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This paper discusses the theoretical basis of a didactic proposal. It begins from the consideration that the difficulties in the learning process of mathematics among university students of sciences and engineering areas, not only obey to causes of pedagogical or technical order, but fundamentally, in the way in which the mathematical knowledge is selected, articulated and organized with didactical aims. We considered then, that the determination of "what to teach" and not only "how to teach" positivist classic posture is a didactic problem. This search has allowed us to formulate a reasonable >conjecture: it is possible to reconstruct the didactic discourse of a part of the mathematical analysis taking as a central idea the prediction notion >and its links with the Taylor's serie. In another sense, this hypothesis indicates that it is possible to redesign the curriculum and its didactic discorse around of that, we considered, was indispensable for the genesis of the knowledge. We will consider to the Taylor's serie, its contextual antecedents, motivations, situations, temporary evolutions, presentations on classic texts and possibilities of use, some still unexplored in current texts. The article provided with the theoretical base that sustained a Doctoral research in the field of Physics Didactis in Spain. [ABSTRACT FROM AUTHOR]