Functions of Complex Variables (2nd Edition)

Complex analysis is indeed a beautiful and useful branch of mathematics. It is one of the classical subjects with most of the main results extending back into the nineteenth century and earlier. It lies on the intersec- tion of several areas of mathematics, both pure and applied, and has important connections to asymptotic, harmonic and numerical analysis. Techniques based on complex variables are very powerful, with a large number of applications to the solution of physical problems. The discipline covers a wide range of different techniques including solution methods to free-boundary problems such as Hele-Shaw and Stokes flow, conformal mappings, Fourier and other transform methods and Riemann-Hilbert problems. In practice many problems that may be difficult to solve in the real domain can be more easily solved when trans- formed into complex variables due to a number of special properties of the complex domain. The information in this edition is completely revised. This book gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions.