Harmonic Function, written by William Elwood Byerly and first published in 1896, is a comprehensive and detailed exploration of the mathematical concept of harmonic functions. The book covers a wide range of topics related to harmonic functions, including their definition, properties, and applications in various areas of mathematics and physics.The first part of the book provides an introduction to the basic concepts of harmonic functions, such as the Laplace equation and the principle of superposition. Byerly then goes on to explore the properties of harmonic functions, including their behavior at boundaries and the relationship between harmonic functions and conformal mappings.The second part of the book focuses on applications of harmonic functions in areas such as potential theory, fluid dynamics, and electromagnetism. Byerly provides numerous examples and exercises throughout the book to help readers deepen their understanding of the concepts and techniques presented.Overall, Harmonic Function is a classic text in the field of mathematical analysis and an essential resource for anyone interested in the theory and applications of harmonic functions.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.