Formulation and development of mathematical models for engineering problems: an active-inductive approach

The paper describes the advances in methodology, materials and status for an engineering undergraduate course designed to fill the gap between the basic freshman year (two years in Brazil, for five-year engineering programs) and the following engineering science courses. A preliminary report on this effort has been presented at FIE-97 under the title "Formulation and Development of Mathematical Models for Engineering Problems. An Experience on the Integration of Theory and the Laboratory". Up to 1997, the course had been offered as an elective in two Brazilian universities. Three different engineering schools have now incorporated the course unto their regular curriculum. The project persists on its investment on the poor integration between the so-called "theoretical courses" and \´laboratory courses\´: by addressing the two issues consecutively. Moreover, it opts, whenever possible, for a methodology that could be described as both inductive and active. Experiments are planned to be easily performed in class with intensive student participation without, necessarily, a prior knowledge of a theoretical approach to the phenomenon under analysis. Emphasis is given to the fundamental sequence of observation of facts or phenomena, election of parameters to quantify them, measurement and data acquisition, and finally, modeling (formulation) and simulation.