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Excerpt from Differential Equations
The subject of Differential Equations has grown so rapidly in recent years that it is difficult to do justice to all branches of the subject in a single volume. In writing this book I have endeavoured to supply some elementary material suitable for the needs of students who are studying the subject for the first time, and also some more advanced work which may be useful to men who are interested more in physical mathematics than in the developments of differential geometry and the theory of functions. The chapters on partial differential equations have consequently been devoted almost entirely to the discussion of linear equations.
The order in which the material has been arranged is slightly different from that which is usually adopted. Instead of beginning with the standard forms of equations which can be solved very easily, I have devoted the second chapter to the method of integrating factors and the third to the method of transformation. A reader who is not already familiar with the subject will find it worth while to postpone the reading of 13-17 and 32-35 until he has mastered the more elementary work.
Chapters VII and VIII contain a few results which I think are new. In Chapter VI the treatment of special solutions bears some resemblance to a treatment which has just recently been sketched by Prof. Hill in an abstract of a memoir which will soon be published in the Proceedings of the London Mathematical Society. My work is independent of Prof. Hill's, for the manuscript was sent to the publishers at the beginning of 1915. Example 3, p. 143, was, however, added last September when marking the proof sheets, but these had been returned to the printers before I received my copy of Prof. Hill's abstract. Prof. Hill has evidently discussed the matter much more thoroughly than I have done, and I hope that some of my readers will consult his memoir.
The subject of Differential Equations has grown so rapidly in recent years that it is difficult to do justice to all branches of the subject in a single volume. In writing this book I have endeavoured to supply some elementary material suitable for the needs of students who are studying the subject for the first time, and also some more advanced work which may be useful to men who are interested more in physical mathematics than in the developments of differential geometry and the theory of functions. The chapters on partial differential equations have consequently been devoted almost entirely to the discussion of linear equations.
The order in which the material has been arranged is slightly different from that which is usually adopted. Instead of beginning with the standard forms of equations which can be solved very easily, I have devoted the second chapter to the method of integrating factors and the third to the method of transformation. A reader who is not already familiar with the subject will find it worth while to postpone the reading of 13-17 and 32-35 until he has mastered the more elementary work.
Chapters VII and VIII contain a few results which I think are new. In Chapter VI the treatment of special solutions bears some resemblance to a treatment which has just recently been sketched by Prof. Hill in an abstract of a memoir which will soon be published in the Proceedings of the London Mathematical Society. My work is independent of Prof. Hill's, for the manuscript was sent to the publishers at the beginning of 1915. Example 3, p. 143, was, however, added last September when marking the proof sheets, but these had been returned to the printers before I received my copy of Prof. Hill's abstract. Prof. Hill has evidently discussed the matter much more thoroughly than I have done, and I hope that some of my readers will consult his memoir.
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- PublisherForgotten Books
- Publication date2018
- ISBN 10 1330868552
- ISBN 13 9781330868553
- BindingPaperback
- Number of pages321
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Differential Equations (Classic Reprint)
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Book Description Paperback. Condition: New. Print on Demand. Excerpt from Differential Equations. About the Publisher, Forgotten Books publishes hundreds of thousands of rare and classic books. 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. This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value. The digital edition of all books may be viewed on our website before purchase. print-on-demand item. Seller Inventory # 9781330868553_0
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