Module name (EN): Mathematics I |
Degree programme: Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011 |
Module code: MST.MA1 |
SAP-Submodule-No.: P231-0053 |
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] |
Applicability / Curricular relevance: MST.MA1 (P231-0053) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012, semester 1, mandatory course MST.MA1 (P231-0053) 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 Vision MST.MA2 Mathematics II MST.NSW Numerical Software MST.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 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 [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", 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 [updated 10.05.2021] |
[Mon Aug 15 11:45:56 CEST 2022, CKEY=ymmathe1, BKEY=yst, CID=MST.MA1, LANGUAGE=en, DATE=15.08.2022]