INTRODUÇÃO AO CÁLCULO NO PLANO COMPLEXO E FUNÇÕES DE GREEN - MEDEIROS, David M. Farias (2024)
The present work explores the residue theorem and Green's functions, highlighting their application in problems involving improper integrals of real variables and differential equations. The study reveals the depth and versatility of these concepts, demonstrating their importance in solving complex physical and mathematical problems. Additionally, it introduces Green's functions and the Dirac delta function, showing their applicability in relevant differential equations for physics. The use of the Fourier transform to simplify differential equations is also emphasized, exemplified in solving problems such as the harmonic oscillator and the Schrödinger equation. This study provides a valuable introduction to the field of mathematical physics, emphasizing its utility in understanding and solving physical problems. The methodology used in this research consists of a literature review of mathematical literature related to the topic.