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DIFFERENTIAL CALCULUS.

Cambridge:

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

DIFFERENTIAL CALCULUS

WITH NUMEROUS EXAMPLES.

BY

I. TODHUNTER, M.A., F.R.S.,

FELLOW AND PRINCIPAL MATHEMATICAL LECTURER OF

ST JOHN'S COLLEGE, CAMBRIDGE.

FOURTH EDITION.

Cambridge and London.
MACMILLAN AND CO.

1864.

[The Right of Translation and Reproduction is reserver.]

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PREFACE.

I HAVE endeavoured in the present work to exhibit a comprehensive view of the Differential Calculus on the method of Limits. In the more elementary portions I have entered into considerable detail in the explanations with the hope that a reader who is without the assistance of a tutor may be enabled to acquire a competent acquaintance with the subject. To the different chapters will be found appended Examples sufficiently numerous to render another book unnecessary.

These examples have been selected almost exclusively from the College and University Examination Papers; the greater part of them will be found to present no very serious difficulty to the student, although a few may require peculiar analytical skill.

My own experience with pupils has been decidedly unfavourable to the system of Differentials; many successful teachers whom I have consulted have expressed a similar opinion, and I have therefore adopted exclusively the method of Differential Coefficients.

I have frequently given more than one investigation of a theorem, because I believe that the student derives advantage from viewing the same proposition under different aspects, and that, in order to succeed in the examinations which he may have to undergo, he should be prepared for a considerable variety in the order of arranging the several

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