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Module code: MST103 |
4V+2U (6 hours per week) |
6 |
Semester: 1 |
Mandatory course: yes |
Language of instruction:
German |
Required academic prerequisites (ASPO):
Higher education entrance qualification |
Assessment:
Written exam
[updated 22.07.2012]
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MST103 Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2005
, semester 1, mandatory course
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90 class hours (= 67.5 clock hours) over a 15-week period. The total student study time is 180 hours (equivalent to 6 ECTS credits). There are therefore 112.5 hours available for class preparation and follow-up work and exam preparation.
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Recommended prerequisites (modules):
None.
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Recommended as prerequisite for:
MST203 Mathematics II MST302 Mathematics III MST401 Applied Mathematics MST403 Fundamentals of Mechatronic Systems
[updated 02.08.2012]
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Module coordinator:
Prof. Dr. Barbara Grabowski |
Lecturer: Prof. Dr. Barbara Grabowski
[updated 01.10.2005]
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Learning outcomes:
This course of lectures aims to teach students the basic mathematical skills, particularly in linear algebra, that are needed to understand the subjects covered during phase I of the bachelor programme and the specialist subjects treated in phase II.
[updated 22.07.2012]
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Module content:
1 - Fundamentals 1.1…Logic; set theory; principles of mathematical proof; the binomial theorem 1.2 …The structure of number systems and the calculus of real numbers 1.3 …Determining the roots of polynomials; Horner’s scheme; decomposition into linear factors 2 – Vectors in Rn and analytical geometry 2.1 …The definition of a vector and its representation in the Cartesian coordinate system / Vector calculus 2.2… Scalar product, vector product, mixed product 2.3… Application of vector calculus to elementary problems in engineering mechanics Application of vector calculus to elementary geometrical problems (representation and position of points, straight lines and planes relative to one another) 3 - Vector spaces and affine spaces 3.1… The definition of a vector space 3.2… Linear independence, basis, dimension 3.3… The definition of an affine space 3.4… Subspaces 4 – Matrices and determinants 4.1… Matrices and matrix calculations 4.2….Matrix rank 4.3….Gaussian algorithm 4.4… Determinants 4.5… Laplace expansion 4.6… Properties of determinants, Gaussian elimination 5 – Sets of n x n linear equations with a regular matrix of coefficients 5.1… Cramer’s rule 5.2 …The inverse matrix 6 - Systems of linear equations 6.1… n x n homogeneous system of linear equations (solvability conditions, methods of solving) 6.2….n x m homogeneous system of linear equations (solvability conditions, methods of solving) 6.3… n x m inhomogeneous system of linear equations (solvability conditions, methods of solving) 6.4… n x n inhomogeneous system of linear equations (solvability conditions, methods of solving) 7 - Complex numbers 7.1… Definition 7.2….Representation (normal form, trigonometric form, Eulerian form) 7.3… Addition, subtraction, multiplication, division, extracting the roots of complex numbers, logarithms of complex numbers 7.4… Functions of complex variables 7.5 …Loci 7.6… Applications
[updated 22.07.2012]
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Teaching methods/Media:
Lectures, problem-solving sessions
[updated 22.07.2012]
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Recommended or required reading:
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 Materials http://www.htw-saarland.de/fb/gis/mathematik/
[updated 22.07.2012]
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