Abstract:

In mathematics courses for engineers, student motivation frequently suffers from the lack of a clear connection of the purely mathematical subjects to topics that the students feel are more relevant for their specific field of study. One method to establish such a connection is the additional employment of application-driven exercises. In this paper, we describe the development of such exercises and their implementation with the courses Analysis I and II for engineers held at the Technische Universität Berlin, Germany.

One particular novelty of the problem sheets we developed, compared to commonly available application-based problem collections, is the fact that they are especially designed so that the mathematical content parallels the regular curriculum of the course. Very similar to a student project, each set of exercises examines one basic topic in engineering or natural science with particular emphasis on mathematical problem solving. Each student chooses a project at the beginning of the semester which is then worked on collaboratively in small groups during the whole term.

In total, we developed 13 problem sheets that aim at covering the scope of at least 14 different fields of engineering as well as computer science while conveying the skills and knowledge necessary for successfully completing the mathematics course. As particular examples, we will discuss two of the projects in more detail, namely on the subjects of the tractrix (limits and differentiability) and image processing (partial differential equations). The latter was particularly designed for students of computer science to show them that some inherently discrete problems they will be confronted with, like the processing of digital images, may be efficiently modeled with the continuous methods of mathematical analysis. In this project, the students make extensive use of the numerical computing software MATLAB.

Finally, we will present the results of a student evaluation showing a generally positive reaction to the new curriculum.

Keywords:

mathematics education for engineers, application-based exercises.