L’esponenziale: modello matematico di una classe di fenomeni

In this paper we start from the analysis of some problems leading to the finite difference equation: (delta f / delta x) = k * f(x) + a , f(0) = f0, k and a being constants, related to the differential equation: (df / dx) = k *f(x) + a. Then we study the properties of f(x) by a numerical method and we get an estimate of the Neper number “e”. And then we go to the physics laboratory to test the model, measuring the potential versus time dependence of a capacitor during an electric transient. The work is organized in units with the aim to improve the students’ ability in modelling and working in laboratory. It takes 14-16 hours for the theoretical part and 8-10 for the exercises and tests.