Applications of Complex Variables: Asymptotics and Integral Transforms

Applied complex variables are so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the rather more specialized topics that are less commonplace. The materials are presented in a systematic and relatively easy-to-follow fashion, culminating in a one-stop reference for complex variables in engineering and theoretical physics. The applications of conformal mapping in this book are more extensive than what is normally available in AEM textbooks, while the treatments of complex Laplace and Fourier transforms are unique. This scope results in a much larger class of functions that can be transformed; and hence in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotic behavior of integrals enables the analysis of engineering model equations with irregular singular points. Modern developments in applied complex variables relevant to engineering analysis are presented in a chapter. The book, which has more than 300 illustrations, is generous with example problems that would help students in their quest for mastery of the subject matter. A solution manual that fully solves all the exercise problems accompanies the textbook, as is a deck of presentation slides that comprise proposed lecture notes.