The Fundamental Theorems of the Differential Calculus (Classic Reprint)

Excerpt from The Fundamental Theorems of the Differential CalculusIn this Tract rigidity of proof and novelty of treatment have been aimed at rather than simplicity of presentation, though this has never been lightly sacrificed. The Differential Calculus is concerned with those continuous functions that possess differential coefficients and with these differential coefficients themselves. As a differential coefficient is not necessarily a continuous function, the subject merges naturally into the wider one of the Theory of Functions of one or more Real Variables, and cannot, therefore, be completely mastered without some knowledge of the Theory of Sets of Points. No more knowledge of the language or concepts of this theory will however here be required than a serious mathematical student may now be supposed to have gained before completing his Degree course, and, with this exception, the present account of the fundamental theorems of the Differential Calculus will, it is hoped, be found to be complete in itself. For the rest a brief account is given in Appendix III of the definitions and results from the Theory of Sets of Points actually employed in the Tract.The theory of those functions that correspond to the differential coefficient at a point at which this latter does not exist, does not fall naturally within our scope. Some of the remarkable properties of these interesting functions, with other generalities, are, however, stated without proof in Appendix I.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.