On Fluctuating Functions is a mathematical treatise written by William Rowan Hamilton and published in 1842. The book is a collection of Hamilton's research on the theory of functions and their properties, specifically those that exhibit fluctuations or oscillations. Hamilton's work in this book builds upon the mathematical concepts of calculus and differential equations, and explores the behavior of functions that have a tendency to oscillate or fluctuate. He discusses the properties of these functions, including their periodicity, amplitude, and frequency, and shows how they can be used to model and analyze various physical phenomena.Throughout the book, Hamilton presents a rigorous and detailed analysis of his theories, using mathematical proofs and examples to illustrate his points. He also includes numerous equations and formulas, which he derives and explains in great detail.On Fluctuating Functions is considered to be a significant contribution to the field of mathematics, and it has been praised for its clarity and precision. The book remains a valuable resource for mathematicians and scientists today, and it continues to be studied and referenced in the field of mathematical analysis.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.