"Complex analysis", said a physicist once, "is the only subject clearly created by God." A new complex analysis textbook by Rothrock Senior Lecturer Dr. Vladimir Eiderman has been published by Chapman and Hall/CRC Press.The formula on the cover is part of Cauchy's Integral Formula, which under suitable conditions expresses the value of an analytic function at a point in terms of its values on a simple closed curve surrounding that point. The image on the cover references one of numerous important applications, including to the study of fluid flow.From the publisher:"The aim of this comparatively short textbook is a sufficiently full exposition of the fundamentals of the theory of functions of a complex variable to prepare the student for various applications. Several important applications in physics and engineering are considered in the book.This thorough presentation includes all theorems (with a few exceptions) presented with proofs. No previous exposure to complex numbers is assumed. The textbook can be used in one-semester or two-semester courses.In one respect this book is larger than usual, namely in the number of detailed solutions of typical problems. This, together with various problems, makes the book useful both for self- study and for the instructor as well.A specific point of the book is the inclusion of the Laplace transform. These two topics are closely related. Concepts in complex analysis are needed to formulate and prove basic theorems in Laplace transforms, such as the inverse Laplace transform formula. Methods of complex analysis provide solutions for problems involving Laplace transforms.
Complex numbers lend clarity and completion to some areas of classical analysis. These numbers found important applications not only in the mathematical theory, but in the mathematical descriptions of processes in physics and engineering."