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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 01.10.2005
Module code: MST103
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+2U (6 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.
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]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

MST103 Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2005 , semester 1, mandatory course
Workload:
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).
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.
Recommended prerequisites (modules):
None.
Recommended as prerequisite for:
MST203 Mathematics II
MST302 Mathematics III
MST401 Applied Mathematics
MST403 Fundamentals of Mechatronic Systems


[updated 02.08.2012]
Module coordinator:
Prof. Dr. Barbara Grabowski
Lecturer: Prof. Dr. Barbara Grabowski

[updated 01.10.2005]
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]
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]
Teaching methods/Media:
Lectures, problem-solving sessions

[updated 22.07.2012]
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]
[Fri Mar 29 14:44:50 CET 2024, CKEY=mmathe1, BKEY=mst, CID=MST103, LANGUAGE=en, DATE=29.03.2024]