The residue theorem is a powerful result in complex analysis that relates contour integrals of holomorphic functions around singularities to the residues at those singularities. It states that the integral of a function over a closed contour can be calculated by summing the residues of the function's singular points enclosed by the contour, multiplied by $2\pi i$. This theorem serves as a cornerstone for evaluating integrals and series in complex analysis and has broad applications in real integrals, physics, and engineering.
congrats on reading the definition of Residue Theorem. now let's actually learn it.