CONSTRUÇÃO DE MODELOS MATEMÁTICOS COM O PYTHON: UMA MOTIVAÇÃO PARA O ESTUDO DE CÁLCULO DIFERENCIAL E LÓGICA MATEMÁTICA

Abstract

This article has as objective approach the construction of mathematical models using Python, providing motivational resources for the study of differential calculus and mathematical logic. We produced a short course called "Python e Aplicações Matemáticas" in 2021, offering an alternative perspective for study of these concepts. In this work, we discuss the topics covered in the short course. Using the techniques of curve fitting and ordinary differential equations for we illustrate properties of real functions and their derivatives, which are fundamental to differential calculus. As an example of curve fitting application, we discussed a model that relates the size of tilapias from the Nile River to their age, and another model that relates credit card fees. We also discuss models with differential equations, including the classical model of exponential population growth proposed by Thomas Robert Malthus and the epidemiological SIR model (Susceptible-Infected-Recovered), developed by Kermack and McKendrick in 1927. We present a step-by-step construction of these models and display their graphics using Python in the Google Colaboratory environment, which allows us to visualize the mathematical logic of the language. In addition to what was mentioned, we offer exercise suggestions for teaching mathematics and provide a link to access the solutions and codes created by the authors.

Keywords: Mathematical Models, Curve Fitting, Differential Equations, Python, Differential Calculus, Mathematical Logic.