Didactic Engineering in the study of the Theorem of Existence and Uniqueness of Ordinary Differential Equations

Authors

DOI:

https://doi.org/10.5902/2179460X88519

Keywords:

Theorem of Ordinary Differential Equations, Didactic Engineering, Prior analysis, A priori analysis

Abstract

The Theorem of Existence and Uniqueness of Ordinary Differential Equations (ODEs) can be considered one of the fundamental pillars of the theory of differential equations, as it establishes conditions under which an ODE has a unique and determined solution in a specific interval. The importance of this theorem in various fields of mathematics and applied sciences arises from the fact that it ensures that the solutions of certain differential equations are well-defined and unique. This theorem is essential to guarantee the consistency and reliability of the mathematical models used to understand and predict the behavior of these complex systems. This article describes two stages of investigation of this theorem foreseen by Didactic Engineering (DE): the phases of prior analysis and a priori analysis. In order to develop structured activities with the support of technology, with the aim of avoiding certain elements that act as obstacles to a broad understanding of the theorem.

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Author Biographies

Ana Carla Pimentel Paiva, Instituto Federal de Educação, Ciência e Tecnologia do Ceará

Degree in Mathematics at the Federal University of Ceará.

Francisco Régis Vieira Alves, Instituto Federal de Educação, Ciência e Tecnologia do Ceará

PhD with emphasis on teaching Mathematics from the Federal University of Ceará.

Helena Campos, University of Trás-os-Montes and Alto Douro

PhD in Mathematics with a Specialisation in Topology and Geometry from UNED.

Diego Silva, Universidade Estadual do Ceará

PhD in Pure Mathematics from the Federal University of Ceará.

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Published

2024-12-19

How to Cite

Paiva, A. C. P., Alves, F. R. V., Campos, H., & Silva, D. (2024). Didactic Engineering in the study of the Theorem of Existence and Uniqueness of Ordinary Differential Equations. Ciência E Natura, 46. https://doi.org/10.5902/2179460X88519

Issue

Vol. 46 (2024): Publicação contínua

Section

Teaching

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