An introduction to complex analysis

Part 1 The complex plane: complex numbers open and closed sets in the complex plane limits and continuity. Part 2 Holomorphic function and power series: complex power series elementary functions. Part 3 Prelude to Cauchy's theorem: paths integration along paths connectedness and simple connectedness properties of paths and contours. Part 4 Cauchy's theorem: Cauchy's theorem, level I and II logarithms, argument and index Cauchy's theorem revisited. Part 5 Consequences of Cauchy's theorem: Cauchy's formulae power series representation zeros of holomorphic functions the maximum-modulus theorem. Part 6 Singularities and multifunctions: Laurent's theorem singularities meromorphic functions multifunctions. Part 7…