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Inhaltsangabe
Excerpt from A Treatise on Ordinary and Partial Differential Equations
The treatment of the subject of Differential Equations here presented will, it is hoped, be found complete in all those portions which bear upon their practical applications, and in the discussion of their theory so far as it can be adequately treated without the use of the complex variable. The topics included and the order pursued are sufficiently indicated by the table of contents.
An amount of space somewhat greater than usual has been devoted to the geometrical illustrations which arise when the variables are regarded as the rectangular coordinates of a point. This has been done in the belief that the conceptions peculiar to the subject are more readily grasped when embodied in their geometric representations. In this connection the sub ject of singular solutions of ordinary differential equations and the conception of the characteristic in partial differential equa tions may be particularly mentioned.
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Excerpt from A Treatise on Ordinary and Partial Differential Equations
The treatment of the subject of Differential Equations here presented will, it is hoped, be found complete in all those portions which bear upon their practical applications, and in the discussion of their theory so far as it can be adequately treated without the use of the complex variable. The topics included and the order pursued are sufficiently indicated by the table of contents.
An amount of space somewhat greater than usual has been devoted to the geometrical illustrations which arise when the variables are regarded as the rectangular coordinates of a point. This has been done in the belief that the conceptions peculiar to the subject are more readily grasped when embodied in their geometric representations. In this connection the sub ject of singular solutions of ordinary differential equations and the conception of the characteristic in partial differential equa tions may be particularly mentioned.
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.
Reseña del editor
The expression binomial equations is applied in this work (in a sense introduced by Boole) to those linear equations which are included in the general form ,(S)y -f x% (tf)y =o, and which constitute the class of equations best adapted to solution by development in series. In the sections treating of this method a uniform process has been adopted for the secondary or logarithmic solutions which occur in certain cases. The development of the particular integral when the second member is a power of xis also considered. Chapter VIII is devoted to the general solution of the binomial equation in the notation of the hypergeometric series, and Chapter IX toR iccati s, Bessel sand Legendre sequations. The examples at the ends of the sections have been derived from various sources, and not a few prepared expressly for this work. They are arranged in order of difficulty, and the solutions are given. These have been verified in the proof-sheets, so that it is believed that they will be found free from errors. The ordinary references in the text are toR ice and Johnson sB iff. Calc, and Johnson sI nt. Calc., published by John Wiley andS ons uniformly with the present volume. W. W. J. U. S. NAVAL ACADEMY, May,
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