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2022S, UE, 1.5h, 1.5EC, to be held in blocked form

## Properties

• Semester hours: 1.5
• Credits: 1.5
• Type: UE Exercise
• 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 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

Introduction to Fourier analysis, complex analysis and PDEs.

## Teaching methods

The course will be held online in TUWEL.

Immanent

## Course dates

DayTimeDateLocationDescription
Wed14:00 - 16:0016.03.2022 Zoom-Meeting1. Übung
Wed14:00 - 16:0023.03.2022 Zoom-Meeting2. Übung
Wed15:00 - 16:0030.03.2022 Online-Prüfung in TUWEL1. Onlinetest
Wed14:00 - 16:0027.04.2022 Zoom-Meeting3. Übung
Wed14:00 - 16:0004.05.2022 Zoom-Meeting4. Übung
Wed15:00 - 16:0011.05.2022 Online-Prüfung in TUWEL2. Onlinetest
Wed14:00 - 16:0025.05.2022 Zoom-Meeting5. Übung
Wed14:00 - 16:0001.06.2022 Zoom-Meeting6. Übung
Wed15:00 - 16:0008.06.2022 Online-Prüfung in TUWEL3. Onlinetest
Wed14:00 - 16:0015.06.2022 Prüfung Online mit Zoom-Beobachtung oder im Freihaus, 7. Stock, grüner Bereich, SeminarraumEntscheidungstest
Course is held blocked

## Examination modalities

The course evaluation is based on 3 online exams. The online exams will be held via TUWEL and will take up to 60 Minutes. The online exam has two parts, a Multiplie-Choice test and a part where an answer has to be prepared on paper and uploaded to TUWEL within the timeframe of the exam.

## Course registration

Begin End Deregistration end
11.02.2022 12:00 07.04.2022 08:00 07.04.2022 08:00

## Curricula

Study CodeObligationSemesterPrecon.Info
033 245 Mechanical Engineering Mandatory3. Semester
Course requires the completion of the introductory and orientation phase
033 273 Chemical and Process Engineering Mandatory3. Semester
033 282 Mechanical Engineering - Management Mandatory3. Semester

## Literature

No lecture notes are available.

German