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Mathematics III / Applied Mathematics

Module name (EN):
Name of module in study programme. It should be precise and clear.
Mathematics III / Applied Mathematics
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012
Module code: MST.MA3
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.
4V+1U (5 hours per week, accumulated)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
Semester: 3
Duration: 2 semester
Mandatory course: yes
Language of instruction:
Test + term paper

[updated 10.05.2021]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

MST.MA3 (P231-0055) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012 , semester 3, mandatory course
MST.MA3 (P231-0055) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011 , semester 3, 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).
75 class hours (= 56.25 clock hours) over a 15-week period.
The total student study time is 180 hours (equivalent to 6 ECTS credits).
There are therefore 123.75 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
MST.NSW Numerical Software

[updated 01.10.2012]
Recommended as prerequisite for:
MST.CVI Computer Vision
MST.TMM Mechanical Engineering and Machine Dynamics

[updated 01.10.2012]
Module coordinator:
Lecturer: N.N.

[updated 01.10.2012]
Learning outcomes:
The objective of this module is to teach the applied mathematical methods required for engineering disciplines such as control engineering and physics.
In addition, it is designed to teach applied methods of higher mathematics in a problem-oriented manner (in particular numerics and statistics) using practical examples.
After successfully completing this module, students will be able to solve minor problems based on given measured data using MATLAB and SIMULINK, and present their solution in writing.
Part I

[updated 10.05.2021]
Module content:
1 - Ordinary differential equations
•        Separable DG
•        Linear differential equation with constant coefficients of the 1st order
•        Linear differential equation with constant coefficients of the 2nd order
•        Applications in technology
2 - The Fourier transform
•        Fourier series for periodic functions
•        Fourier series for non-periodic functions
•        Applications
3 - The Laplace transform
•        Definition
•        Algorithms
•        Inverse transformation methods (convolution, partial fraction decomposition)
•        Applications
4 – Functions with multiple variables
•        Partial derivatives, tangent plane    
3.        Coordinate transformations,
•        Multiple integrals and integral transform
5 – Introduction to vector analysis  
Part II
1.  Introduction to Matlab
1.1 Calculating with vectors and matrices, creating graphics
2.  Interpolations (Newton polynomials, Spline functions)
2.1 Mini-project
3.  Least squares fitting  
3.1 Linear balance functions
3.2 Non-linear balanced functions
3.3 Mini-project
4.  Simple statistical measures for one, two, and more than two characteristics
4.1 Mini-project
5.  Numerical differentiation and integration - Introduction
5.1 Mini-project
6.  Introduction to SIMULINK
6.1 Solving initial value problems of ordinary differential equations with SIMULINK
6.2 Mini-project

[updated 10.05.2021]
Teaching methods/Media:
The numerics part II will take place in the PC lab AMSEL (Angewandte Mathematik, Statistik, eLearning (Room 5306).
All practical exercises for the lecture, as well as solving exercises, homework and case studies will be done with the e-learning system MathCoach (AMSEL lab: PC lab: "Angewandte Mathematik, Statistik und eLearning").
In addition, a performance-relevant midterm exam will be written as an online exam using the MathCoach elearning system.

[updated 10.05.2021]
Recommended or required reading:
Part I
0. B.Grabowski:"Mathematik III für Ingenieure", e-book mit MathCoach, 2011
1. L. Papula : "Mathematik für Ingenieure", Band 1-3 und Formelsammlungen, Vieweg, 2000
2. Engeln-Müllges, Schäfer, Trippler: "Kompaktkurs Ingenieurmathematik". Fachbuchverlag  Leipzig im Carl Hanser Verlag: München/Wien, 1999.
3. Brauch/Dreyer/Haacke, Mathematik für Ingenieure, Teubner, 2003
Part II
0. B.Grabowski:  "E-Learning: Numerik mit MathCoach", e-book, 2011
1. Preuss/Wenisch, Numerische Mathematik, Fachbuchverlag, 2001
2. Faires/Burden, Numerische methoden, Spektrum Akademischer Verlag, 2000
3. Gramlich/Werner, Numerische Mathematik mit MATLAB, dpunktverlag, 2000
4. Beucher, MATLAB und SIMULINK lernen, Addison-Wesley, 2000
5. Bartsch H.-J., Tachenbuch Mathematischer Formeln, Fachbuchverlag Leipzig, 2003
   (only available within the htw)
   Script I and formula collection 1 for descriptive statistics

[updated 10.05.2021]
[Sat Jul 13 01:32:17 CEST 2024, CKEY=ymmathe3, BKEY=mst2, CID=MST.MA3, LANGUAGE=en, DATE=13.07.2024]