Physical Exemplars for Elementary Calculus Optimization Problems

Abstract

ABSTRACT. CALCULUS is one of the most important branches of Mathematics, whose range of application is wide and varied, which positions it as a foundation for any area that uses any part of its content to any extent. By virtue of the above, the concise study of Calculus requires the support, as much as possible, of additional non-traditional resources to prosper its teaching-learning process. A feasible, relevant and motivating option for science or engineering students to understand various Calculus concepts and results in an effective, precise and entertaining way is to have the possibility of contrasting the results obtained in a purely mathematical way with practical and palpable evidence using simple tangible gadgets. In this paper, six typical optimization problems of real functions of real variables are presented, with their respective solutions and conclusions, and a suitable prototype or “physical sampler” is described for each case. This particular selection is a representative sample of a collection of more than twenty problems of the maxima and minima topic for which it was possible to make rudimentary materials, with the aim of complementing the theoretical aspect of the Differential an Integral Calculus subject. These auxiliary physical objects are the product of a formally registered basic teaching project, which was supported by joint work of students during several semesters.