An elementary treatise on differential equations and their applications . Cornell UniversityLibrary The original of this book is inthe Cornell University Library. There are no known copyright restrictions inthe United States on the use of the text. BELLS MATHEMATICAL SERIES ADVANCED SECTION General Editor: WILLIAM P. MILNE, , of Mathematics, Leeds University AN ELEMENTARY TREATISE ON DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS G. BELL AND SONS, LTD. LONDON : PORTUGAL ST., KINGSWAYCAMBRIDGE : DEIGHTON, BELL & YORK : THE MACMIL
An elementary treatise on differential equations and their applications . Cornell UniversityLibrary The original of this book is inthe Cornell University Library. There are no known copyright restrictions inthe United States on the use of the text. BELLS MATHEMATICAL SERIES ADVANCED SECTION General Editor: WILLIAM P. MILNE, , of Mathematics, Leeds University AN ELEMENTARY TREATISE ON DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS G. BELL AND SONS, LTD. LONDON : PORTUGAL ST., KINGSWAYCAMBRIDGE : DEIGHTON, BELL & YORK : THE MACMILLAN COMrPANY BOMBAY : A. H. WHEELER & CO. AN ELEMENTARY TREATISE ON DIFFERENTIALEQUATIONS AND THEIR APPLICATIONS BY H. T. H. PIAGGIO, , PROFESSOR OF MATHEMATICS, UNIVERSITY COLLEGE, NOTTINGHAMFORMERLY SENIOR SCHOLAR OF ST. JOHNS COLLEGE, CAMBRIDGE. LONDON G. BELL AND SONS, LTD. 1920 ^jSoz^lo GLASGOW : PRINTED AT THE UNIVERSITY PRESSBY ROBERT MACLEHOSE AND CO. LTD. PREFACE The Theory of Differential Equations, said Sophus Lie, is themost important branch of modern mathematics. The subject maybe considered to occupy a central position from which differentlines of development extend in many directions. If we travel alongthe purely analytical path, we are soon led to discuss Infinite Series,Existence Theorems and the Theory of Functions. Another leadsus to the Differential Geometry of Curves and Surfaces. Betweenthe two lies the path first discovered by Lie, leading to continuousgroups of transformation and their geometrical in another direction, we are led to the study of mechanicaland electrical vibrations of all kinds and the important phenomenonof resonance. Certain partial differential equations form the start-ing point for the study of the conduction of heat, the transmissionof electric waves, and manycu31924001126766
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