  Back to Main Page

Choose Module Version:

## Mathematics I

 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 Semester: 1 Mandatory course: yes Language of instruction: German Assessment: [still undocumented] Curricular relevance: 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 Workload: 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): None. Recommended as prerequisite for: MST.CVI Computer VisionMST.MA2 Mathematics IIMST.NSW Numerical SoftwareMST.SYS [updated 10.05.2019] Module coordinator: N.N. Lecturer: N.N. [updated 01.10.2005] 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 numbers1.3 …Determining zeros of polynomials, Horner scheme, linear factorization 2 – Vectors in Rn and analytic geometry2.1 …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 determinants4.1… Matrices, arithmetic operations with matrices 4.2….Matrix rank 4.3….Gauss algorithm 4.4… Determinants 4.5… The Laplace Transform4.6… Properties of determinants, Gaussian algorithm for determining determinats. 5 – (nxn) linear systems of equations with regular coefficient matrix  5.1… Cramer´s rule5.2 …Inverse of a matrix6 - Linear systems of equations6.1… 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 numbers7.1… 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 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. [updated 10.05.2021] Recommended or required reading: 0.) B.Grabowski: "Mathematik I für Ingenieure:  e-book mit MathCoach", 20111.) L. Papula : "Mathematik für Ingenieure", Band 1-3 und Formelsammlungen, Vieweg, 20002.) Engeln-Müllges, 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]
```[Sun Sep 19 16:12:28 CEST 2021, CKEY=ymmathe1, BKEY=yst, CID=MST.MA1, LANGUAGE=en, DATE=19.09.2021]
```