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.
Harmonic Function Theory and Mathematica
For readers who wish to explore harmonic function theory on a computer, the authors have developed a Mathematica package to manipulate many of the expressions that arise in harmonic function theory. Our 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.
Our 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.