Background
Osgood, William Fogg was born on March 10, 1864 in Boston, Massachusetts, United States. Son of William and Mary Rogers (Gannett) Osgood.
(From the PREFACE. IN an introductory course on the Diffe...)
From the PREFACE. IN an introductory course on the Differential and Integral Calculus the subject of Infinite Series forms an important topic. The presentation of this subject should have in view first to make the beginner acquainted with the nature and use of infinite series and secondly to introduce him to the theory of these series in such a way that he sees at each step precisely what the question at issue is and never enters on the proof of a theorem till he feels that the theorem actually requires proof. Aids to the attainment of these ends are: (a) a variety of illustrations, taken from the cases that actually arise in practice, of the application of series to computation both in pure and applied mathematics; (b) a full and careful exposition of the meaning and scope of the more difficult theorems; (c) the use of diagrams and graphical illustrations in the proofs. The pamphlet that follows is designed to give a presentation of the kind here indicated. The references are to Byerly's Differential Calculus, Integral Calculus, and Problems in Differential Calculus; and to B. O. Peirce's Short Table of Integrals. WM. F. OSGOOD.
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(The following computer-generated description may contain ...)
The following computer-generated description may contain errors and does not represent the quality of the book. The treatment of tlie calculus that here follows is based on the courses which I have given in this subject in Harvard College for a number of years and corresponds in its main outlines to the course as given by Professor B.0. Peirce in the early eighties. The introduction of the integral as the limit of a sum at an early stage is due to Professor Byerly, who made this important change more than a dozen years ago. Professor Byerly, moreover, was a pioneer in this country in teaching the calculus by means of problems, his work in this direction dating from the seventies. The chief characteristics of the treatment are the close touch between the calculus and those problems of physics, including geometry, to which it owed its origin; and the simplicity and directness with which the principles of the calculus are set forth. It is important that the formal side of the calculus should be thoroughly taught in a first course, and great stress has been laid on this side. But nowhere do the ideas that underlie the calculus come out more clearly than in its applications to curve tracing and the study of curves and surfaces, in definite integrals with their varied applications to physics and geometry, and in mechanics. Por this reason these subjects have been taken up at an early stage and illustrated by many examples not usually found in American text-books. It is exceedingly difficult to cover in a first course in the calculus all the subjects that claim a place there. Some teachers will wish to see a fuller treatment of the geometry of special Professor Campbells book: The Elements of the Differential and Integral Calculus, Macmillan, 1904, in its excellent treatment of the integral as the limit of a sum, is a notable exception. This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally-enhance 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. Tags: hence limit curve cos function calculus sin theorem value ans functions equation plane order integral line axis form approaches surface
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(This is a reproduction of a book published before 1923. T...)
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Leopold Classic Library is delighted to publish this classic book as part of our extensive collection. As part of our on-going commitment to delivering value to the reader, we have also provided you with a link to a website, where you may download a digital version of this work for free. Many of the books in our collection have been out of print for decades, and therefore have not been accessible to the general public. Whilst the books in this collection have not been hand curated, an aim of our publishing program is to facilitate rapid access to this vast reservoir of literature. As a result of this book being first published many decades ago, it may have occasional imperfections. These imperfections may include poor picture quality, blurred or missing text. While some of these imperfections may have appeared in the original work, others may have resulted from the scanning process that has been applied. However, our view is that this is a significant literary work, which deserves to be brought back into print after many decades. While some publishers have applied optical character recognition (OCR), this approach has its own drawbacks, which include formatting errors, misspelt words, or the presence of inappropriate characters. Our philosophy has been guided by a desire to provide the reader with an experience that is as close as possible to ownership of the original work. We hope that you will enjoy this wonderful classic book, and that the occasional imperfection that it might contain will not detract from the experience.
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(Leopold Classic Library is delighted to publish this clas...)
Leopold Classic Library is delighted to publish this classic book as part of our extensive collection. As part of our on-going commitment to delivering value to the reader, we have also provided you with a link to a website, where you may download a digital version of this work for free. Many of the books in our collection have been out of print for decades, and therefore have not been accessible to the general public. Whilst the books in this collection have not been hand curated, an aim of our publishing program is to facilitate rapid access to this vast reservoir of literature. As a result of this book being first published many decades ago, it may have occasional imperfections. These imperfections may include poor picture quality, blurred or missing text. While some of these imperfections may have appeared in the original work, others may have resulted from the scanning process that has been applied. However, our view is that this is a significant literary work, which deserves to be brought back into print after many decades. While some publishers have applied optical character recognition (OCR), this approach has its own drawbacks, which include formatting errors, misspelt words, or the presence of inappropriate characters. Our philosophy has been guided by a desire to provide the reader with an experience that is as close as possible to ownership of the original work. We hope that you will enjoy this wonderful classic book, and that the occasional imperfection that it might contain will not detract from the experience.
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(This is a reproduction of a book published before 1923. T...)
This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
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(Osgood's Funktiontheorie originally appeared in three vol...)
Osgood's Funktiontheorie originally appeared in three volumes: Volume I, General Theory (5th edition, 1928, 818 pages); Volume II, Theory of Functions of Several Complex Variables (2nd edition, 1929, 307 pages), and Volume II$_2$, Abelian Integrals and Periodic Functions (1932, 378 pages). This edition is a reprint, in one volume, of the second and third of the three volumes, paged consecutively, and with a common index. The text is in German.
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(Excerpt from Lehrbuch der Funktionentheorie Der erste Ba...)
Excerpt from Lehrbuch der Funktionentheorie Der erste Band dieses Werkes will eine systematische Entwicklung der Funktionentheorie auf Grundlage der Infinitesimalrechnung und in engster Fühlung mit der Geometrie und der mathematischen Physik geben. Die eigentlichen Entwicklungen beginnen erst mit dem zweiten Abschnitte, Kap. 6, S. 179, und behandeln in Kap. 6 und 7 vornehmlich Funktionen, welche in einem gegebenen Bereiche der Zahlenebene eindeutig und mit einer Ableitung versehen sind. Dabei werden aueh die elementaren Funktionen für komplexe Werte des Argumente, sowie die linearen Transformationen einer komplexen Veränderlichen besprochen. Da ß die konforme Abbildung gleich von vornherein in den Vordergrund gerückt wird, braucht wohl kaum erwahnt zu werden. Hierauf wird der Cauchysche Integralsatz eingeführt, woran sich dann jener Zyklus von Lehrsatzen anknüpft, welche das natürliche Fundament für die Funktionentheorie bilden. Der hier behandelte Stoff umfaßt u. a. die Weierstraßschen Reihensätze, während die rationalen Funktionen auf ihre funktionentheoretischen Eigenschaften hin untersucht werden. Kapitel 8 ist der Theorie der mehrdeutigen Funktionen gewidmet und bringt die Riemannschen Flächen in geometrischer Behandlungsweise, also unter ausgiebigem Gebrauche der konformen Abbildung. Mit dem 9. Kapitel über analytische Fortsetzung wird dann ein bestimmter Abschluß für die Grundlagen der Funktionentheorie erreicht. Hierauf folgen Anwendungen der Theorie auf periodische Funktionen, sowie eine Besprechung der Reihen- und Produktentwicklungen, nebst einem Kapitel über die elementaren Funktionen vom Standpunkte der Funktionentheorie. Der Band schließt mit einer independenten Behandlung des logarithmischen Potentials, wobei der Gesichtspunkt maßgebend ist, daß die ganze Funktionentheorie auch, auf dieser Grundlage, also ohne jeglichen Bezug auf das Vorhergehende, entwickelt werden kann. Die Theorie der analytischen Funktionen mehrerer veränderlichem sowie diejenige der bestimmten lntegrale konnten in diesen Band nicht mehr aufgenommen werden. 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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(High Quality FACSIMILE REPRODUCTION: Osgood, William F. (...)
High Quality FACSIMILE REPRODUCTION: Osgood, William F. (William Fogg) :Introduction To Infinite Series :Originally published by Cambridge, Harvard University in 1897. Book will be printed in black and white, with grayscale images. Book will be 6 inches wide by 9 inches tall and soft cover bound. Any foldouts will be scaled to page size. If the book is larger than 1000 pages, it will be printed and bound in two parts. Due to the age of the original titles, we cannot be held responsible for missing pages, faded, or cut off text.
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Osgood, William Fogg was born on March 10, 1864 in Boston, Massachusetts, United States. Son of William and Mary Rogers (Gannett) Osgood.
In 1886, he graduated from Harvard, where, after studying at the universities of Göttingen (1887–1889) and Erlangen (Doctor of Philosophy, 1890), he was instructor (1890–1893), assistant professor (1893–1903), and thenceforth professor of mathematics.
He became professor emeritus in 1933. Osgood was chairman of the department of mathematics in Harvard from 1918 to 1922. From 1899 to 1902, he served as editor of the Annals of Mathematics and in 1904–1905 was president of the American Mathematical Society, whose Transactions he edited in 1909–1910.
(Osgood's Funktiontheorie originally appeared in three vol...)
(Excerpt from Lehrbuch der Funktionentheorie Der erste Ba...)
( This work has been selected by scholars as being cultur...)
(The following computer-generated description may contain ...)
(Leopold Classic Library is delighted to publish this clas...)
(Leopold Classic Library is delighted to publish this clas...)
(This is a reproduction of a book published before 1923. T...)
(This is a reproduction of a book published before 1923. T...)
(High Quality FACSIMILE REPRODUCTION: Osgood, William F. (...)
(From the PREFACE. IN an introductory course on the Diffe...)
(New)
Member International Commision on the Teaching of Mathematics. Member National Academy of Sciences, American Philosophical Society, American Mathematics Society (president, 1904-1905), Deutsche Mathematiker-Vereinigung, Leopoldinisch-Carolinisch Deutsche Akademie der Naturforscher, Circolo Matematico de Palermo. Member Mathematics Society of Charkow, Göttinger Gesellschaft der Wissenschaften.
Member Calcutta Mathematics Society.
Member Phi Beta Kappa.
Married Therese Ruprecht, July 17, 1890. Married second, Mistress. Children: William Ruprecht, Frieda Bertha (Mistress Walter Silz.