We will use the book Edward B. Saff & Arthur David Snider: Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3/E, Prentice Hall.
Chapter 1 (Complex numbers): Sections 1-7.
Chapter 2 (Analytic functions): Sections 1-4.
Chapter 3 (Elementary functions): Sections 1-3 & 5.
Chapter 4 (Complex integration): Sections 1-6.
Chapter 5 (Series representations of analytic functions): Sections 1-3 & 5-6.
Chapter 6 (Residue theory): Sections 1, 3, 7.
Chapter 7 (Conformal mapping): Sections 2, 3.