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Excerpt from The Fundamental Theorems of the Differential Calculus
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.
The theory of Maxima and Minima has been barely alluded to, and the complex variable has been rigorously excluded. Apart from other considerations the space at our disposal has here been decisive. For the same reason it has been impossible to give more than a few isolated examples. Appendix II consists of references to some of the existing literature, where such examples may be found.
It is perhaps well to warn the English reader in conclusion that such initial difficulties as he may feel are likely to be due, in part at least, to a lack of familiarity with the modern formulation of the concept of an irrational number.
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Excerpt from The Fundamental Theorems of the Differential Calculus
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.
The theory of Maxima and Minima has been barely alluded to, and the complex variable has been rigorously excluded. Apart from other considerations the space at our disposal has here been decisive. For the same reason it has been impossible to give more than a few isolated examples. Appendix II consists of references to some of the existing literature, where such examples may be found.
It is perhaps well to warn the English reader in conclusion that such initial difficulties as he may feel are likely to be due, in part at least, to a lack of familiarity with the modern formulation of the concept of an irrational number.
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.
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Excerpt from The Fundamental Theorems of the Differential Calculus
In 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 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.
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The Fundamental Theorems of the Differential Calculus (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book delves into the fundamental theorems of differential calculus, exploring the concept of a function and its derivatives. The author provides readers with a rigorous foundation in the theory of functions, examining ideas such as continuity, semi-continuity, and the existence and uniqueness of limits. The book situates differential calculus within its broader mathematical context, establishing connections with other areas and demonstrating its importance in real-world applications. Differential calculus, as the author shows, is a versatile tool used to study rates of change and analyze functions, making it essential in various fields such as physics, economics, and engineering. Beyond its theoretical underpinnings, this book emphasizes the practical applications of differential calculus. Readers will learn to use differential calculus to solve problems in optimization, approximation, and curve sketching. By providing a comprehensive treatment of the subject, this book empowers readers to confidently apply differential calculus in their chosen fields. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781330299944_0
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