Complex Variables : A Physical Approach with Applications book cover
2nd Edition

Complex Variables
A Physical Approach with Applications

ISBN 9780367222673
Published May 14, 2019 by Chapman and Hall/CRC
377 Pages 96 B/W Illustrations

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Book Description

The idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers.

This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications.


  • This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis
  • This book has an exceptionally large number of examples and a large number of figures.
  • The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking.
  • Incisive applications appear throughout the book.
  • Partial differential equations are used as a unifying theme.

Table of Contents

Basic Ideas

The Exponential and Applications

Holomorphic and Harmonic Functions

The Cauchy Theory

Applications of the Cauchy Theory

Isolated Singularities

Meromorphic Functions

The Calculus of Residues

The Argument Principle

The Maximum Principle

The Geometric Theory

Applications of Conformal Mapping

Harmonic Functions

The Fourier Theory

Other Transforms

Boundary Value Problems



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Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 130 books and more than 250 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.