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Version: 01.10.2005 Syllabus Book Master of Science Control and Information Systems

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Page 1: Syllabus Book Master of Science Control and Information ...bd0003/_iw/upload/ise/syllabus/M-CIS.pdf · Master of Science Control and Information Systems -2- V Ü P S Cr Master of

Version: 01.10.2005

Syllabus Book Master of Science Control and Information Systems

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V Ü P S Cr

Master of Science in Control and Information Systems 39 17 5 0 117

Fluid Dynamics Hänel e 2 1 0 0 5

Mathematics 4 Schreiber e 2 2 0 0 5

Non-Technical Subject 1 NN 2 0 0 0 2

Non-Technical Subject 2 NN 2 0 0 0 2

Nonlinear Control Systems Ding e 2 2 1 0 7

Security, Safety and Reliability of Digital Systems Hunger Geisselhardt Kochs

d 2 1 0 0 5

1.

Elective 1 NN 2 1 0 0 4

Summe: 14 7 1 0 30

Advanced Systems and Control Theory Ding e 2 1 0 0 4

Informatics and Numerical Methods 1 Petersen d 2 1 0 0 5

Human-Machine-Systems Söffker d 3 0 0 0 4

Non-Technical Subject 3 NN 2 0 0 0 2

Advanced Control Lab Ding d 0 0 3 0 5

Software Technology Heisel e 2 1 0 0 5

2.

Stochastic Estimation and Control Maier e 2 1 0 0 4

Summe: 13 4 3 0 29

Fault Diagnosis and Fault Tolerance in Technical Systems

Köppen-Seliger d 2 1 0 0 5

Informatics and Numerical Methods 2 Petersen d 2 1 0 0 5

Robust Control Ding e 2 1 0 0 4

Distributed Systems Hoppe d 2 1 1 0 6

Elective 2 NN 2 1 0 0 4

3.

Elective 3 NN 2 1 0 0 4

Summe: 12 6 1 0 28

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4. Master Thesis NN 0 0 0 0 30

Summe: 0 0 0 0 30

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Description of the degree course

name of the degree course shorthand expression of degree course

Master of Science in Control and Information Systems

type period of study SWS ECTS-Credits Master 4 61 117

description In principle the Master of Science in “Control and Information Systems” enables the graduates for careers as engineers in several occupation areas in technical applications which were normally carried out by electrical engineers or mechanical engineers or computer engineers. Furthermore there exists a particular suitability to solving particularly complex or demanding tasks. Therefore the following additional occupations come into play for the Master’s graduates: • Research, • Management of projects, • Management positions with personnel responsibilities.

After fulfilling the broad basic principles, in-depth knowledge in the following fields will be provided: • Mathematics (among others vector analysis, numerical mathematics) and additional physical

basics (fluid dynamics), • Automation technology (with in depth theoretical methods), • Computer science (in particular distributed computer systems).

With this the following special goals are aimed at: • The ability to familiarise with theoretical complex themes, • Ability to also solve complex automation tasks, which require demanding methods of

modelling, simulation and controlling.

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Modul- und lecture catalogue

modul name shorthand expression of module

Thesis

course coordinator faculty Prof. Dr.-Ing. Axel Hunger Prof. Dr.-Ing. Uwe Maier Prof. Dr.-Ing. Paul Josef Mauk Prof. Dr.-Ing. Klaus Solbach Prof. Dr. rer. nat. Jan-Dirk Herbell

-

used in degree course

• Master of Science in Computer Engineering • Master of Science in Computer Science and Communications Engineering • Master of Science in Control and Information Systems • Master of Science in Electrical and Electronic Engineering (Communications Engineering) • Master of Science in Electrical and Electronic Engineering (Power and Automation) • Master of Science in Mechanical Engineering (Water Resources and Environmental Engineering) • Master of Science in Mechanical Engineering (Production and Logistics) • Master of Science in Mechanical Engineering (Mechatronics) nr courses semester sws workload ECTS-credits 1 Master Thesis 4 0 0 30

total 0 0 30

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modul name shorthand expression of module Thesis

lecture name shorthand expression of lecture

Master Thesis

lecturer department NN semester cycle language requirements 4 SWS presence hours self-study hours workload ECTS-Credits 0 0 0 0 30 description

kind of examination

literature

remark

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modul name shorthand expression of module

Advanced Computer Systems Technology

course coordinator faculty Prof. Dr.-Ing. Axel Hunger Prof. Dr.-Ing. Uwe Maier -

used in degree course

• Master of Science in Control and Information Systems nr courses semester sws workload ECTS-credits 1 Distributed Systems 3 4 180 6

2 Security, Safety and Reliability of Digital Systems 1 3 150 5 3 Software Technology 2 3 150 5

total 10 480 16 description: The module Advanced Computer Systems Technology shows the need for a systematic approach to software development, which includes programming as just one activity among many other ones. The basic concepts of distributed systems are described and the fundamentals of network security and the reliability of hardware and software systems are treated.

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modul name shorthand expression of module Advanced Computer Systems Technology

lecture name shorthand expression of lecture

Distributed Systems

lecturer department Prof. Dr. rer. soc. Heinz Ulrich Hoppe semester cycle language requirements 3 German Data structures and algorithms; object-oriented programming SWS presence hours self-study hours workload ECTS-Credits 4 60 120 180 6 description The first section deals with basic concepts and definitions such as "distributed system", client-server and peer-to-peer architectures, concurrency and synchronisation, replication. Section 2 is dedicated to technical foundations and principles which include: - System models and architectures, - Communication protocols and layers, - Operating system level support (incl. threads and processes), - Communication mechanisms (incl. RMI and CORBA), - Synchronisation, - Replication and consistency. In the latter subsections, also formal analyses of algorithms in distributed systems are covered. Section 3 elaborates on formal methodology by introducing Petri nets and different types of agent models. The forth and last section is dedicated to CSCW and CSCL applications. A number of examples are presented and several classification principles are elaborated. Design and evaluation methodologies are covered in a broad overview.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature ·1 Coulouris/Dollimore/Kindberg: Distributed Systems - Concepts and Design, Addison-Wesley 2001 (3rd edition). ·2 Tannenbaum/van Steen: Distributed Systems - Principles and Paradigms, Prentice Hall 2002. ·3 Borghoff/Schlichter: Rechnergestützte Gruppenarbeit (in German), Springer 1998.

remark

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modul name shorthand expression of module Advanced Computer Systems Technology

lecture name shorthand expression of lecture

Security, Safety and Reliability of Digital Systems

lecturer department Prof. Dr.-Ing. Axel Hunger Prof. Dr.-Ing. Walter Geisselhardt Prof. Dr.-Ing. Hans-Dieter Kochs

semester cycle language requirements 1 German SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description Part 1 shows general aspects of network security. First different cryptographic algorithms are described, then the principles of IPSec and SSL are shown and last but not least the young field of quantum computing and quantum cryptography is introduced. Part 2 IIa) Introduction into the classical theory on reliability. The notions of reliability and availability are being outlined, and the most common reliability measures in conjunction with their typical distribution-functions are being presented. Reliability schematic diagrams are being used to model the availability-function of technical systems and to estimate their reliability. IIb) Hardware Reliability of digital circuits. This section emphasizes on the causes of hardware faults in digital circuits and the resulting effects. Based on the classical stuck-at fault model, fault-simulation procedures for combinational circuits are being presented. Also, measures to increase the fault-tolerance of digital circuits are being discussed. IIc) Software Reliability. The last section spots on the life cycle of software and the various development-procedures in software design. The effects of hardware faults onto the software are being emphasized, and the method of signature-monitoring in software is being presented in detail. Part 3 is an introduction to dependability (reliability and safety) of technical systems. The following chapters are outlined in detail: 1) Introduction of dependability theory, 2) Introduction of basic probability theory, 3) Markovian processes, 4) Minimal cut method and approximation procedures.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature Teil 1 / Part 1: ·1 W. Stallings : Cryptography and Network Security, (Prentice Hall, Upper Saddle River, 1999, ISBN 0-13-869017-0) ·2 B. Huber : Der Quantencomputer, (url: http://pluslucis.univie.ac.at/FBA/FBA00/huber/ ) Teil 2 / Part 2:

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Teil 3 / Part 3: ·1 H.-D. Kochs, 1984: Zuverlässigkeit elektrotechnischer Anlagen. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-13475-1 und ISBN 0-387-13475-1. ·2 Weitere umfangreiche und neue Literaturangaben sind zu finden in: Mitteilungen der Fachgruppe Fehlertolerierende Rechensysteme. Nr. 30. Dezember 2002. ISSN 0724-5319. Dieser Band gibt auch einen Überblick über die Arbeiten und Aktivitäten im Germansprachigen Raum. Dieser Band ist zu beziehen über: Dr. Karl-Erwin Großpietsch, FhG - AiS, Schloss Birlinghoven, D-53754 St. Augustin, Email: grosspietsch"ad"ais.fraunhofer.de

remark

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modul name shorthand expression of module Advanced Computer Systems Technology

lecture name shorthand expression of lecture

Software Technology

lecturer department Prof. Dr. rer. nat. Maritta Heisel semester cycle language requirements 2 English SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description This lecture gives a general introduction into software technology (or software engineering). It motivates the need for a systematic approach to software development, which includes programming as just one activity among many other ones. In particular, the lecture covers the following subject: software process models, requirements engineering, programming-in-the-large, quality assurance, documentation, management.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature ·1 Helmut Balzert: Lehrbuch der Softwaretechnik - Softwareentwicklung, Spektrum Verlag, 2000 ·2 Helmut Balzert: Lehrbuch der Softwaretechnik - Software-Management, Software-Qualitätssicherung, Unternehmensmodellierung, Spektrum Verlag, 1998 ·3 Carlo Ghezzi, Mehdi Jazayeri, Dino Mandrioli: Fundamentals of Software Engineering, Prentice Hall, 2002

remark

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modul name shorthand expression of module

Advanced Systems and Control Theory

course coordinator faculty Prof. Dr.-Ing. Uwe Maier -

used in degree course

• Master of Science in Control and Information Systems nr courses semester sws workload ECTS-credits 1 Advanced Systems and Control Theory 2 3 120 4

2 Nonlinear Control Systems 1 5 210 7 3 Robust Control 3 3 120 4

4 Stochastic Estimation and Control 2 3 120 4

total 14 570 19 description: This module teaches extended theoretically oriented knowledge of systems theory and control theory, which are not so often used in practice, but are needed for some complicated applications. Systems theory is deepened, nonlinear and stochastically disturbed systems are treated, as well as theoretically oriented methods for robust controller design.

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modul name shorthand expression of module Advanced Systems and Control Theory

lecture name shorthand expression of lecture

Advanced Systems and Control Theory

lecturer department Prof. Dr.-Ing. Steven X. Ding semester cycle language requirements 2 English Essentials of control engineering SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description This course is devoted to the analysis and synthesis of sampled-data, multi-rate sampled data, periodic and networked control systems. During the last decade, the rapid development of computer, information and communication technologies strongly stimulated the wide application of digital control systems, distributed and networked systems in practice. As a result, advanced system and control theory of sampled-data, multi-rate sampled data, periodic and networked control systems receives much attention. In this course, basic ideas and methods of - system description, -analysis of system dynamics and - controller and observer design of sampled-data, multi-rate sampled data, periodic and networked control systems are presented.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · T. Chen and B. Francis, Optimal Sampled-data Control Systems; · selected Journal papers and book chapters

remark

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modul name shorthand expression of module Advanced Systems and Control Theory

lecture name shorthand expression of lecture

Nonlinear Control Systems

lecturer department Prof. Dr.-Ing. Steven X. Ding semester cycle language requirements 1 English Linear control theory (Systems and control 1) SWS presence hours self-study hours workload ECTS-Credits 5 75 135 210 7 description During the last two decades, development of advanced nonlinear control system theory has received much attention. This course is devoted to the essentials of the nonlinear system analysis and to the introduction of some advanced methods of analyzing and designing nonlinear control systems developed in recent years. First, different methods and tools for the description of nonlinear systems are introduced. Stability study with emphasis on the Lyapunov’s method builds the basis for the further study. It is followed by the presentation of advanced stability theory and introduction of different methods of nonlinear controller design including the feedback linearization method, sliding mode control and adaptive control schemes.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · A. Isidori, Nonlinear Control Systems, Springer-Verlag. · K.S. Narendra and A.M. Annaswamy, Stable Adaptive Control, Prentice-Hall International, Inc., 1989. · Ch. Edwards and S. Spurgeon, Sliding Mode Control, Taylor Francis Ltd, 1998

remark

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modul name shorthand expression of module Advanced Systems and Control Theory

lecture name shorthand expression of lecture

Robust Control

lecturer department Prof. Dr.-Ing. Steven X. Ding semester cycle language requirements 3 English Linear control theory SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description Due to its importance in practice, robust control technique is one of the research and development fields in control engineering, which continuously received the most attention during the last two decades. The focus of this course is the introduction to the essentials of the robust control theory, to the computational tools and some design methods. First, basics of mathematical and system theoretical tools are introduced. It is followed by the description of different concepts of modelling system uncertainties. The final part of this course is devoted to the different optimal controller design schemes including H_2- and H_infinity-optimal control and their computational aspects.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · K. Zhou et al., Robust and Optimal Control, Prentice Hall, 1996.

remark

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modul name shorthand expression of module Advanced Systems and Control Theory

lecture name shorthand expression of lecture

Stochastic Estimation and Control

lecturer department Prof. Dr.-Ing. Uwe Maier semester cycle language requirements

2 English lecture "Regelungstechnik 1" = "Systems and Control 1"; basic knowledge of probability theory

SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description Basics, theory and applications of state estimation for systems with stochastic disturbances: basics of stochastic processes and systems, deterministic state observers, optimal state estimators (Kalman filter, Wiener filter), extensions (correlated noise, coloured noise, nonlinear filtering), applications, control.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · Maier, Uwe: Lecture Notes "Stochastic Estimation and Control". · Sage, Andrew P.; Melsa, J.L.: Estimation Theory with Applications to Communications and Control. McGraw-Hill, New York et.al. · Grewal, Mohinder S.; Andrews, A.P.: Kalman Filtering: Theory and Practice. Prentice Hall, Englewood Cliffs.

remark

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modul name shorthand expression of module

Advanced Control Technology and Applications

course coordinator faculty Prof. Dr.-Ing. Uwe Maier -

used in degree course

• Master of Science in Control and Information Systems

nr courses semester sws workload ECTS-credits

1 Advanced Control Lab 2 3 150 5

2 Fault Diagnosis and Fault Tolerance in Technical Systems 3 3 150 5

3 Man-Machine-Systems 2 3 120 4

total 9 420 14 description: Application oriented, but on a high theoretical level, special technologies and applications of automation are treated. Belonging to it are human machine systems, considering e.g. human machine interfaces between automated systems and the human operators, as well as questions of safety and reliability. In the “Advanced Control Lab” the theoretical methods find application for real systems as examples.

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modul name shorthand expression of module Advanced Control Technology and Applications

lecture name shorthand expression of lecture

Advanced Control Lab

lecturer department Prof. Dr.-Ing. Steven X. Ding semester cycle language requirements 2 German Systems and control 1, 2 (RT 1, 2) SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description The students will learn how to develop a control scheme for a given process and how to realize the developed controller on-line under real application conditions. For this purpose, different laboratory systems with real plants and design software (MATLAB) are available.

kind of examination

literature · AKS internal document: Instruction to Advanced Control Lab

remark

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modul name shorthand expression of module Advanced Control Technology and Applications

lecture name shorthand expression of lecture

Fault Diagnosis and Fault Tolerance in Technical Systems

lecturer department Dr.-Ing. Birgit Köppen-Seliger semester cycle language requirements 3 German Introduction to Automation; Systems and Control 1 SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description Introduction to and history of technical fault diagnosis; problem definition and technical definitions; model-based fault diagnosis techniques; residual generation: parameter estimation, parity space, observer-based methods, neural networks, fuzzy logic; residual evaluation: thresholds, classification; fault tolerance; reconfiguration; fault tolerant control; applications.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · selected publications from international conferences and technical journals

remark

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modul name shorthand expression of module Advanced Control Technology and Applications

lecture name shorthand expression of lecture

Man-Machine-Systems

lecturer department Prof. Dr.-Ing. Dirk Söffker semester cycle language requirements 2 German SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description Human control: the human in the interaction with technical systems especially within automatic control: classification and example of human interaction, models for human control and supervision, man-machine-communication (ergonomics, graphical interfaces, cognitive science basics, user orientation, objects and taskorientation, representation of text and graphics, dialog technics, design of operating centers), modeling of cognition (acting, decision and planning, human factors, human errors), training Within the course an excursion to a training center for plant supervision is mandatory.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · G. Johannsen: Mensch-Maschine-Systeme, Springer.

remark

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modul name shorthand expression of module

Mathematics, Numerics and Physics

course coordinator faculty Prof. Dr.-Ing. Uwe Maier -

used in degree course

• Master of Science in Control and Information Systems nr courses semester sws workload ECTS-credits 1 Fluid Dynamics 1 3 150 5

2 Informatics and Numerical Methods 1 2 3 150 5 3 Informatics and Numerical Methods 2 3 3 150 5

4 Mathematics 4 1 4 150 5

total 13 600 20 description: This module contains different lessons teaching extended fundamentals for the master study: · “Mathematics 4” deals with vector analysis as base for description of fields, e.g. as needed for fluid dynamics. The theories of analytic functions and distributions are needed in systems theory. · “Informatics and Numerical Methods 1,2” are numerical mathematics, but software implementation oriented. The contents are needed e.g. for dynamic systems simulation, for control optimisation and other control problems to be solved numerically. · “Fluid Dynamics” deals with fields describing fluid currents, as a base for modelling and simulation of fluid currents, e.g. in pipes, valves, flow measurement devices, or around moving cars, ships or planes. At the same time this subject serves as an example for the case of time and position dependant processes, i.e. for systems with distributed parameters described by partial differential equations.

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modul name shorthand expression of module Mathematics, Numerics and Physics

lecture name shorthand expression of lecture

Fluid Dynamics

lecturer department Prof. Dr.-Ing. Dieter Hänel semester cycle language requirements 1 English BC SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description The lecture offers an extension to important problems of fluid dynamics and is divided in the following chapters: · conservation equations of fluid dynamics conservation of mass, momentum and energy (Navier-Stokes equations) stress-strain relations thermal and calorical equations of state · similarity theory of fluids · creeping flows · boundary layer theory · introduction to turbulent flows · one-dimensional gasdynamics

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature ·1 Umdruck ·2 Script

remark

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modul name shorthand expression of module Mathematics, Numerics and Physics

lecture name shorthand expression of lecture

Informatics and Numerical Methods 1

lecturer department Dr.-Ing. Jörg Petersen semester cycle language requirements

2 German Grundlagen der Linearen Algebra (Vektor-, Matrixrechnung), Grundlagen der Analysis (Reihen, stetige Funktionen, Differentiation, Integration, Taylorentwicklung)

SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description The course gives an introduction into numerical methods and their design and implementation by algorithms and programs. Starting with an introduction and overview of numerical areas of application, in the first semester of this two semester course the following topics are taught: coding of numbers in computers, error analysis and error propagation, condition, stability, norms of vectors and matrices, non-linear equations, searching for roots of continous functions, fixed point iteration, Newton and secant method, algebraic equations, simple and complete Horner scheme, roots of polynoms, direct and iterative methods solving linear equation systems, Gaussian, Jacobi, and Gauss Seidel method, relaxation method, discrete and continous approximation, approximation of periodical functions, discrete fast Fourier transform, interpolation and interpolation polynoms, spline interpolation, Bézier polynoms, and Bézier splines.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · Chapra, Steven C.; Canale, Raymond P. Numerical Methods for Engineers: With Programming and Software Applications. 3. Auflage, McGraw-Hill Verlag, 1998 · Gramlich, G.; Werner, W. Numerische Mathematik mit Matlab. dpunkt-Verlag, 2000 · Weller, F. Numerische Mathematik für Ingenieure und Naturwissenschaftler. Eine Einführung für Studium und Praxis. Vieweg Verlag,1996

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modul name shorthand expression of module Mathematics, Numerics and Physics

lecture name shorthand expression of lecture

Informatics and Numerical Methods 2

lecturer department Dr.-Ing. Jörg Petersen semester cycle language requirements 3 German Informatik und numerische Methoden 1 SWS presence hours self-study hours workload ECTS-Credits 3 45 105 150 5 description Continuation of "Informatics and Numerical Methods 1" with the following topics: integration, Newton-Cotes Formulas, Gaussian Quadrature Numerical Integration, Monte Carlo integration, linear optimisation, transport problems, numerical differentiation with differential quotients and substitution functions, ordinary differential equations, starting value problems, boundary value problems, one and multi step methods, systems of ordinary differential equations, Schiess methods, partial differential equations with starting and boundary value problems, finite difference equations, matrix Eigenvalues and vectors, power method, QR algorithm, numerical classification.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · Chapra, Steven C.; Canale, Raymond P. Numerical Methods for Engineers: With Program-ming and Software Applications. 3. Auflage, McGraw-Hill Verlag, 1998 · Gramlich, G.; Werner, W. Numerische Mathematik mit Matlab. dpunkt-Verlag, 2000 · Weller, F. Numerische Mathematik für Ingenieure und Naturwissenschaftler. Eine Einführung für Studium und Praxis. Vieweg Verlag,1996

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modul name shorthand expression of module Mathematics, Numerics and Physics

lecture name shorthand expression of lecture

Mathematics 4

lecturer department Prof. Dr. rer. nat. Wolfgang Schreiber semester cycle language requirements 1 English SWS presence hours self-study hours workload ECTS-Credits 4 60 90 150 5 description 1 Vectoranalysis 1.1. Surfaces 1.2 Flux of a Vector Field through a surface 1.3 Green‘ s Theorem 1.4 Stoke‘s Theorem 1.5 The Divergence Theorem 2 Function Theory 2.1 Holomorphic Functions 2.2 Analytic Functions 2.3 Complex Line Integrals 2.4 Cauchy‘s Theorem 2.5 Laurent-Series 2.6 Calculus of Residues 3 Distributions

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature · Burg, Haf, Wille: Höhere Mathematik für Ingenieure, Band 4. Teubner 1987

remark

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modul name shorthand expression of module

Non-Technical Subjects

course coordinator faculty Prof. Dr.-Ing. Axel Hunger Prof. Dr.-Ing. Uwe Maier Prof. Dr.-Ing. Paul Josef Mauk Prof. Dr.-Ing. Klaus Solbach Prof. Dr. rer. nat. Jan-Dirk Herbell

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used in degree course

• Master of Science in Computer Engineering • Master of Science in Computer Science and Communications Engineering • Master of Science in Control and Information Systems • Master of Science in Electrical and Electronic Engineering (Communications Engineering) • Master of Science in Electrical and Electronic Engineering (Power and Automation) • Master of Science in Mechanical Engineering (Water Resources and Environmental Engineering) • Master of Science in Mechanical Engineering (Production and Logistics) • Master of Science in Mechanical Engineering (Mechatronics) nr courses semester sws workload ECTS-credits 1 Non-Technical Subject 1 1 2 60 2 2 Non-Technical Subject 2 1 2 60 2

3 Non-Technical Subject 3 2 2 60 2

total 6 180 6 description: This module gives Master-students the opportunity to demonstrate their participation in non-technical subjects. Students are able to choose from all offers of the University Duisburg-Essen, e.g. language courses or lectures on business administration and sociology and culture.

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modul name shorthand expression of module Non-Technical Subjects

lecture name shorthand expression of lecture

Non-Technical Subject 1

lecturer department NN semester cycle language requirements 1 SWS presence hours self-study hours workload ECTS-Credits 2 30 30 60 2 description

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature

remark

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modul name shorthand expression of module Non-Technical Subjects

lecture name shorthand expression of lecture

Non-Technical Subject 2

lecturer department NN semester cycle language requirements 1 SWS presence hours self-study hours workload ECTS-Credits 2 30 30 60 2 description

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature

remark

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modul name shorthand expression of module Non-Technical Subjects

lecture name shorthand expression of lecture

Non-Technical Subject 3

lecturer department NN semester cycle language requirements 2 SWS presence hours self-study hours workload ECTS-Credits 2 30 30 60 2 description

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature

remark

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modul name shorthand expression of module

Electives

course coordinator faculty Prof. Dr.-Ing. Axel Hunger Prof. Dr.-Ing. Uwe Maier Prof. Dr.-Ing. Paul Josef Mauk Prof. Dr.-Ing. Klaus Solbach Prof. Dr. rer. nat. Jan-Dirk Herbell

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used in degree course

• Master of Science in Computer Engineering • Master of Science in Control and Information Systems • Master of Science in Electrical and Electronic Engineering (Communications Engineering) • Master of Science in Electrical and Electronic Engineering (Power and Automation) • Master of Science in Mechanical Engineering (Water Resources and Environmental Engineering) • Master of Science in Mechanical Engineering (Production and Logistics) • Master of Science in Mechanical Engineering (Mechatronics) nr courses semester sws workload ECTS-credits 1 Elective 1 1 3 120 4

2 Elective 2 3 3 120 4 3 Elective 3 3 3 120 4

total 9 360 12 description: Electives are defined for profund education to prepare for a job or to continue studies for Dr. degree. It is also possible to choose different topics in order to get double qualification.

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modul name shorthand expression of module Electives

lecture name shorthand expression of lecture

Elective 1

lecturer department NN semester cycle language requirements 1 German/English SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description Electives are defined for profund education to prepare for a job or to continue studies for Dr. degree. It is also possible to choose different topics in order to get double qualification.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature

remark

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modul name shorthand expression of module Electives

lecture name shorthand expression of lecture

Elective 2

lecturer department NN semester cycle language requirements 3 German/English SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description Electives are defined for profund education to prepare for a job or to continue studies for Dr. degree. It is also possible to choose different topics in order to get double qualification.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature

remark

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modul name shorthand expression of module Electives

lecture name shorthand expression of lecture

Elective 3

lecturer department NN semester cycle language requirements 3 German/English SWS presence hours self-study hours workload ECTS-Credits 3 45 75 120 4 description Electives are defined for profund education to prepare for a job or to continue studies for Dr. degree. It is also possible to choose different topics in order to get double qualification.

kind of examination According to § 17 of the examination regulation the type and duration of the examination will be defined from the lecturer before the semester starts. Therefore an examination can be a written test with a length of 30 to 120 minutes or an oral examination with a length of 30 to 60 minutes. The language of the examination is the same as the language of the lecture.

literature

remark