Transformada de Laplace: uma analise de seus teoremas e algumas aplicacões

Abstract

The Laplace Transform (LT) is a transformation method that was developed by various mathe- maticians throughout history and was named in honor of Pierre-Simon Laplace, who contribu- ted to the consolidation of the method. The LT transforms a function in the time domain into a function in the frequency domain, resulting in an algebraic equation, which makes its calcu- lation simpler. This method is an alternative to the Ordinary Differential Equation (ODE). Its applications are present in several fields of knowledge. In this monograph, two applications are presented: one in pharmacology, in which we calculate the concentration of a drug in the body system and find the function that describes the drug concentration over time since administra- tion; and the second application in engineering, in which we find the function that shows the displacement of two masses connected to springs at any given moment in time. Based on the results obtained, we conclude that the Laplace Transform is an effective and versatile mathe- matical tool, capable of simplifying the solution of problems modeled by differential equations and providing accurate interpretations in real-world contexts.