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DIFFERENTIAL EQUATIONS.

CAMBRIDGE:

PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.

A TREATISE

ON

DIFFERENTIAL EQUATIONS.

BY

GEORGE BOOLE, F.R.S.

PROFESSOR OF MATHEMATICS IN THE QUEEN'S UNIVERSITY, IRELAND,
HONORARY MEMBER OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY.

Cambridge:

MACMILLAN AND CO.

AND 23, HENRIETTA STREET, COVENT GARDEN, LONDON.
1859.

[The right of Translation is reserved.]

182.6.1.

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PREFACE.

I HAVE endeavoured, in the following treatise, to convey as complete an account of the present state of knowledge on the subject of Differential Equations, as was consistent with the idea of a work intended, primarily, for elementary instruction. It was my object, first of all, to meet the wants of those who had no previous acquaintance with the subject, but I also desired not quite to disappoint others who might seek for more advanced information. These distinct, but not inconsistent aims determined the plan of composition. The earlier sections of each chapter contain that kind of matter which has usually been thought suitable for the beginner, while the latter ones are devoted either to an account of recent discovery, or to the discussion of such deeper questions of principle as are likely to present themselves to the reflective student in connexion with the methods and processes of his previous course. An appendix to the table of contents will shew what portions of the work are regarded as sufficient for the less complete, but still not unconnected study of the subject.

The principles which I have kept in view in carrying out the above design, are the following:

1st, In the exposition of methods I have adhered as closely as possible to the historical order of their development.

I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary-being determined, either by steps. of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had

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