The role of computer simulations in learning analytic mechanics towards chaos theory: a course experimentation

We present the results of an experimental project, made at the University of Calabria, which uses computer simulations and scientific computational systems in teaching and learning the fundamentals of analytic mechanics, in particular the classical Lagrangian and Hamiltonian formulation of the matter. Starting with examples of classical dynamical systems we also introduced students to appreciate chaos concepts going step by step to more complex settings. The success obtained with the use of computer-based methodologies has been very clear and the final students' tests confirm it. In this paper, in particular, we compare the results obtained by four groups of students: the first two attended such an experimental course and employed computer support for their individual work at home, while the learning environment of the second two groups (the control ones) was based only on traditional classroom lectures with paper and pencil home activities. If on the one hand a better overall performance of the first two groups was evident, it is very interesting (and not so easy) to investigate how much in quantity and quality, the learning of the experimental groups differs from that of the other groups, and why. For example, we illustrate some relevant differences between them in the comprehension of the studied phenomena, in dealing with and solving the proposed problems, and also in the individual development of further personal ideas.     

Hypergeometric solutions for Coulomb self-energy model of uniformly charged hollow cylinder

The article aims at studying hypergeometric-type mathematical techniques based on the extension of a model previously used to describe the Coulomb self-energy of a uniformly charged a three-dimensional cylinder. The associated crossed term integral is investigated and solved by introducing a computational series built from hypergeometric-type terms for different values of parameters involved. The approach considered may be appealing for a broad audience of researchers working in mathematical physics or related disciplines.