

Module code: MST.MA1 

6V+1U (7 hours per week) 
7 
Semester: 1 
Mandatory course: yes 
Language of instruction:
German 
Assessment:
[still undocumented]

MST.MA1 (P2310053) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012
, semester 1, mandatory course
MST.MA1 (P2310053) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011
, semester 1, mandatory course

105 class hours (= 78.75 clock hours) over a 15week 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 followup work and exam preparation.

Recommended prerequisites (modules):
None.

Recommended as prerequisite for:
MST.CVI Computer Vision MST.MA2 Mathematics II MST.NSW Numerical Software MST.SYS
[updated 01.10.2012]

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

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 elearning system MathCoach (AMSEL lab: PC lab: "Angewandte Mathematik, Statistik und eLearning"). In addition, a performancerelevant 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: ebook mit MathCoach", 2011 1.) L. Papula : "Mathematik für Ingenieure", Band 13 und Formelsammlungen, Vieweg, 2000 2.) EngelnMüllges, 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]
