First year mathematics teaching for engineering students at a university of applied sciences is often guided by the need to address very different prerequisites in knowledge. Revision of basic calculus takes a front seat, conducting proofs is seldom an explicit teaching objective and applications to engineering problems are a necessity.
However, advanced lectures in electrical engineering, signal processing and control theory call for a deeper understanding of series and transforms. They are part of a second-year maths lecture at Hochschule Esslingen. Yet for students with little mathematical background the topics of Fourier series, Fourier- Laplace- and z-transforms appear to be an arbitrary collection of rules and random integration.
The current literature on integral transforms seems to leave only two choices: they either address university students focussing on a rigorous mathematical treatment or - catering for the applied clientele - provide recipes leaving students more often than not at a loss concerning a bigger picture.
In this contribution, we show how we tried to bridge this gap by introducing the concept of a vector space in a lecture for students of electrical engineering. This allows to present series and transforms as a universal technique extending from basic linear algebra to complex transforms.