Complex Analysis

This course is an introduction to the theory of complex variables that is useful in many branches of pure and applied mathematics. Analytic functions of one complex variable, Cauchy-Riemann equations. Contour integrals, Cauchy's theorem and Cauchy's integral formula, maximum modulus theorem, Liouville's theorem, fundamental theorem of algebra, Morera's theorem. Taylor series, Laurent series, singularities of analytic functions. Residue theorem, calculus of residues. Fourier transforms, inversion formula, convolution, Parseval's formula. Applications.