## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-81-23-M-4

## Module Identification

Module Number Module Name CP (Effort)
MAT-81-23-M-4 Differential-Algebraic Equations 4.5 CP (135 h)

## Basedata

CP, Effort 4.5 CP = 135 h 1 Sem. irreg. SuSe [4] Bachelor (Specialization) [EN] English Simeon, Bernd, Prof. Dr. (PROF | DEPT: MAT) Simeon, Bernd, Prof. Dr. (PROF | DEPT: MAT) [MAT-TEMA] Industrial Mathematics [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Notice

Without a proof of successful participation in the exercise classes, only 3 credit points will be awarded for the module.

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-81-23-K-4
Differential-Algebraic Equations
P 42 h 93 h
U-Schein
- PL1 4.5 irreg. SuSe
• About [MAT-81-23-K-4]: Title: "Differential-Algebraic Equations"; Presence-Time: 42 h; Self-Study: 93 h
• About [MAT-81-23-K-4]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 86195 ("Differential-Algebraic Equations")

## Contents

The theory and numerical analysis of differential-algebraic equations is discussed, in particular:
• application fields (electrical circuits and multibody mechanical systems),
• relation with singularly perturbed problems,
• solution theory and index concepts,
• normal form for linear DAEs,
• numerical aspects

## Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand the basic concepts of the theory and numerical analysis of differential-algebraic equations. They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. They have learnt how to apply these techniques to new problems, analyze them and develop solution strategies indepently or by team work.

## Literature

• P. Kunkel, V. Mehrmann: Differential-Algebraic Equations. Analysis and Numerical Solution,
• B. Simeon: Computational Flexible Multibody Dynamics,
• S. Trenn: Solution concepts for linear DAEs: a survey; in: Surveys in Differential-Algebraic Equations I (Eds. A. Ilchmann, T. Reis).

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

## References to Module / Module Number [MAT-81-23-M-4]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective