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NEW TOOLS FOR THE VIRTUAL LAB OF NUMERICAL ANALYSIS

M. Caligaris, G. Rodriguez, L. Laugero

Universidad Tecnológica Nacional, Facultad Regional San Nicolás (ARGENTINA)
Nowadays, engineers have to deal with mathematical problems that are either too complicated or do not even have analytical solution. On an increasingly frequent basis, they need to resort to approaching procedures. Using this kind of problem to introduce the topics to be developed in Numerical Analysis courses may be a way to motivate students.
Since year 2008, the research Group GIE (Spanish initials for Engineering & Education Group) has been developing many apps with different programs like Maple, Mathematica and Scilab. These apps are tailor-made windows related to the issues of Numerical Analysis included in different courses at the Facultad Regional San Nicolás, from the Universidad Tecnológica Nacional, Argentina. A collection of these applications, which are created with Mathematica® and embedded in a website, constitutes the Virtual Lab of Numerical Analysis. This lab addresses several topics of numerical analysis: nonlinear equations, linear equations systems, interpolation, curves fitting, numerical integration, numerical methods for ordinary differential equations, numerical approximation of partial differential equations and the Finite Element Method for one dimensioned problems.
These tools can help students to gain deeper understanding of hard-to-grasp topics by letting them interact by changing parameters to analyse results. Moreover, websites specifically designed for each issue, including theory, practice and tools for learning are also available, sharing a common structure: an overview with some introductory problems, the corresponding theory exposed using clear and simple language, interactive applications, solved and proposed exercises, a self-assessment with multiple choice questions, links with related information and bibliography. There is no restricted access to these sites, as they can be retrieved from anywhere with the URL http://www.frsn.utn.edu.ar/gie, just by clicking the “Recursos” (Spanish for Resources) button.
During 2016 some specific tools for solving particular engineering problems where numerical methods are required to achieve a solution, have been incorporated to the lab. This paper discusses some of the new visual tools designed for the 2017 course, for problems dealing with ordinary differential equations. In particular, the movement of a uniform rigid bar pivoted at one end and symmetrically connected by two springs at the other end is analysed. Also, circuits consisting of a voltage source, a resistor, an inductor and a capacitor are studied, starting from the Kirchhoff law.