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2020W, VO, 2.0h, 3.0EC, to be held in blocked form

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Distance Learning

## 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 Laplace 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

Laplace and Fourier transform, complex analysis, fourier series, partial differential equations

## Teaching methods

Lecture (a excercise course on the subjects of the lecture is offered as a sperate course)

## Mode of examination

Written

The lecture will be held online. There will be prerecorded Videos for the lecture sessions. All further Information is provided on the course page in TUWEL.

written exam

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Fri15:30 - 18:0008.10.2021 Prüfung findet via TUWEL unter Zoom-Beobachtung statt. TUWEL: https://tuwel.tuwien.ac.at/course/view.php?id=41274written20.09.2021 00:00 - 06.10.2021 08:00TISS[Online-Prüfung] Besau Oktober
Fri15:30 - 18:0019.11.2021 Prüfung findet via TUWEL unter Zoom-Beobachtung statt. TUWEL: https://tuwel.tuwien.ac.at/course/view.php?id=41286written01.11.2021 00:00 - 17.11.2021 08:00TISS[Online-Prüfung] Besau November

## Course registration

Begin End Deregistration end
23.09.2020 08:00 16.12.2020 03:00 16.12.2020 03:00

## Curricula

Study CodeSemesterPrecon.Info
033 245 Mechanical Engineering 3. Semester
Course requires the completion of the introductory and orientation phase
033 273 Chemical and Process Engineering 3. Semester
033 282 Mechanical Engineering - Management 3. Semester

## Literature

The lecture notes are available at the Grafisches Zentrum.

## Previous knowledge

Calculus, ODEs, vector spaces

German