A Jupyter Notebook for teaching mathematical modeling with experiments

Abstract

Mathematical modeling and numerical simulation have a considerable presence in the vast universe of engineering disciplines, given their usefulness in explaining, comprehending, and simulating phenomena and processes with which engineers are in contact in their daily creative and problem-solving work. For this reason, engineering study programs have at least one course dedicated to dealing with the mathematical modeling of dynamic systems as an essential complement to subsequent courses such as automatic control, structural dynamics, and mechanical vibrations. Nowadays, many technological tools illustrate the applications of mathematical modeling interactively through experiments that offer an incomparable motivation to the students to corroborate with real-world examples, the utility and veracity of the theory presented to them in the classroom and that in many occasions seems lacking utility and direct relation with the world in which they develop. Based on those mentioned above, this paper presents an example of applying the Laplace transform in modeling physical systems, using a second-order circuit attached to an Arduino Due board in conjunction with the Jupyter Notebook environment. The numerical and experimental results can be obtained through three optional kernels: Python, Octave, or MATLAB®. For educational purposes, the resulting computer application was presented to undergraduate students of Mechatronics Engineering as an illustrative complement to two courses entitled Signals and Systems Analysis, part of the second semester, and Mathematical Modeling, part of the fifth semester.