This course is an introduction to complex analysis in one variable. The topics of the course include complex numbers and topology in the complex plane, analytic and harmonic functions, the Cauchy-Riemann equations, complex integration, Cauchy's integral formula, power series and Laurent series, roots and singularities, residue theory and Cauchy's residue theorem, the argument principle and conformal mappings – in particular Möbius mappings. The course also treats application of the presented theory.
