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Numerical Methods and Statistics

Module name (EN): Numerical Methods and Statistics
Degree programme: Mechatronics, Master, ASPO 01.04.2020
Module code: MTM.NUS
SAP-Submodule-No.: P231-0012
Hours per semester week / Teaching method: 5V+1U (6 hours per week)
ECTS credits: 7
Semester: 1
Mandatory course: yes
Language of instruction:
Written exam 150 min.

[updated 01.10.2020]
Applicability / Curricular relevance:
MTM.NUS (P231-0012) Mechatronics, Master, ASPO 01.04.2020, semester 1, mandatory course
90 class hours (= 67.5 clock hours) over a 15-week period.
The total student study time is 210 hours (equivalent to 7 ECTS credits).
There are therefore 142.5 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
Recommended as prerequisite for:
MTM.SIM Simulation of Mechatronic Systems

[updated 23.11.2020]
Module coordinator:
Prof. Dr. Gerald Kroisandt
Lecturer: Prof. Dr. Gerald Kroisandt

[updated 11.04.2019]
Learning outcomes:
After successfully completing this part of the module, students will have mastered the use of MATLAB and Simulink.
Students will be able to represent linear and non-linear systems of equations in the programs and will be familiar with various solution methods.
They will understand the significance of the Fourier transform and will be able to calculate and evaluate given time signals independently.
Based on the theory of differentiation and integration, they will be able to differentiate and integrate functions numerically using various methods.
Afterwards, students will be able to apply the different methods to practical examples.
In the field of statistics, they will be proficient in the graphical representation of a single characteristic, as well as the calculation of various key figures.
In order to evaluate different characteristics, students will be familiar with and be able to apply different measures of correlation.
They will also be able to carry out a linear regression and know how to transform data if necessary.
In the field of probability theory, students will understand the basic concepts and have a repertoire of different distributions for various standard applications.
Finally, they will be able to use key figures of the data to infer the optimal parameters of a chosen model and derive various statements about further events (tests).

[updated 01.10.2020]
Module content:
I. Numerical methods
1. Working with MATLAB and Simulink (repetition)
2. Linear and nonlinear systems of equations
3. Discrete/Fast Fourier transform
4. Numerical Integration and Differentiation (continuation from Bachelor program)
5. Applications (simulation of mechatronic systems) - Mini-project
II. Statistics
1.  Descriptive statistics
 1.1 Analyzing observation data
 1.2 Evaluation of several characteristics
 1.3 Linear regression
2. Principles of probability calculus
 2.1 Definition of probability
 2.2 Discrete and continuous random variables and their distributions   
 2.3. Special continuous and discrete distributions
 2.4. Limit theorems
3. Inferential statistics
 3.1 Estimating probabilities, mean value and dispersion
 3.2 Confidence intervals
 3.3 Tests

[updated 01.10.2020]
Teaching methods/Media:
Blackboard, projector, transparencies with lecture notes

[updated 01.10.2020]
Recommended or required reading:
Brigham: FFT-Anwendungen, Oldenburg Verlag 1997
E. Cramer, U. Kamps: Grundlagen der Wahrscheinlichkeitsrechnung und Statistik, Springer 2017

[updated 01.10.2020]
[Wed Oct  5 10:22:44 CEST 2022, CKEY=mnus, BKEY=mechm, CID=MTM.NUS, LANGUAGE=en, DATE=05.10.2022]