differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, a detailed discussion on the construction of Riemann surfaces for elementary functions leading to its abstract concept, step-by-step development of the most general form of Cauchy's theorem, complex version of the real intermediate value theorem, exhaustive treatment of contour integration and an introduction to the theory of univalent functions on the unit disc including a brief history of the Bieberbach's conjecture and its solution.

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