| Course Description : | Complex numbers: geometric interpretation, polar form, exponential form: powers and roots; regions in the complex plane; analytic functions; functions of complex variables: exponential and logarithmic functions ; trigonometric and hyperbolic functions; definite integrals; Cauchy theorem; Cauchy integral formula; Series; convergence of sequence and series, Taylor series; Laurrent series; uniform convergence; integration and differentiation of power series, zeros of analytic functions; singularity ; principle part; residues; poles; residue theorem of a function; residues at poles; evaluation of improper integrals; integration through a branch cut. |