© 1999

Handbook of Complex Variables


Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Steven G. Krantz
    Pages 1-17
  3. Steven G. Krantz
    Pages 19-29
  4. Steven G. Krantz
    Pages 31-39
  5. Steven G. Krantz
    Pages 41-68
  6. Steven G. Krantz
    Pages 69-78
  7. Steven G. Krantz
    Pages 79-88
  8. Steven G. Krantz
    Pages 89-101
  9. Steven G. Krantz
    Pages 103-115
  10. Steven G. Krantz
    Pages 117-122
  11. Steven G. Krantz
    Pages 123-141
  12. Steven G. Krantz
    Pages 143-147
  13. Steven G. Krantz
    Pages 149-154
  14. Steven G. Krantz
    Pages 155-162
  15. Steven G. Krantz
    Pages 163-194
  16. Steven G. Krantz
    Pages 195-217
  17. Steven G. Krantz
    Pages 219-229
  18. Back Matter
    Pages 231-290

About this book


This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica­ tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground­ ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com­ pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.


Argument principle Blaschke product Complex analysis Mathematik Meromorphic function Monodromy Residue theorem Riemann surfaces Schwarz lemma Variable analytic function gamma function ksa

Authors and affiliations

  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA

Bibliographic information


"This modern book can be warmly recommended to mathematicians as well as to users of applied texts in complex analysis; in particular it will be useful to students preparing for an examination in the subject."   —Mathematical Reviews

"Creating a 'handbook' such as this is an interesting concept, and to this reviewer’s knowledge this is the only one of its type in complex analysis. . . . This book may well be timely and useful to the readers it is intended for: working scientists, students, and engineers . . . The topics contained are quite broad . . .  It is noteworthy that a glossary is included that provides the reader with a useful guide to terminology and basic concepts. Other valuable features are: (1) a discussion of the available computer packages that can do some complex analysis such as Maple and Mathematica, (2) a pictorial catalog of conformal well-known maps, and (3) tables of Laplace transforms."   —SIAM Review

"Krantz...has two audiences in mind for this handbook: first, the working scientist, with no background in complex analysis, who seeks a specific result to solve a specific problem; and second, the mathematician or scientist who once studied complex analysis and now seeks a compendium of results as an aid to memory. Though Krantz warns that this handbook contains no theory...and thus cannot serve as a textbook, the undergraduate student of complex analysis will nevertheless find certain sections replete with instructive examples (e.g., applications of contour integrations to definite integrals and sums; conformal mapping). Also, the glossary of terminology and notation should offer a useful aid to study.... Students should also see the chapter devoted to surveying computer packages for the study of complex variables. In an undergraduate library, this book can be counted as a supplement to an otherwise strong collection in functions of a single complex variable."   —Choice

"This handbook of complex variables is a comprehensive references work for scientists, students and engineers who need to know and use the basic concepts in complex analysis of one variable. It is not a book of mathematical theory but a book of mathematical practice. All basic ideas of complex analysis and many typical applications are treated. It is also written in a very vivid style and it contains many helpful figures and graphs." ---Zentralblatt MATH