The use of graphs in specific situations of the initial conditions of linear differential equations

• Autores: Gabriela Buendía, Francisco Cordero
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 6, 2013, págs. 927-937
• Idioma: inglés
• DOI: 10.1080/0020739x.2013.790501
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• Resumen

  • In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the traditional analytical frames that are widely favoured in school mathematics. As a result, the different forms and functions of graphs support their redefinition in a specific situation of the initial conditions. To that end, graphs are presented as a means to explore the nature of differential equations; thus, considering an epistemology based on the uses of graphs to explain the construction of mathematical knowledge.