Polinómios de aproximação e séries de Taylor: análise teória e prática

Abstract

The main objective of this work is to study approximation polynomials, with an emphasis on the application of Taylor Series, as fundamental tools in the analysis and solution of problems. Additionally, it aims to show to what extent these approximations can be useful in areas such as Engineering, Medicine, Chemistry, and Physics. The work begins with a theoretical review of polynomials and their properties, followed by an introduction to the concepts of function approximation. From there, the theory of Taylor Series is explored, demonstrating how they allow the approximation of real functions around a point using an infinite sum of terms based on the derivatives of the function. The study also addresses the importance of series convergence and the errors associated with approximation, including practical examples that illustrate the application of these concepts in real-world situations. Additionally, graphical representations are provided to illustrate how closely the original functions resemble the approximated functions. Finally, critical and comparative analyses between approximation polynomials and Taylor Series are discussed.