Présentation de l'éditeur
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 ofF unctions 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 theD ifferential 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
(Typographical errors above are due to OCR software and don't occur in the book.)
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Présentation de l'éditeur
Originally published in 1910 as number eleven in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book deals with differential calculus and its underlying structures. Appendices on further reading and clarification of certain points are also included. This tract will be of value to anyone with an interest in the history of mathematics or calculus.
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The Fundamental Theorems of the Differential Calculus (Classic Reprint)
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Paperback. Etat : 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. N° de réf. du vendeur 9781330299944_0
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