Complex Analysis (Series in Pure Mathematics)

This is a textbook for a first course in functions of complex variable, assuming a knowledge of freshman calculus. It is designed for students in engineering, physics, and mathematics. Without sacrificing ease and clarity of proofs, mathematical preciseness and rigor are stressed. Cross references are used to justify almost every step in each proof. Solutions and hints are given to many exercises.

"This is a further introductory text on the theory of analytic functions in one complex variable. It contains an extensive chapter on the residue calculus including interesting applications to the evaluation of improper real integrals. Another emphasis lies on harmonic functions. One finds a well organized chapter on the Dirichlet problem for the unit disk and for a half plane together with Green's functions and their most important properties. There are many interesting exercises some of which with solutions or at least hints for solution."