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Excerpt from Elements of the Differential and Integral Calculus: With Examples and Applications The object of the following treatise is to present simply and concisely the fundamental problems of the Calculus, their solution, and more common applications. Since variables are its characteristic quantities, the first fundamental problem of the Calculus is, To find the ratio of the rates of change of related variables. To enable the learner most clearly to comprehend this problem, the author has employed the conception of rates, which affords finite differentials and the simplest demonstration of many principles. The problem of Differentiation having been clearly presented, a general method of its solution is obtained by the use of limits. This order of development avoids the use of the indeterminate form 0/0, and secures all the advantages of the differential notation. Many principles are proved, both by the method of rates and that of limits, and thus each is made to throw light upon the other. In a final chapter, the method of infinitesimals is briefly presented; its underlying principles having been previously established. 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.