MAT 4280 – Functions of a Complex Variable

Algebra, geometry, and topology of complex numbers; limits of complex functions, complex functions as mappings, continuity; multivalued functions and branches; complex differentiability and analyticity, harmonic functions; differentiation of power series functions; definition and properties of the elementary functions; contour integration and the Cauchy integral theorems; the maximum modulus principle; Taylor and Laurent series; the residue theorem; conformal mapping; the argument principle; applications to problems in mathematics, physics, and engineering at the discretion of the instructor.