2nd Edition

Complex Variables A Physical Approach with Applications

By Steven G. Krantz Copyright 2019
    378 Pages 96 B/W Illustrations
    by Chapman & Hall

    378 Pages 96 B/W Illustrations
    by Chapman & Hall

    377 Pages 96 B/W Illustrations
    by Chapman & Hall

    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.

    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




    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.