Project-based teaching in Calculus courses: Estimation of the surface and perimeter of the Iberian Peninsula

We have been working, for some years, in the application of mathematics to different engineering problems with the main goal of improving our students' motivation and make possible for them to connect and apply what they learn in Calculus classes to other engineering subjects. We describe a case study with students of Electrotechnical Engineering from the Coimbra Institute of Engineering (ISEC) and from Biologist and Geological Engineering degrees students from the University of Salamanca (USAL) in a Calculus course. The study involves the application of mathematical software in the calculus of a real situation: the estimation of the surface and length of an irregular figure: the Iberian Peninsula. Furthermore, we include the results of a pre- and post-test control group study, before and after using that application in the classroom. The results indicate that those experiences were very enriching for the students in different degrees and in both countries. We tested at different centers from two different countries with similar results.