Conformal Mapping: Methods and Applications

Conformal mapping is a powerful method of analysis with many successful applications in modern technology. The aim of this book is to enlighten readers on the advantages of conformal mapping by illustrating its wide applicability and describing the new mathematical techniques available. Conformal mapping uses functions of complex variables to transform complicated boundaries into simpler, more readily analyzed configurations. It has usually been assumed to be restricted to planar fields satisfying Laplace's equation, fields in uniform media, and regions which are not awkwardly connected in multiple ways. This book shows how these restrictions can be lifted in many cases of practical significance by analytical and numerical techniques. Modern Applications involve not only new or revised algorithms; equally significant is the use of classical methods in new technologies. It is particularly in the latter category that many problems are found which are amenable to elegant, insightful solutions by conformal mapping without resorting to routine, lengthy numerical procedures.