Bringing partial differential equations to life for students

Abstract

Teaching partial differential equations (PDEs) carries inherent difficulties that an interactive visualization might help overcome in an active learning process. However, the generation of this kind of teaching material implies serious difficulties, mainly in terms of coding efforts. This work describes how to use an authoring tool, Easy Java Simulations, to build interactive simulations using FreeFem++ (Hecht F 2012 J. Numer. Math. 20 251) as a PDE solver engine. It makes possible to build simulations where students can change parameters, the geometry and the equations themselves getting an immediate feedback. But it is also possible for them to edit the simulations to set deeper changes. The process is ilustrated with some basic examples. These simulations show PDEs in a pedagogic manner and can be tuned by no experts in the field, teachers or students. Finally, we report a classroom experience and a survey from the third year students in the Degree of Mathematics at the University of Murcia.

Embedding online, design-focused data visualization instruction in an upper-division undergraduate atmospheric science course

“…Overall, this work makes a case for incorporating visualization strategies in interdisciplinary geoscience education and suggests promising opportunities for bringing student-created data-driven visualizations into the classroom. Doing so also answers a wider call in the science education literature for more active learning experiences, interactivity, and an increased emphasis on teaching problem-solving techniques that students can apply in multiple disciplines (Cano, Chac on-Vera, & Esquembre, 2015;Edens & Potter, 2003;Ellwein et al, 2014;Ernst & Clark, 2007;Marshman & Singh, 2016;Zhang & Linn, 2011; Zuza, Garmendia, Barragu es, & Guisasola, 2016).…”

Simulation of partial differential equations models in Java

“…Our library supports both simple educational examples, as those shown in a previous publication of the authors (Cano et al, 2015), and more elaborated examples aimed to research tasks or more advanced courses. We present now three of these possible advanced examples.…”

“…This facilitates learning to create new simulations with EJS but also adapting simulations created by others. An introduction to the creation of PDE-based simulations using this alternative, EJS-based approach, can be found in a previous paper of the Cano et al (2015). A large amount of existing EJS simulations are also available in the ComPADRE (2016) Digital Library.…”