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Mathematics I

Module name (EN):
Name of module in study programme. It should be precise and clear.
Mathematics I
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011
Module code: MST.MA1
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.
6V+1U (7 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: 1
Mandatory course: yes
Language of instruction:

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

MST.MA1 (P231-0053) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012 , semester 1, mandatory course
MST.MA1 (P231-0053) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011 , semester 1, 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).
105 class hours (= 78.75 clock hours) over a 15-week period.
The total student study time is 210 hours (equivalent to 7 ECTS credits).
There are therefore 131.25 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
Recommended as prerequisite for:
MST.CVI Computer Vision
MST.MA2 Mathematics II
MST.NSW Numerical Software

[updated 10.05.2019]
Module coordinator:
Lecturer: N.N.

[updated 01.10.2005]
Learning outcomes:
This course is designed to teach the mathematical fundamentals, specifically linear algebra, required for undergraduate and graduate subjects.

[updated 10.05.2021]
Module content:
1 - Basics
1.1…Logic ,set theory, mathematical proofs ,binomial theorem
1.2 …Structure of number systems and calculating with real numbers
1.3 …Determining zeros of polynomials, Horner scheme, linear factorization
2 – Vectors in Rn and analytic geometry
2.1 …Defining a vector and its representation in the Cartesian coordinate system;
          Arithmetic operations
2.2… Dot product, vector product and triple product
2.3… Applying vector calculus to elementary problems in engineering mechanics; Applying vector calculus to elementary geometric problems (representation and position of points, straight lines and planes in relation to each other)
3 - Vector spaces and affine spaces
3.1… Definition of vector spaces
3.2… Linear independence, basis, dimension
3.3… Definition of affine spaces
3.4… Subspaces
4 – Matrices and determinants
4.1… Matrices, arithmetic operations with matrices
4.2….Matrix rank
4.3….Gauss algorithm
4.4… Determinants
4.5… The Laplace Transform
4.6… Properties of determinants, Gaussian algorithm for determining determinats.
5 – (nxn) linear systems of equations with regular coefficient matrix
5.1… Cramer´s rule
5.2 …Inverse of a matrix
6 - Linear systems of equations
6.1… Homogeneous n x n - systems of equations (solvability conditions, solution methods)
6.2….Homogeneous n x m - systems of equations (solvability conditions, solution methods)
6.3… Inhomogeneous n x n - systems of equations (solvability conditions, solution methods)
6.2….Inhomogeneous n x m - systems of equations (solvability conditions, solution methods)
7 - Complex numbers
7.1… Definition
7.2….Representations (normal form, trigonometric form, Euler’s formula)
7.3… Addition, subtraction, multiplication, division, root extraction, logarithmic calculus
7.4… Complex functions
7.5 …Locus
7.6… Applications

[updated 10.05.2021]
Teaching methods/Media:
All of the 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:
0.) B.Grabowski: "Mathematik I für Ingenieure:  e-book mit MathCoach", 2011
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

[updated 10.05.2021]
[Tue Feb 27 11:20:11 CET 2024, CKEY=ymmathe1, BKEY=yst, CID=MST.MA1, LANGUAGE=en, DATE=27.02.2024]