Harmonic Function Theory

second edition

Sheldon Axler, Paul Bourdon, and Wade Ramey

The second edition of this book about harmonic functions in Euclidean space was published in 2001 by Springer in its Graduate Texts in Mathematics series. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors took unusual care to motivate concepts and simplify proofs.

The electronic version of his book is available without charge by clicking on the link below: Printing has been disabled from within this pdf file, so although you can view the entire book, you will not be able to print it.
The ISBN for the print version of this book is 978-0-387-95218-5.

Harmonic Function Theory and Mathematica

For readers who wish to explore harmonic function theory on a computer, the Mathematica package available at the link below allows users to manipulate many of the expressions that arise in harmonic function theory. This software, which uses many results from this book, can perform symbolic calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral of any polynomial can be computed exactly.

This Mathematica package and its documentation are available electronically without charge by clicking below. This Mathematica package will work on any computer that runs Mathematica. It can be used with or without the book Harmonic Function Theory, just as the book can be used with or without the software.