Complex Analysis

(4 Credits)

Complex analysis, also known as the theory of functions of a complex variable, is the branch of mathematical analysis devoted to complex valued functions of complex variable. It is further used in other branches of mathematics, including algebraic geometry and number theory, and also has diverse applications in science and engineering: fluid dynamics, elasticity, nuclear and electrical engineering, to name just a few examples. The geometrical content of analysis in the complex plane is especially appealing. Topics covered include: complex numbers and complex functions; differentiation and the Cauchy-Riemann equations, Cauchy's theorem, and the Cauchy integral formula; singularities, residues, Taylor and Laurent series; fractional linear transformations and conformal mappings.