MAT 205E - Theory of Complex Functions

Course Objectives

I. To teach the fundamental concept of complex analysis, i.e., complex plane, analytic function and Riemann surface to engineering students
II. To teach the residue theory and integration in complex plane, conformal mapping and power series expansion.
III. To apply the complex analysis methods to various electromagnetic and signal processing problems

Course Description

Definition of Complex plane, Riemann surface, multi-valued functions such as square-root and logarithmic function. Derivative in complex domain, analytic function and Laplace equation.
Introduction to conformal mapping and its application to boundary value problems. Residue theorem and its application to evaluate definite integrals. Infinite series, power series, Taylor and Laurent expansion of functions.