Complex Analysis

Topics covered include: Complex numbers, limits, continuity, derivative, Cauchy-Riemann equations, analytic and harmonic functions, elementary functions, definite integrals, contour integrals, Cauchy theorem, Cauchy integral formula, Liouville’s theorem, fundamental theorem of algebra, maximum modulus principle, Taylor’s series, Laurent series, residue theorem with its application to computations of trigonometric and improper integrals.