NUMERICAL DIFFERENTIATION: A VIRTUAL LABORATORY

F. Giménez Palomares, J.A. Monsoriu Serrá, J.F. Giménez Luján

Universitat Politècnica de València (SPAIN)
The approximate calculation of the derivatives of a function is of great interest in many fields of engineering, for example in the case of functions for which it is not known its analytical expression or it is complicated, are tabulated or come from the result of an experiment. The classical methods for solving approximately differential equations and the finite difference method (applicable to both differential equations and partial differential equations) are based on the use of numerical differentiation formulas. The technique used to obtain the formulas is based on the Taylor series development of a function, so the derivatives of a function at a point are calculated from the valuesof the function at that point and other nearby points. Other techniques use polynomial interpolation and splines.

In this work we develop an application designed as a graphical user interface of Matlab, which allows to obtain the numerical values and to visualize the approximate derivatives and, in the case of knowing explicitly the function, the exact derivatives, the errors committed and the dependence of these with respect to the points used. The virtual laboratory has been designed for use in both computer rooms and personal computers, even if the Matlab package is not available, since an executable version has been generated. In any case, the student will be given a detailed guide with a description of the different parameters of the application and accompanied by illustrative examples.