9781332750917 - treatise on differential equations: with a collection of examples, arranged in classes, corresponding to the several divisions of the subject (classic reprint) de ottley, w. c. (3 resultados)
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Paperback. Condición: New. Print on Demand. This book collects and organizes differential equation propositions crucial to the investigation of physical or geometrical science. Demonstrations derived from various sources aim to be both simple and satisfactory. The author favors extending general methods of solution over exhibiti…ng particular articles applicable only to specific cases. Examples are included in the text, with the remainder organized in an appendix according to the subject's natural divisions. Both differentials and differential coefficients are used, with equations expressed via the former before integration. The author retains the old notation if; dx, etc., rather than adopting a system using equations between two variables, which they deem irreconcilable with either system. They acknowledge the task is not simple, and look forward to frank criticism from those qualified to offer it. The ultimate goal of differential equations between two variables is finding the primitive from the differential equation. For every differential equation of a given order between two variables, there is an integral involving an arbitrary constant. Every differential equation of order n likewise has n first integrals, which are differential equations of order n-1, each involving an arbitrary constant. The author investigates whether a differential equation satisfies the criterion of integrability, and provides theorems for finding integrating factors and solving homogeneous equations. They also delve into singular or particular solutions, which satisfy a differential equation but are not contained in the general integral. The book concludes with a chapter on equations of the first order but not the first degree, examining particular forms of equations and discussing methods for solving them. It is hoped that this book will prove useful to students and researchers alike, providing a comprehensive and accessible resource on differential equations. 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.
