August 3rd, 2024

Harmonic Function Theory

The second edition of "Harmonic Function Theory" by Axler, Bourdon, and Ramey is aimed at graduate students, offering free electronic access and a complementary Mathematica package for computational applications.

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Harmonic Function Theory

The second edition of "Harmonic Function Theory," authored by Sheldon Axler, Paul Bourdon, and Wade Ramey, was published in 2001 by Springer as part of its Graduate Texts in Mathematics series. This book is designed for readers with a foundational understanding of real and complex analysis at the graduate level. The authors emphasize motivation for concepts and clarity in proofs. An electronic version of the book is available for free, although printing is disabled. The print version has the ISBN 978-0-387-95218-5 and can be ordered from Springer. Additionally, a Mathematica package is provided for those interested in applying harmonic function theory computationally. This software allows users to perform symbolic calculations efficiently, including the exact computation of the Poisson integral for polynomials. The Mathematica package is also available for free and can be utilized independently of the book.

- "Harmonic Function Theory" is aimed at graduate students with a background in analysis.

- The book emphasizes motivation and simplification of concepts and proofs.

- An electronic version is available for free, but printing is disabled.

- A Mathematica package complements the book, enabling computational exploration of harmonic functions.

- The print version can be ordered from Springer with a specific ISBN.

Link Icon 5 comments
By @jfubgnpp - 4 months
If any of you LLM optimists want a project to try to justify those silicon fires I'd suggest starting with an automated service that converts all of the troves of academic material written in proprietary mathematical source code (mathematica) into open alternatives (sage, python).

See also: https://oeis.org/

By @sgdpk - 4 months
I don't know about this book, but I highly recommend "Linear Algebra Done Right" by the same author. It is a very clear presentation of Linear Algebra. Although I would recommend it for someone who already took a first course on it.
By @jey - 4 months
I never really got the hang of Laplacians, which are fundamental to the motivation behind and study of harmonic functions. But here’s a short Khan Academy video I just watched which gives a nice intuitive explanation of the Laplacian operator: https://youtu.be/EW08rD-GFh0
By @jfoutz - 4 months
Any book that gives a full pdf preview, I’m at least considering purchasing. I don’t want to take money out of the author’s pocket, but this,

> 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.

Yeah, I don’t believe that. The goal of the author is admirable. I feel like they got fooled somehow, but maybe they do understand and are just hinting that if you’re going to read it, kick them some cash.

By @mmorse1217 - 4 months
Awesome book; great reference in grad school.