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Applied Mathematics

Module name (EN):
Name of module in study programme. It should be precise and clear.
Applied Mathematics
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Industrial Engineering, Master, ASPO 01.10.2014
Module code: WIMASc235
The exam administration creates a SAP-Submodule-No for every exam type in every module. The SAP-Submodule-No is equal for the same module in different study programs.
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
2V+2U (4 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
Semester: 2
Mandatory course: yes
Language of instruction:
Written exam

[updated 18.12.2018]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

WIMASc235 (P450-0101) Industrial Engineering, Master, ASPO 01.10.2014 , semester 2, mandatory course
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
60 class hours (= 45 clock hours) over a 15-week period.
The total student study time is 180 hours (equivalent to 6 ECTS credits).
There are therefore 135 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
Recommended as prerequisite for:

[updated 11.03.2020]
Module coordinator:
Prof. Dr. Frank Kneip
Prof. Dr. Frank Kneip

[updated 11.02.2020]
Learning outcomes:
After successfully completing this module students will:
_        be proficient in solving nonlinear equations, can select a suitable solution method and be able to justify their choice.
_        be able to model suitable systems in the form of a linear equation system and identify unknown parameters based on given measurement data.
_        be able to describe the principles of state estimation and time series analysis using hidden Markov models and reproduce known examples, as well as adapt the methods to similar systems.
_        be able to implement the algorithms learned in Matlab
_        be able to interpret their results and check their plausibility

[updated 18.12.2018]
Module content:
1.        Numerical methods: solving nonlinear equations
1.1.         Bisection method
1.2.         Fixed-point iteration
1.3.         Secant method
1.4.         Newton´s method
1.5.         Accuracy and termination criteria
1.6.         Convergence characteristics
1.7.         Applications
2.        Parameter estimation: linear equalization
2.1.         Modeling
2.2.         Method of least squares
2.3.         Weighted least squares
2.4.         Recursive least squares
2.5.         Applications
3.        State estimation and time series analysis: hidden Markov models
3.1.         Definition and modeling hidden Markov models
3.2.         Forward algorithm
3.3.         Backward algorithm
3.4.         Viterbi algorithm
3.5.         Baum-Welch algorithm
3.6.         Applications

[updated 18.12.2018]
Teaching methods/Media:
Presentation with projector, lecture notes, blackboard, PC, Matlab/Simulink, computer-aided exercises

[updated 18.12.2018]
Recommended or required reading:
_        Dahmen, W., Reusken, A.: Numerik für Ingenieure und Naturwissenschaftler; 2. Auflage, Springer, 2008
_        Gramlich, G., Werner, W.: Numerische Mathematik mit Matlab; dpunkt verlag, 2000
_        Björck, A.: Numerical Methods for Least Squares Problems; Society for Industrial and Applied Mathematics (SIAM), 1996
_        Rabiner, L. R.: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition; Proceedings of the IEEE, Band 77, Nr. 2, S. 257_286, 1989
_        Fraser, A. M.: Hidden Markov Models and Dynamical Systems; Society for Industrial and Applied Mathematics (SIAM), 2009

[updated 18.12.2018]
[Thu Apr 18 00:00:01 CEST 2024, CKEY=wwxam, BKEY=wim2, CID=WIMASc235, LANGUAGE=en, DATE=18.04.2024]