Freya: An educational MATLAB GUI-based tool for generalized Fourier series

The Fourier analysis is a very powerful mathematical tool to decompose functions into their frequency components. Due to this, it has applications in a wide variety of fields inside the realm of science and engineering. As usual, this theory starts with a discussion about the trigonometric Fourier series, the expansion of a function in terms of sines and cosines, and then is generalized in the sense that other functions rather than the trigonometric ones can be used as an orthogonal basis, as the eigenfunctions of some specific Sturm-Liouville problems, such as Bessel functions and Legendre polynomials. In this direction, we present the so- called Freya, an educational graphical user interface (GUI) for the generalized Fourier series developed using the interactive MATLAB (MATrix Laboratory) App Designer environment. We aim to provide a user-friendly tool as a learning aid system for students to gain a comprehensive understanding of the subject as well as for teaching.