A three-hour, one semester course on the theory of the complex variable from elementary functions, differentiation and integration of the complex functions and their application to some areas in mathematics and in the physicial sciences.             Prerequisite:    A minimum grade of C – in MATH 248

The main topics for each are as follows:

Complex variables and regions, analytuic functions, Cauchy-Riemann conditions and harmonic functions, Elementary functions in  z ,  as exponential, trigonometric, hyperbolic    and  trigonometric and their corresponding inverses, Mapping by elementary functions, integration, Cauhy-Goursat Theorem, Residues andpoles and conformal mapping, Applications of conformal mapping and Schwarz-Christoffel transformation