MULTIDISCIPLINARY PRACTICES FOR FIRST ENGINEERING LEVEL: OBTAINING THE GRAVITATIONAL ACCELERATION EXPERIMENTALLY. DATA COLLECTION AND MATHEMATICAL TREATMENT

One of most important challenges of the degree of Engineering is the achievement of a comprehensive education of the students in order to provide an appropriate response to the requirements of the working world. This overall goal can be reached through a proper coordination between the different subjects that form the curricula of different yet closely related degrees. Especially important is the case of the first year in engineering studies, where some basic subjects such as Physics or Mathematics are taught. Success in the global learning of a graduate degree involves a correct cross-coordination of these basic subjects, because they provide the foundations of the technological knowledge that the students need to acquire. In addition, a well-designed teaching of these basic subjects may contribute to reduce the dropout rate, attracting the interest of students due to a more global problem-solving approach, avoiding undesirable repetition of certain concepts and preparing the students to address engineering problems with a strong scientific baseline. In this paper we present a coordinated practice for the first year of the Geomatic and Topography Degree, regarding three core subjects, namely, Algebra, Calculus and Mechanics. The proposed practice has two representative parts: first, the students have to obtain experimental physical data using basic specific equipment and, second, they have to treat, properly sort and then interpret the data obtained by means of the adequate algorithms using a commercial mathematical program. Using as a pretext the calculation of the gravitational acceleration, the students have to obtain first a series of experimental data using a simple pendulum. Collecting these values has to be consistent with the physical standards and, for this purpose, students have to learn how the experimental system works. Students play with several variables in relation with the movement to obtain the required experimental data for the development of this practice. The second step of the practice involves handling the data with mathematical software from two different and complementary points of view. The first one seeks to study the extreme values of functions of several variables, and the second one deals with the application of the least square method. A noteworthy aspect of these practices is that each group of students works with their own data obtained in a previous experimentation carried out in the course of Mechanics. For Calculus we take advantage of this real problem raised in Physics to study and analyze the theory of relative and absolute extreme values in the context of functions of several variables, minimizing a functional error. The treatment in Algebra entails an application of the method of least squares analyzing different types: linear fit, parabolic fit, logarithmic and square root fit. Moreover, since teamwork sessions are developed in the laboratories of Mathematics, competences such as group work, analysis and problem solving can be easily assessed. Even though the study of these competences is not the purpose of this article, it has been considered and valued positively for their general interest as a way of setting the stage for more detailed analysis to be further developed.