An Introduction To The Theory Of Infinite Series Classic Reprint

Excerpt from An Introduction to the Theory of Infinite Series The investigations of Chapter XI. Imply an acquaintance with the convergence of infinite integrals, but when the manu script was being prepared for printing no English book was available from which the necessary theorems could be quoted. 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.

Excerpt from Introduction to Infinite Series N 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; (6) 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. 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.

Based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907, this title includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; and a discussion of trigonometrical series.

This Is A New Release Of The Original 1908 Edition.

Excerpt from An Introduction to the Theory of Infinite Series This book is based on courses of lectures on Elementary Analysis given at Queen's College, Galway, during each of the sessions 1902-1907. But additions have naturally been made in preparing the manuscript for press: in particular the whole of Chapter XI. and the greater part of the Appendices have been added. In selecting the subject-matter, I have attempted to include proofs of all theorems stated in Pringsheim's article, Irrationalzahlen und Konvergenz unendlicher Prozesse, with the exception of theorems relating to continued fractions. In Chapter I. a preliminary account is given of the notions of a limit and of convergence. I have not in this chapter attempted to supply arithmetic proofs of the fundamental theorems concerning the existence of limits, but have allowed their truth to rest on an appeal to the reader's intuition, in the hope that the discussion may thus be made more attractive to beginners. An arithmetic treatment will be found in Appendix I., where Dedekind's definition of irrational numbers is adopted as fundamental; this method leads at once to the monotonic principle of convergence (Art. 149), from which the existence of extreme limits is deduced (Arts. 5, 150);it is then easy to establish the general principle of convergence (Art. 151). 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.