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

Abstract

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.

Keywords:

• linear differential equations
• initial conditions
• form and function of the graph
• socio-epistemology
• redefinition

Acknowledgements

This research has received financial support from the projects SIP 20121671 Análisis del papel de las gráficas en el discurso matemático escolar and Conacyt 0177368 Las Resignificaciones del Uso del Conocimiento Matemático: la Escuela, el Trabajo y la Ciudad.

Notes

As long as the conditions of the Theorem of Unity are fulfiled.

‘Redefinition’ is a translation of the Spanish word ‘resignificación’, which refers to the process of taking the significance discussion about the use and form of knowledge in a specific situation as the source. This discussion is based on the organization of human groups.