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.

Dan Romik, University of California, Davis. U.S.A.