der 3 Online-Quiz teilgenommen haben.

## Course registration

Begin End Deregistration end
02.10.2023 09:00 16.11.2023 12:00

## Curricula

Study CodeObligationSemesterPrecon.Info
No records found.

## Literature

No lecture notes are available.

## Previous knowledge

Die Studierenden sollten die in der Inhaltsangabe genannten Vorlesungen regelmäßig besuchen und sich mit den dort vorgetragenen Inhalten beschäftigen um gezielte Fragen stellen zu können.

German