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Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman, ""

Preface

The main purpose of this second edition is essentially the same as the first edition with changes noted below.

Accordingly, first we quote from the preface by Murray R. Spiegel in the first edition of this text.

“The theory of functions of a complex variable, also called for brevity complex variables or complex

analysis, is one of the beautiful as well as useful branches of mathematics. Although originating in an

atmosphere of mystery, suspicion and distrust, as evidenced by the terms imaginary and complex

present in the literature, it was finally placed on a sound foundation in the 19th century through the

efforts of Cauchy, Riemann, Weierstrass, Gauss, and other great mathematicians.”

“This book is designed for use as a supplement to all current standards texts or as a textbook for a formal

course in complex variable theory and applications. It should also be of considerable value to those taking

courses in mathematics, physics, aerodynamics, elasticity, and many other fields of science and

engineering.”

“Each chapter begins with a clear statement of pertinent definitions, principles and theorems together

with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary

problems. ... Numerous proofs of theorems and derivations of formulas are included among the solved pro-

blems. The large number of supplementary problems with answers serve as complete review of the material

of each chapter.”

“Topics covered include the algebra and geometry of complex numbers, complex differential and inte-

gral calculus, infinite series including Taylor and Laurent series, the theory of residues with applications to

the evaluation of integrals and series, and conformal mapping with applications drawn from various fields.”

“Considerable more material has been included here than can be covered in most first courses. This has

been done to make the book more flexible, to provide a more useful book of reference and to stimulate

further interest in the topics.”

Some of the changes we have made to the first edition are as follows: (a) We have expanded and cor-

rected many of the sections to make it more accessible for our readers. (b) We have reformatted the

text, such as, the chapter number is now included in the label of all sections, examples, and problems.

(c) Many results are stated formally as Propositions and Theorems.

Seymour Lipschutz, John Schiller, Dennis Spellman

Temple University

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