A Treatise on the Integral Calculus Vol. 2: With Applications Examples and Problems (Classic Reprint)

Excerpt from A Treatise on the Integral Calculus Vol. 2: With Applications Examples and Problems<br><br>The functions considered are for the most part combinations of the Elementary Functions of Ordinary Analysis continuous and in general bounded and for such the definition of integration as used by Cauchy and generally adopted in text-books will suffice and form an adequate instrument for the treatment of the particular classes discussed. The more elaborate definition by Riemann which furnishes a more powerful and delicate but at the same time somewhat complex instrument for the discussion of generalised functions introduces certain difficulties of con ception likely to be an unnecessary source of trouble to the ordinary student in his earlier studies. It is therefore postponed until it is to be expected that he has arrived at a thorough mastery of the common processes to be used in the various appli cations of the Calculus and has gained a riper experience for its consideration. And it does not appear that any danger is to be apprehended in such delay seeing that Riemann''s definition is specially devised to meet generalities which will only have to be dealt with in a later stage of specialisation.<br><br>About the Publisher<br><br>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com<br><br>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.