(Excerpt from Syllabus of a Course in Plane Analytic Geome...)
Excerpt from Syllabus of a Course in Plane Analytic Geometry Define the locus of an equation; the equation of a curve. If a curve is given by its equation and a point by its coordinates, show how it can be ascertained whether the point does or does not lie on the curve. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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(Excerpt from Harmonic Functions The use of Trigonometric...)
Excerpt from Harmonic Functions The use of Trigonometric Series was first suggested by Daniel Bernouilli in 1753 in his researches on the musical vibrations Of stretched elastic strings, although Bessel's Func tions had been already (1732) employed by him and by Euler in dealing with the-vibrations of a heavy string suspended from one end; and Zonal and Spherical Harmonics were introduced by Legendre and Laplace in 1782 in dealing with the attrac tion Of solids Of revolution. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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( This work has been selected by scholars as being cultur...)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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( Originally published over a century ago, this work rema...)
Originally published over a century ago, this work remains among the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. The subsequent growth of science into a diverse range of specialties has enhanced the value of this classic, whose thorough, basic treatment presents material that is assumed in many other studies but seldom available in such concise form. The development of functions, series, and their differential equations receives detailed explanations, and throughout the text, theory is applied to practical problems, with the solutions fully worked out. In addition, 190 problems, many with hints, are included. 1893 edition. Appendix of 6 tables.
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(Excerpt from Syllabus of a Course Analytical Geometry of ...)
Excerpt from Syllabus of a Course Analytical Geometry of Three Dimensions Show that a single equation between at, y, and z represents a surface. That a pair of such equations represent a line. Show how the form of a surface whose equation is given may be investigated by means of its plane sections. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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( This work has been selected by scholars as being cultur...)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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(This text serves as an introduction to the use of coordin...)
This text serves as an introduction to the use of coordinates in physics and mechanics. Topics covered include Hamiltonian Equations, Routh's Modified Lagrangian Expression, Impulsive Forces, Conservative Forces, and more.
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(First published in 1893, Byerly's classic treatise on Fou...)
First published in 1893, Byerly's classic treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics has been used in classrooms for well over a century. This practical exposition acts as a primer for fields such as wave mechanics, advanced engineering, and mathematical physics. Topics covered include: . development in trigonometric series . convergence on Fourier's series . solution of problems in physics by the aid of Fourier's integrals and Fourier's series . zonal harmonics . spherical harmonics . cylindrical harmonics (Bessel's functions) . and more. Containing 190 exercises and a helpful appendix, this reissue of Fourier's Series will be welcomed by students of higher mathematics everywhere. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) also wrote Elements of Differential Calculus (1879) and Elements of Integral Calculus (1881).
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( This work has been selected by scholars as being cultur...)
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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(An Elementary Treatise on Fourier's Series and Spherical,...)
An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics by William Elwood Byerly. This book is a reproduction of the original book published in 1895 and may have some imperfections such as marks or hand-written notes.
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William Elwood Byerly was an elder child and only son of Elwood and Rebecca Potts (Wayne) Byerly, was born on December 13, 1849 in Philadelphia. About 1850, when his father became a commission merchant in New York City, the family moved to Orange, New Jersey.
Fitted for college by a private tutor, their son entered Harvard University, where he graduated at the head of the class of 1871, which also included Charles J. Bonaparte, Henry C. Lodge, William E. Story, and William Lawrence. Benjamin Peirce, then professor of mathematics at Harvard, deeply influenced young Byerly, who was appointed a fellow and returned for graduate work. In 1873 he was one of the first two candidates to receive the degree of doctor of philosophy at Harvard, his dissertation dealing with the heat of the sun.
After receiving the doctor of philosophy degree at Harvard, during the next three years William Byerly was an assistant professor of mathematics at Cornell University. He then returned to Harvard with the same rank. In 1881 he was promoted to a professorship, and became Perkins Professor of Mathematics in 1906 after the death of James M. Peirce.
Being threatened with blindness in 1913, he severed his academic ties and was made professor emeritus. While he was still an assistant professor, there appeared his Elements of the Differential Calculus (1879), which went through several editions, and Elements of the Integral Calculus, with a Key to the Solution of Differential Equations (1881), a revised and enlarged edition of which appeared in 1889 (facsimile reprint, 1926).
These were the best and most vital American texts of their time dealing with these topics and the first texts to avoid the fallacies of the "little zero" definition of an infinitesimal.
They were based on works of Bertrand and other French writers, whose methods opened Byerly's eyes to new possibilities in teaching. An admirable and timely work was his Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics (1893), which was, with Benjamin O. Peirce's Elements of the Theory of Newtonian Potential Function (1886), the basis of a largely attended Harvard course for many years.
This was followed by Problems in Differential Calculus (1895) and during his emeritus days, by An Introduction to the Use of Generalized Coordinates in Mechanics and Physics (1916) and Introduction to the Calculus of Variations (1917), a French translation of which was published in 1935. His Harmonic Functions, first appearing as a monograph in Mansfield Merriman's Higher Mathematics (1896), was issued in its fourth edition, 1906, as a separate volume.
He was also the author of various course syllabi (1882 - 84), and the editor of Chauvenet's Treatise on Elementary Geometry (1895), which went through several editions. He served as an editor of Annals of Mathematics, 1899-1911, and published articles in the April 1909 and April 1911 numbers. He had also an article in the American Mathematical Monthly for December 1916. Among the eighty leading mathematicians in the United States in 1903 he was ranked by his colleagues as twenty-eighth.
He was not a creative mathematician of great originality, but his outstanding success in exposition entitled him to this rank. He was a fellow of the American Academy of Arts and Sciences (1878-85, 1899 - 1935). Byerly was a born teacher, and he inspired many pupils with a real love of mathematics. Teaching well was the one thing in the world he cared most to do.
He taught at Radcliffe for ten years, and in 1882 was one of the incorporators of the institution; he remained a member of the corporation for forty-two years, serving as a member of its executive board for thirty-one years.
In later years he made his home in Swarthmore, Pennsylvania, where he died in his eighty-seventh year, several days after having suffered a cerebral hemorrhage.
An important part of his life-work was service in promoting the higher education of women. When the Society for the Collegiate Instruction of Women, which later became Radcliffe College, was founded in 1879, Byerly was the first member of the Harvard faculty to agree to give courses for women--perhaps partly because at Cornell he had taught M. Carey Thomas, later president of Bryn Mawr, and Christine Ladd-Franklin, later to become a well-known mathematician. His greatest service here, however, was as chairman of its academic board from 1882 until his retirement from Harvard. In this capacity he was the official spokesman in the not invariably friendly forum of the Harvard faculty, where he was one of its most influential members. His work for Radcliffe was recognized in 1933 when its physics and chemistry laboratory was named William Elwood Byerly Hall.
(Excerpt from Harmonic Functions The use of Trigonometric...)
( Originally published over a century ago, this work rema...)
(First published in 1893, Byerly's classic treatise on Fou...)
(Excerpt from Syllabus of a Course Analytical Geometry of ...)
( This work has been selected by scholars as being cultur...)
( This work has been selected by scholars as being cultur...)
( This work has been selected by scholars as being cultur...)
( This work has been selected by scholars as being cultur...)
(An Elementary Treatise on Fourier's Series and Spherical,...)
(Excerpt from Syllabus of a Course in Plane Analytic Geome...)
(This text serves as an introduction to the use of coordin...)
His religious affiliation was with the Society of Friends, which was a Christian group.
William Byerly was a member of the Society of Friends.
Byerly was wise, gentle, and quietly forceful, and was endowed with great mental and physical ability. He had an innate love of quiet and always devoted himself to things that seemed to him most worth while.
Quotes from others about the person
As President LeBaron R. Briggs of Radcliffe once said of him, "Others teach the subject; Byerly taught the class. "
On retiring from this office President Eliot said "he has been the most indispensable person connected with the growth and development of Radcliffe College".
"He was preëminently a thoughtful man. He did not do or say heedless things. In fact, his friends sometimes complained that he was always right. He was steadfast in his few intimate friendships and in all his ways of life".
He was married on May 28, 1885, to Alice Worcester Parsons, by whom he had two sons--Robert Wayne and Francis Parkman. She died in 1918, and on July 23, 1921, he was married to Mrs. Anne Carter (Wickham) Renshaw of Virginia.
