ODEs together PDEs and Vector Fields in the SoftAge

Abstract

At this moment when we can employ software, mathematics education has to be reviewed. In this article, we point out that ODEs should be taught from a geometric and qualitative point of view together with an introduction to PDEs and vector fields.  This would increase the skills of the future mathematics user, not only to obtain explicit solutions from a straight command like DSolve, but also in the situations where this command does not help. The geometric interpretation and the concept of direction fields with images generated by software will give us a good understanding of possible system evolutions.