|Module name (EN): Mathematics I|
|Degree programme: Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011|
|Module code: MST.MA1|
|Hours per semester week / Teaching method: 6V+1U (7 hours per week)|
|ECTS credits: 7|
|Mandatory course: yes|
|Language of instruction:
MST.MA1 Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012, semester 1, mandatory course
MST.MA1 Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011, semester 1, mandatory course
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
This course is designed to teach the mathematical fundamentals, specifically linear algebra, required for undergraduate and graduate subjects.
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;
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
4 – Matrices and determinants
4.1… Matrices, arithmetic operations with matrices
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
7.2….Representations (normal form, trigonometric form, Euler’s formula)
7.3… Addition, subtraction, multiplication, division, root extraction, logarithmic calculus
7.4… Complex functions
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.
|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
[Sun Sep 19 16:12:28 CEST 2021, CKEY=ymmathe1, BKEY=yst, CID=MST.MA1, LANGUAGE=en, DATE=19.09.2021]