Topics in Complex Analysis - Romik, Dan (De Gruyter Textbook, 2023)
Begins with an introduction to the theory of functions of a complex variable, covers complex numbers and their properties, analytic functions and the Cauchy-Riemann equations, the logarithm and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem, the residue theorem, and definite integrals. Definitions and proofs are discussed as are applications to physics and engineering.