GRAPHICAL RESOLUTION OF ENGINEERING PROBLEMS USING MATHEMATICAL SOFTWARE

This work is focused on the digital competence in the subjects of two Engineering Degrees taught in the University College of Technical Mining and Civil Engineering (University of the Basque Country): the Technical Civil Engineering Degree and the Technical Mining Engineering. This design expects to provide the students with a learning methodology based in the use of digital tools, making possible the development of visualizations that will lead them from the theoretical aspects to the resolution of problems related to engineering. To achieve this aim, the professors have selected some topics of the basic subjects of the engineering degrees and they have suggested some activities in which mathematical concepts have been developed using graphical representations. The selected topics are the following: the graphical representation of functions given in different form (explicit form, implicit form, parametric form and polar form), the analytical and numerical solution of Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) and their graphical representation. These topics have been selected because they are present in the majority of the engineering degrees and because many phenomena of science and engineering are modelled using ODEs and PDEs.

Two softwares have been selected to accomplish this work: Mathematica and MATLAB. Mathematica is one of the most powerful computation systems. Though in the beginning it was used mainly by physicist, engineers and mathematicians, nowadays it is used in different areas such as, biology, social seciences, et cetera. It is a powerful tool for symbolic calculations and able to manipulate the expressions in algebraic form. The second software considered in this work is MATLAB (matrix laboratory), which is a mathematical environment to do interactive calculations. It is a tool used not only in the academic and research field, but also in the industry. It stands out for its conventional syntax, for its potential when doing calculations with vectors and matrices, and for its strength for performing simulations.

The graphical representation of functions by means of digital tools allows for doing simulations changing the data in an easy and fast way. This is a good way to capture students’ attention, reinforcing their learning. From this work it can be concluded that the development of the digital competence means an improvement of the students’ abilities, favouring their self-learning and their decision-making.