Information on individual educational components (ECTS-Course descriptions) per semester

Degree programme: Master Sustainable Energy Systems
Type of degree: FH Master´s Degree Programme
Winter Semester 2022

Course unit title Individual Skills Development
Course unit code 072722010202
Language of instruction German
Type of course unit (compulsory, optional) Compulsory
Semester when the course unit is delivered Winter Semester 2022
Teaching hours per week 2
Year of study 2022
Number of ECTS credits allocated Second Cycle (Master)
Number of ECTS credits allocated 6
Name of lecturer(s) Elias EDER, Andreas SCHREINER

Prerequisites and co-requisites


Course content

This course covers basic methods of technical mathematics, thermodynamics and electrical engineering, which are assumed in further studies.


  • Linear algebra: vector spaces, inner product, linear equation systems, geometry, matrix calculation, regression
  • Multidimensional differential calculus: partial derivatives, total differential, gradient
  • Multidimensional integral calculation: work, area and volume integrals
  • Ordinary differential equations: Types, linear 1st and 2nd orde


  • State, state variables, equation of state
  • Energy balance: 1. main law for closed and open systems
  • Entropy balance: 2nd law for closed and open systems
  • Equations of state: ideal gas, ideal liquid, media tables and diagrams, mixture of ideal gas and water
  • Circular processes with simple tools: Carnot, steam processes, gas processes, heat pumps, refrigerating machines
  • Circular processes with moist air: drying, humidification

Electrical engineering:

  • Electromagnetism: characteristics of electric fields, capacitance, inductance
  • Circuit, direct current, alternating current and three-phase current, circuits
  • Complex pointers, display in pointer diagram, equivalent circuit diagrams
  • Temporal processes, switching processes
  • Mechanisms of the power line
  • Electromechanical energy conversion: basic principle of generators and motors (synchronous, asynchronous, direct current)
  • Transformers, switchgears
  • Fundamentals of semiconductor technology, power electronics (components and processes)
  • Basics of electrochemistry, batteries, accumulators, fuel cells, electrolysis
  • Mains protection, electromagnetic compatibilit

Students with highly qualified previous knowledge in the above-mentioned subjects will complete a research seminar as part of this course. For this purpose, they prepare a seminar paper in which they independently work out a research question defined in the current research environment of the FH Vorarlberg and put it into context. The teaching contents are:

  • Literature research (non-fiction, scientific articles, patents)
  • Identifying topics, finding research gaps and deriving research questions with a clear reference to the Energy Research Centre
  • Presentation, discussion and reflection on possible questions
  • Selection of methods, discussion of methods for dealing with the research question
  • Writing a seminar paper with literature research, research question and methodology
  • Getting to know methods and specialist knowledge that go beyond the core curriculum
  • Reflection on professional scientific work within the framework of research

A continuation of the research project in the context of the course "Research Project Energy Technology 1" as well as "Research Project Energy Technology 2" and a Master's thesis is planned.

Learning outcomes

The course " Individual Skills Promotion " has the objective to balance the different pre-knowledge of the students. The focus is on mathematics, thermodynamics and electrical engineering. Alternatively, students who already have all competences in the mentioned fields as well as scientific interest and the ability to work independently and ask questions can attend a research seminar.

Students will understand the basic mathematical methods used in the courses of the following semesters.  Students have a basic understanding of classical termodynamics and electrical engineering. They can apply the methods to simple examples in power engineering and power economics.

Mathematics: The students

  • understand the basic concepts of linear algebra and multidimensional analysis.
  • know typical engineering applications of the discussed mathematical concepts.
  • know the computational techniques of linear algebra and multidimensional analysis.
  • can use the basic solution methods for applied problems in the energy technology and energy economy.
  • are able to set up common differential equations for applied problems.
  • can evaluate the complexity and the degree of abstraction of technical and economic modelling.
  • are able to dissolve larger calculations into partial steps and have developed a feeling for promising solutions.

Thermodynamics: The students

  • understand the basics of thermodynamics. You can explain the relevant state variables as well as the main laws of thermodynamics.
  • can describe different ideal and real equations of state and their applicability.
  • are able to thermodynamically model cyclic processes with pure substances.
  • can represent these cyclic processes in state diagrams and calculate them using equations of state or tables.
  • can calculate simple processes with moist gases.
  • are able to make proposals for the design, layout and optimisation of processes on the basis of thermodynamic considerations.

Electrical Engineering: The Students

  • understand the basics of electromagnetism. They can explain the relevant parameters and components.
  • are able to calculate stationary circuits with direct current, alternating current and three-phase current.
  • can describe the dynamics of circuits, especially during switching operations.
  • can explain the functional principle of components, e.g. motors, generators and transformers, model them in equivalent circuit diagrams, display them in pointer diagrams and calculate them.
  • know the basic principles of semiconductor technology and electrochemistry, their applications in power engineering and can perform simple calculations.
  • know the basic principles of network protection and electromagnetic compatibility.
  • can select power electronics components and processes for the respective application.

Students attending the research seminar gain an insight into scientific work in energy research, in particular on topics of the Energy Research Center. The students can independently define a research question, discuss the methodology for answering the research question and carry out the necessary literature research. The students

  • have an overview of research questions and current activities in energy research, especially in the Energy Research Centre.
  • are familiar with a selected topic in energy research. They can present the current state of energy research on this topic.
  • can carry out a search of the scientific literature and prepare it scientifically.
  • are able to derive possible research questions from an analysis of the technical literature.
  • are able to justify their research results and deal with technical criticism.
  • can develop the methodology to answer a research question.
  • acquire in-depth specialist knowledge which prepares them for later scientific activities during their studies (e.g. research project, master's thesis) or thereafter (e.g. dissertation)

Planned learning activities and teaching methods

Depending on requirements, a mixture of:

  •     Slef-study exercises
  •     Team coaching
  •     Discussion

Assessment methods and criteria

The examination takes place in one of the four subject areas (mathematics, thermodynamics, electrical engineering, research seminar). Which of the four areas is examined is determined individually for each student within the framework of the admission procedure.

The examination takes the form of a written or oral examination in mathematics, thermodynamics or electrical engineering, or by submitting a seminar paper in the research seminar.


The topics in mathematics, thermodynamics and electrical engineering listed in this course are assumed in all other courses of the study.

Recommended or required reading

At the beginning of the course, different possibilities of knowledge inclination are pointed out. Depending on the subject, video recordings, attendance at a course in another course of study, specialist books and other documents are available. Recommended Literature


  • Papula, Lothar (2018): Mathematik für Ingenieure und Naturwissenschaftler Band 1. Wiesbaden: Springer Fachmedien Wiesbaden. Online im Internet: DOI: 10.1007/978-3-658-21746-4 (Zugriff am: 23.09.2019).
  • Papula, Lothar (2015): Mathematik für Ingenieure und Naturwissenschaftler Band 2. Wiesbaden: Springer Fachmedien Wiesbaden. Online im Internet: DOI: 10.1007/978-3-658-07790-7 (Zugriff am: 23.09.2019).
  • Papula, Lothar (2016): Mathematik für Ingenieure und Naturwissenschaftler Band 3. Wiesbaden: Springer Fachmedien Wiesbaden. Online im Internet: DOI: 10.1007/978-3-658-11924-9 (Zugriff am: 23.09.2019).
  • Papula, Lothar (2019): Mathematik für Ingenieure und Naturwissenschaftler - Anwendungsbeispiele: 222 Aufgabenstellungen mit ausführlichen Lösungen. 8., überarb. Auflage 2019. Wiesbaden: Springer Fachmedien Wiesbaden GmbH.
  • Arens, Tilo u.a. (Hrsg.) (2013): Mathematik. 2. Aufl., 1. korrigierter Nachdr. Heidelberg: Spektrum, Akad. Verl.



  • Baehr, Hans Dieter; Kabelac, Stephan (2016): Thermodynamik: Grundlagen und technische Anwendungen. 16., aktualisierte Auflage. Berlin: Springer Vieweg (= Lehrbuch).
  • Weigand, Bernhard; Köhler, Jürgen; Wolfersdorf, Jens von (2016a): Thermodynamik kompakt. 4., aktualisierte Auflage. Berlin Heidelberg: Springer Vieweg (= Springer-Lehrbuch).
  • Weigand, Bernhard; Köhler, Jürgen; Wolfersdorf, Jens von (2016b): Thermodynamik kompakt - Formeln und Aufgaben. 2. Auflage. Berlin Heidelberg: Springer Vieweg (= Lehrbuch).

Electrical Engineering:

  • Busch, Rudolf (2015): Elektrotechnik und Elektronik für Maschinenbauer und Verfahrenstechniker. Wiesbaden: Springer Vieweg.
  • Meister, Heinz (2007): Elektrotechnische Grundlagen: mit Versuchsanleitungen, Rechenbeispielen und Lernziel-Tests. 14. Aufl. Würzburg: Vogel-Buchverl (= Elektronik).
  • Schwab, Adolf J. (2017): Elektroenergiesysteme: Erzeugung, Übertragung und Verteilung elektrischer Energie. 5. Auflage. Berlin: Springer Berlin.

Mode of delivery (face-to-face, distance learning)

Self study