Complex Analysis

Complex analysis is where calculus suddenly becomes rigid in a useful way: once a function is differentiable in the complex sense, it is automatically infinitely differentiable, locally a power series, and pinned down by its values on any small contour. You will spend the term computing contour integrals, expanding functions in Taylor and Laurent series, classifying singularities, and using residues to crack real integrals that resist ordinary calculus. Building on MATH 102 and the analysis taste from MATH 225, it is the standard toolkit you will reach for in PDEs, signal processing, and any later course where transforms, generating functions, or conformal maps show up.