Abstract:

Many engineering problems are modeled by differential equations in partial derivatives. A partial differential equation (PDE) is an equation that relates a function of several independent variables with its partial derivatives with respect to these variables. The dependent variable depends on the problem being modeled. In most engineering problems, the independent variables are spatial (x, y, z) or space and time (x, y, z, t) coordinates.

Each PDE has an infinite set of solutions. To particularize a solution some boundary and/or initial conditions must be established.
The solution of a problem modeled by a PDE is a particular function that satisfies both the equation in the domain of interest and the conditions imposed. Although in some cases it is possible to find the exact solution to this type of problem, most of them cannot be solved by applying an analytical procedure. However, an approximate solution can be obtained by applying an appropriate numerical method.

The research group Engineering & Education (Grupo Ingeniería & Educación - GIE) from the Universidad Tecnológica Nacional, Argentina, designed some learning objects for solving problems involving PDE. The use of technology in the learning process has generated substantial changes in the way that mathematical objects are appropriated by students. The available tools provide favorable conditions for students to develop skills to argue, conjecture, analyze, among others. Moreover, different abilities may be developed by applying numerical methods to real and specific problems.

This paper describes many applications for working with PDE, including one that models the distribution of the potential of a transmission line, free of losses, as a function of time. Examples of activities that will be assigned to students and the rubrics prepared to assess the developed mathematical skills are also shown.

Keywords:

Partial differential equations, numerical solutions, visual tools.