Modelagem matemática: Equações Diferenciais ordinárias de Primeira ordem e aplicações

Abstract

Mathematical modeling is the process that involves obtaining a model. The mathematical model is the set of symbols and relations that seek to translate, in some way, a real-world problem. Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives. These equations seek to express the mathematical modeling that describes the different algebraic forms of flat figures, solids and surfaces. The objective of the research was to present the importance of mathematical modeling of ordinary differential equations applied to problems in the areas of applied mathematics, physics, engineering and other sciences to solve problems of natural phenomena and dynamic processes. The methodology was investigative strategies and applied research, generating knowledge for practical application, aimed at understanding the mathematical modeling of first-order ordinary differential equations (ODE), with technical procedures of bibliographic research. The research resulted in the resolution of some problems modeled by ODEs in some areas of knowledge, such as: problems in chemistry such as radioactive decay and mixing problems; problems in physics such as Newton’s Law of Cooling; problems in biology such as the Malthus Model for studying the growth of populations of organisms, the Gompertz Model that studies the growth of solid tumors; problems in economics involving compound interest. The general solutions to each problem showed the importance of understanding the theory of ODEs to model, analyze and interpret their behavior and make predictions about their temporal evolution, showing the possibility of changes in the system variables and in the proposed initial conditions.