Mathematics I
MST.MA1
P231-0053
yst
6
V
1
U
7
1
yes
German
MST.MA1
Mechatronics and Sensor Technology
1
mandatory course
MST.MA1
Mechatronics and Sensor Technology
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.
MST.CVI
Computer Vision
MST.MA2
Mathematics II
MST.NSW
Numerical Software
MST.SYS
N.N.
nn
N.N.
nn
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;
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
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.
0.) B.Grabowski: "Mathematik I für Ingenieure: e-book mit MathCoach", 2011
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
Thu Nov 14 19:52:28 CET 2024, CKEY=ymmathe1, BKEY=yst, CID=[?], LANGUAGE=en, DATE=14.11.2024