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The object of the present volume is to offer to the student a fairly complete account of the elementary portions of the Differential Calculus, unencumbered by such parts of the subject as are not usually read in colleges and schools.

Where a choice of method exists, geometrical proofs and illustrations have been in most cases adopted in preference to purely analytical processes.

It has been the constant endeavour of the author to impress upon the mind of the student the geometrical meaning of differentiation and its aspect as a means of measurement of rates of growth. The purely analytical

d character of the operator


as a symbol and the laws of combination which it satisfies have also been fully considered.

The applications of the Calculus to the treatment of

plane curves have been introduced at an earlier stage than usual, from the interesting and important nature of the problems to be discussed. At the same time, the chapters on Undetermined Forms and Maxima and Minima, which have been thereby postponed, may be read in their ordinary place if thought desirable. The direct and inverse hyperbolic functions have

Э been freely used, and the convenient notation to

Ox' denote partial differentiation, has been adopted.

It is hoped that the frequent sets of easy illustrative examples introduced throughout the text will be found useful before attacking the more difficult problems in the copious selections at the ends of the chapters. Many of these examples have been selected from various university and college examination papers, others from papers set in the India and Home Civil Service and Woolwich examinations, and many are new.

I have to thank the Rev. H. P. Gurney, M.A., formerly Senior Fellow of Clare College, Cambridge, for the kind interest he has taken in the preparation of this work, and for many useful suggestions. I have also been much assisted in the revision of proof sheets and in the verification of examples by J. Wilson, Esq., M.A., formerly Fellow of Christ's College, one of H.M. Inspectors of Schools, and also by H. G. Edwards, Esq., B.A., late Scholar of Queen's College. I hope therefore that the book will not be found to contain many serious




November, 1886.

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