Analysis of a Nonlinear Oscillator with CAS through Analytical, Numerical, and Qualitative Approaches: a prototype for teaching

Abstract

It is very common to find in contemporary literature of Differential Equations, the need to incorporate holistically in teaching and learning the three different approaches: analytical, qualitative, and numerical, for continuous dynamical systems. However, nowadays, in some Bachelor of Science that includes only one course in differential equations, it is difficult to introduce the qualitative and numerical approaches due to the excessive time that the analytical approach privileges, and the lack of skills programming of students. On the other hand, robust examples, that can show more realistic features, become very complex and difficult, if not impossible to solve, so they require the students to go further than an analytical solution therefore these kinds of problems must be analysed as the three approaches suggested.