# 101.440 Specialisation - Mathematics (Selected Topics) This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2025S 2024S 2023S 2022S 2021S 2020S 2019S 2018S 2017S 2016S 2015S 2014S 2013S 2012S

2024S, VU, 4.0h, 5.0EC

## Properties

• Semester hours: 4.0
• Credits: 5.0
• Type: VU Lecture and Exercise
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to numerically solve linear equation systems directly and iteratively. Students know to set up boundary and initial boundary value problems in principle and in particular for Maxwell’s equations and to solve them approximately by means of the finite difference method to some extent. Furthermore, students are essentially able to derive the weak formulation of simple boundary value problems and to find an approximate solution either by implementing an own computer code of the finite element method for instance in Python or by using Netgen/NGSolve (Open Source Software) to model and simulate problems in electrical engineering and to carry out a validity check.

## Subject of course

Linear equation systems, introduction to partial differential equations, their classification and some essential properties, establishing the initial boundary and boundary value problems based on Maxwell’s equations, discussion of the practical relevance, approximate solution with the finite difference method, method of weighted residuals, idea of the finite element method, derivation of the weak formulation, assembling of the finite element equation systems using hat functions, weak formulations based on a scalar potential and on a vector potential in the context of the Maxwell’s equations, construction of finite element bases for the Sobolev spaces H^1 and H(curl).

## Teaching methods

Some simple algorithms are to be implemented in the associated exercises. Small but relevant problems in electrical engineering will be solved using Netgen/NGSolve. To this end partly prepared examples in Python will be provided, which have to be completed or extended.

Written and oral

## Course dates

DayTimeDateLocationDescription
Mon15:00 - 16:0004.03.2024 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorbesprechung
Tue15:00 - 17:0005.03.2024 - 25.06.2024 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon15:00 - 17:0011.03.2024 - 24.06.2024 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Specialisation - Mathematics (Selected Topics) - Single appointments
DayDateTimeLocationDescription
Mon04.03.202415:00 - 16:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorbesprechung
Tue05.03.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon11.03.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue12.03.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon18.03.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue19.03.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon08.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue09.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon15.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue16.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon22.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue23.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon29.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue30.04.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon06.05.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue07.05.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon13.05.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue14.05.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Mon27.05.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung
Tue28.05.202415:00 - 17:00 Seminarraum DA03 C22, Freihaus, grüner Bereich, 3. StockVorlesung

## Examination modalities

In small groups of 2 or 3 students mathematical exercises have to be solved, simple algorithms have to be implemented and analyzed and simulation exercises have to be carried out and the results discussed. One protocol has to be prepared together by the group.

## Course registration

Begin End Deregistration end
04.03.2024 00:00 06.04.2024 13:00 12.04.2024 13:00

## Group Registration

GroupRegistration FromTo
Gruppe 106.03.2024 00:0002.04.2024 01:00
Gruppe 206.03.2024 00:0002.04.2024 01:00
Gruppe 306.03.2024 00:0002.04.2024 01:00
Gruppe 406.03.2024 00:0002.04.2024 00:00
Gruppe 506.03.2024 00:0005.04.2024 00:00
Gruppe 606.03.2024 00:0005.04.2024 00:00
Gruppe 706.03.2024 00:0005.04.2024 00:00
Gruppe 806.03.2024 00:0005.04.2024 00:00

## Curricula

Study CodeObligationSemesterPrecon.Info
033 235 Electrical Engineering and Information Technology Mandatory elective
Course requires the completion of the introductory and orientation phase

## Literature

Skript is available

## Previous knowledge

Calculus, Ordinary Differential Equations and Linear Algebra

German