Teorema de Green: conceitos e aplicações

Abstract

The objective of this work is to investigate Green's Theorem and its applications in mathematical and physical problems. Green's Theorem establishes a relationship between line integrals along a closed curve and double integrals over the region enclosed by the curve. Initially, we review and introduce fundamental concepts necessary for understanding this work, such as double and curvilinear integrals, as well as variable change techniques. Then, we present two proofs of Green's Theorem: one for simple regions and another for special regions, always highlighting its usefulness in simplifying calculations in various fields, such as engineering, mathematics, and physics. The research highlights the relevance of Green's Theorem in applications across these fields, particularly in the calculation of fluxes and integrals.