J. L. Synge

""A Collection Of Papers In Memory Of William Rowan Hamilton"" is a book edited by David Eugene Smith, which contains a collection of papers written by various mathematicians in honor of William Rowan Hamilton, an Irish mathematician and physicist who made significant contributions to the fields of optics, algebra, and mechanics. The book includes papers on topics such as Hamilton's life and work, his research on quaternions and algebraic theory, and his contributions to the development of mathematical physics. The papers are written in a scholarly style and provide a detailed analysis of Hamilton's work and its impact on the field of mathematics. This book is a valuable resource for students and researchers interested in the history of mathematics and the contributions of William Rowan Hamilton to the field. This is a new release of the original 1945 edition. 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.

Originally published in 1957, this book was written to provide physicists and engineers with a means of solving partial differential equations subject to boundary conditions. The text gives a systematic and unified approach to a wide class of problems, based on the fact that the solution may be viewed as a point in function-space, this point being the intersection of two linear subspaces orthogonal to one another. Using this method the solution is located on a hypercircle in function-space, and the approximation is improved by reducing the radius of the hypercircle. The complexities of calculation are illuminated throughout by simple, intuitive geometrical pictures. This book will be of value to anyone with an interest in solutions to boundary value problems in mathematical physics.

This book was first published in 1954. Its main focus, almost uniquely for its time, is the application of Hamilton's optical method to variational principles in space-time. Professor J. L. Synge here uses this method to generate a completely relativistic theory of de Broglie waves: a theory both simple and easily visualised in relation to space-time. Throughout this volume Professor Synge systematically develops this theory, engaging with readily accessible examples as well as more abstract concepts. His introduction helpfully contextualizes this study within the field of theoretical physics, whilst individual chapters focus upon the physics of rays and waves in space-time, the application of geometrical mechanics to free and changed particles, and the topic of primitive quantization. This book will be of interest to any physicists involved in the study of either de Broglie waves and Hamilton's optical method, or the work of Professor Synge himself.

It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work and how much to the detailed applications to physics, astronomy, engineering or the design of instruments. To all appearances, Sir William Rowan Hamilton (1850–1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician. Great indeed was the labour which he employed with a view to applying his method to the design of optical instruments, but for him the abstract wand aesthetic side of his work was of so much greater public importance than its practical use that the details of application remained unpublished till long after her death and long after other workers had discovered equivalent processes.