Development of didactial material for Calculus teaching and its application on Engineering

Abstract

The training of undergraduate engineering students in Colombia has been questioned by the national laboral sector due to the steadfast difficulties presented by the recent graduated when solving engineering problems. Those complications appear due to the deficit of skills of the new generation Engineers, related with the fist ABET capability: “an ability to apply knowledge of mathematics, science and Engineering”. Math courses for engineers plays an underlying role in the successful building of skills related with the application of math and science in engineering, as its principal purpose is to develop the logical reasoning capability required to apply the Calculus and other Basic Sciences together in the solving of an engineering problem. Nonetheless, the students themselves recognizes there exists a hurdle between what is learnt in Basic Sciences, more specifically in math courses, and the solving of engineering problems, due to the shortage of applied examples in their formative process. This argument is supported by the CDIO proposal, which objective is to oppose the growing breach among the different branches of engineering and the Basic Sciences through concept transversality, throwing off satisfactory results in the principal Technological and Engineering Universities all over the world. Following CDIO steps, at Mechanical Engineering Faculty of Universidad Santo Tomás, Bogotá, Colombia, it has been proposed a strategy to oppose the trouble guided by the concept transversality. Sixty students of Mechanical Engineering have had voluntary access to three practical sessions specifically designed to strengthen the proficiencies of optimization, results analysis and verification and mathematical modeling; essential skills for engineering problem solving. The partaker students solved a diagnostic test built to quantify the level of development of each one of the three proficiencies mentioned. Only eight of the sixty students (13.3%) submitted optimal solutions, as forty-five of them (75.0%) experienced difficulties related the analysis and verification of the results delivered by their mathematical models. The first practical session consisted in a heat transfer model applied to a conducting wire. The model was analyzed by the students in order to verify that the thermal insulation layer radius of a real wire, measured by themselves using a caliper, is the one which guarantees the optimal heat transfer. The optimal radius was determined via derivation. In the second practical session, the students modeled a fatigue case using a two-variable function. The main trouble of the fatigue exercises is the determination of the maximum stress, which was easy solved using the maximum and minimum criteria learnt in Calculus. The students were surprised with how fast the problem was solved by the hand of math and the software. In the third -and final- practical session the students determined the optimal discharge of a hydraulic bomb in order to reduce the operational cost, based only on math and experimental data. Concepts of curve fitting and critical points were required. When the last practical session was over, the students faced a second diagnostic test designed to quantify the new proficiencies level. Most of the cases translated in overwhelming and satisfying results.