Essential for AC circuit analysis, signal processing, and using Laplace/Fourier transforms to solve differential equations.
Used to model potential flow and aerodynamics.
Representing functions as infinite sums. Laurent series are particularly useful because they describe functions near their singularities.
A powerful tool for evaluating complex (and difficult real) integrals by looking at "poles" (singularities) where the function blows up. 3. Series and Singularities
Analyzing the stability of systems via the "s-plane" or "z-plane."
If a function is analytic within a simple closed loop, the integral around that loop is zero.