Excerpt from The Calculus Although care has been exercised to secure a consistent order of topics, some teachers may desire to alter it; for example, an earlier introduction of transcendental functions and of por tions of the chapter on Approximations may be desired, and is entirely feasible. But it is urged that the comparatively early introduction of Integration as a summation process be retained, since this further impresses the usefulness of the subject, and accustoms the student to the ideas of derivative and integral before his attention is diverted by a variety of formal rules. Purely destructive criticism and abandonment of coherent arrangement are just as dangerous as ultraconservatism. This book attempts to preserve the essential features of the Calculus, to give the student a thorough training in mathematical rea soning, to create in him a sure mathematical imagination, and to meet fairly the reasonable demand for enlivening and eu riching the subject through applications at the expense of purely formal work that contains no essential principle. 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.