Bringing Mathematical Modeling and Engineering Students Closer Together by Seamlessly Linking Theories, Methods, and Applications

Modern engineering careers increasingly demand handling sophisticated physical models to forecast the behavior of technical systems. This requires students to learn and understand how to use numerical tools and evaluate their suitability based on engineering problems. This goes hand in hand with the mathematical, physical, and engineering foundations like signal processing, technical mechanics, and energy networks. It also includes a large number of programming abilities, rendering the challenge very demanding and interdisciplinary. Even though teaching and learning should encompass the whole modeling and simulation process, most textbooks only address individual parts of this interdisciplinary and, above all, application-oriented challenge, as they usually focus on very specific methods. Consequently, students currently do not sufficiently acquire a comprehensive set of tools to reach a high level of competencies. This paper presents a new approach tailored to overcome the above-mentioned shortcomings. The core idea is to bring theories (maths and physics), modeling (how to grasp the right picture of reality), and simulation (transfer of models into code and simulation) as closely together as possible and interlink them as seamlessly as possible. This is realized by creating a textbook directly related to practical examples and engineering applications hosted on an interactive website. Here, it was necessary to make the online content as interactive and result-driven as possible. This allows students to experience theory and methods primarily as tools for successfully solving engineering tasks. Students are trained in handling existing libraries with standard procedures, with which a large class of problems can be accounted for. This skill is required by many employers today. In this paper, we discuss in detail how and for which content we realized these threads. The impact of this new approach was tested with several cohorts in Department of Engineering and Communication of the Bonn-Rhein-Sieg University of Applied Sciences (DEC). In this paper, we also present a summary of the feedback we gathered through a triangulated observation method as well as questionnaires.