Teorema de Clairaut-Schwarz-Young: uma abordagem a partir do estudo de equações diferenciais exatas

Abstract

The work that follows it is a bibliographical nature research whose goal is to speak and demonstrate the theorem clairaut-schawarz-young in the área of the differencial calculus coupled to the initial study of exact differencial equations solutions. In this research we work with some of the especific area: Alexis Claude Clairaut, Karl Hermam Amandus Schwarz and Willian Henry Young who developed the theorem, as well as Works by such authors as Guidorizzi (2015) and Gonçalves (2007) that discuss supercially the topic, this constituting na área of analysis. You can ́t talk in demonstration without talking about the importance of demonstrating, approached through talk about authors like Polya (1987) and Balacheff (2008) who discussing the subject with propety. We chose a sequence considered logic, who Works with aconstruction of the theorem from the use of exact differential equations of first order and their solutions, as well as a deeping through the derivation process until the class C2 functions they have a relationship of equality in section worked whichis stated and guaranted by theorem.