Advanced Mathematics
- Faculty
Faculty of Engineering and Computer Science
- Version
Version 2 of 18.03.2026.
- Module identifier
11M0541
- Module level
Master
- Language of instruction
German
- ECTS credit points and grading
5.0
- Module frequency
winter and summer term
- Duration
1 semester
- Brief description
Nowadays, simulation methods are an integral part of the development process in mechanical engineering and its applications. The high level of development of simulation software makes it increasingly possible to analyze and optimize even complex systems. Although the software frees the user from routine calculations, an understanding of the underlying mathematical models and calculation methods is all the more important. This module teaches students the fundamentals of the mathematical concepts that form the basis of simulation models in many applications. Only in this way can the student recognize the areas and limits of application of simulation models and competently assess the quality of the simulation results.
- Teaching and learning outcomes
- Higher linear algebra
- Advanced matrix calculus
- Spatial transformations
- Eigenvalue problems
- Elements of vector analysis
- Analysis along curves
- Vector fields
- Higher linear algebra
- Overall workload
The total workload for the module is 150 hours (see also "ECTS credit points and grading").
- Teaching and learning methods
Lecturer based learning Workload hours Type of teaching Media implementation Concretization 45 Lecture Presence - Lecturer independent learning Workload hours Type of teaching Media implementation Concretization 85 Preparation/follow-up for course work - 20 Exam preparation -
- Graded examination
- Written examination
- Exam duration and scope
- written exam: see current study regulations
- Recommended prior knowledge
Sound knowledge in the fields of basic engineering mathematics, in particular linear algebra, differential and integral calculus.
- Knowledge Broadening
Students can name advanced mathematical methods and identify their areas of application in engineering problems.
- Knowledge deepening
Students have in-depth knowledge of the mathematical methods which form the basis of common simulation software. They can explain the characteristic properties of the methods and differentiate between them.
- Knowledge Understanding
Students recognize the benefits of mathematical methods and tools in modeling
of engineering problems. They know the requirements of the methods and can critically assess their advantages and disadvantages.
- Literature
- Papula: Mathematik für Ingenieure und Naturwissenschaftler, Band 3, Springer.
- Meyberg, Vachenauer: Höhere Mathematik 2, Springer.
- Christian Karpfinger: Höhere Mathematik in Rezepten, Springer Spektrum.
- Christian Karpfinger: Arbeitsbuch Höhere Mathematik in Rezepten, Springer Spektrum.
- Arens et al.: Mathematik. Springer Spektrum.
- G. M. Gramlich: Lineare Algebra. Hanser.
- G. M. Gramlich: Anwendungen der Linearen Algebra. Hanser.
- J. Liesen, V. Mehrmann: Lineare Algebra. Springer Spektrum.
- K. Jänich, Mathematik 1+2. Springer.
- Kreyszig: Advanced Engineering Mathematics. John Wiley & Sons, Inc.
- Applicability in study programs
- Automotive Engineering (Master)
- Automotive Engineering M.Sc. (01.09.2025)
- Computer Science
- Computer Science M.Sc. (01.09.2025)
- Mechatronic Systems Engineering
- Mechatronic Systems Engineering M.Sc. (01.09.2025)
- Electrical Engineering (Master)
- Electrical Engineering M.Sc. (01.09.2025)
- Mechanical Engineering (Master)
- Mechanical Engineering M.Sc. (01.09.2025)
- Person responsible for the module
- Stelzle, Wolfgang
- Teachers
- Gervens, Theodor
- Stelzle, Wolfgang
- Henkel, Oliver
- Thiesing, Frank
- Lenz, Sandra
- Büscher, Mareike
- Ambrozkiewicz, Mikolaj
- Meyer, Jana