Bibliographic citations
Huaccan, I., (2023). Propuesta didáctica basada en el ETM: análisis cualitativo de sistemas de EDO no lineales para estudiantes de Economía [Pontificia Universidad Católica del Perú]. http://hdl.handle.net/20.500.12404/26011
Huaccan, I., Propuesta didáctica basada en el ETM: análisis cualitativo de sistemas de EDO no lineales para estudiantes de Economía []. PE: Pontificia Universidad Católica del Perú; 2023. http://hdl.handle.net/20.500.12404/26011
@mastersthesis{sunedu/3584240,
title = "Propuesta didáctica basada en el ETM: análisis cualitativo de sistemas de EDO no lineales para estudiantes de Economía",
author = "Huaccan Condori de Tapia, Iris Inés",
publisher = "Pontificia Universidad Católica del Perú",
year = "2023"
}
The present research is motivated by the fact that several models of economics, particularly those associated with nonlinear ODE systems, where it is not possible to obtain explicit solutions or only the stability of the respective system is of interest, such as the Ramsey-Cass-Koopmans model, can be analyzed qualitatively. In this sense, performing such analysis means determining certain characteristics about the behavior of the solutions of the systems of nonlinear Ordinary Differential Equations (ODE) associated with these economic models. Therefore, an effective tool in Economics is the qualitative analysis of nonlinear ODE systems. Its study strengthens the theoretical basis of a nonlinear ODE system and facilitates the interpretation of the mathematical results obtained in relation to the economic models whose analysis is associated with nonlinear ODE systems. These two will allow to focus the bases providing sufficient mathematical tools for the study of notions such as the optimal control process in a course of Macroeconomics in the degree of Economics. The objective of the research is to analyze a didactic proposal addressed to the Economics course of a private University of Lima, oriented to the qualitative analysis of nonlinear ODE systems. To achieve this objective, the proposal is to develop the qualitative analysis through three tasks which are proposed sequentially. In this sense, task T1 is proposed on the mathematical description of the qualitative analysis. Task T2 is proposed through the use of technological tools such as MatLab, Wolfram and Bluffton. Finally, thinking about the link with the subsequent topics and courses in the Economics career, task T3 is proposed on a model of Economics, which has a nonlinear ODE system associated with it, which will be analyzed qualitatively. The research is based on the Mathematical Workspace theory (MWS) and analyzes the mathematical work promoted by the tasks of the didactic proposal, in which the paradigms of analysis that could be privileged will be recognized and the activation of the genesis and vertical planes will be identified, with a qualitative methodology. All of them are relevant aspects in the ETM for the learning and teaching process. Among the main conclusions of this research work, we have that the didactic proposal favors the analysis of certain models of Economics, making use of the qualitative analysis of a nonlinear ODE system and digital technology, both as analysis tools
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