Entre o real e o complexo: uma visão uníficada do conceito de transformada

Abstract

After the four fundamental mathematical operations, the transform techniques lie between the most used in electrical engineering, highlighting the Laplace transform, Fourier transform and Z-transform. Generations of physicists, mathematicians and engineers have been using them as a valued short-cut to solve countless problems. But what is, in essence, a transform? In undergraduate level, they have almost always been taught as isolated disciplines or \merely" tools, usefull in treatment of speci_c problems. It is not rare, moreover, that the student _nishes the course keepping the feeling of lack of conection between the studied subjects. What seems to be the problem? Journals devoted to education have tried to deal with the subject, not being unusual to _nd solutions that focus in changing the undergraduate level curricula: clearly a di_cult process that generates several problems. An alternative would be the approach that consists in develop concepts combined with the human and historical aspect. Given the complexity of those subjects, beyond the natural magnitude of mathematical fundaments necessary to its comprehension, it is proposed a study that seeks to unify the \concept of transform" and its applications, exploring their particular and general characteristics, including in the historical aspects that led those techniques to become what they are today