# Line integrals: 3. Applications to complex analysis


Navigation: 1. Exact, conservative and closed forms | 2. Locally exact forms and singular homology | 3. Applications to complex analysis As in part 1, $$E,F$$ are Banach spaces and $$U\subseteq E$$ is an open set. Recall that a form $$\omega:U\to L(E,F)$$ is exact if $$\omega=Df$$ for some $$f:U\to F$$, closed if it is differentiable […]
Navigation: 1. Exact, conservative and closed forms | 2. Locally exact forms and singular homology | 3. Applications to complex analysis The line integral is a useful tool for working with vector fields on $$\mathbb{R}^n$$, (co)vector fields on manifolds, and complex differentiable functions. However, it is often unclear how these different versions of the line […]