Elements of the Differential and Integral Calculus: With Examples and Applications (Classic Reprint) - Softcover

Taylor, James Morford

9781330362815: Elements of the Differential and Integral Calculus: With Examples and Applications (Classic Reprint)

Softcover

ISBN 10: 1330362810 ISBN 13: 9781330362815

Verlag: Forgotten Books, 2018

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Rese�a del editor

Excerpt from Elements of the Differential and Integral Calculus: With Examples and Applications

The much-abused form 0 /0 cannot arise in the Calculus or elsewhere from any principle of limits a distinctive service of the Theory of Limits is that it enables us to evaluate any determinate expression when it assumes this or any other indeterminate form.

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.

Rese�a del editor

Excerpt from Elements of the Differential and Integral Calculus: With Examples and Applications

In this revision an attempt has been made to present in their unity the three methods commonly used in the Calculus. The concept of Rates is essential to a statement of the problems of the Calculus; the principles of Limits make possible general solutions of these problems, and the laws of Infinitesimals greatly abridge these solutions.

The Method of Rates, generalized and simplified, does not involve "the foreign element of time." For in measuring and comparing the rates of variables, the rate of any variable may be selected as the unit of rates, dy/dx is the x-rate of y, or the ratio of the rate of y to that of x, according as the rate of x is or is not the unit of rates.

The proofs of the principles of differentiation by the Method of Rates, and the numerous applications to geometry, mechanics, etc., found in Chapter II, render familiar the problem of rates before its solution by the Method of Limits or Infinitesimals is introduced.

In Chapter III, by proving that It (Δy/Δx) = dy/dx, the problem of rates is reduced to the problem of finding the limit of the ratio of infinitesimals.

The Theory of Infinitesimals is that part of the Theory of Limits which treats of variables having zero as their common limit. In approaching its limit an infinitesimal passes through a series of finitely small values before it reaches infinitely small values.

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.