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 branches of the subject, and for a corresponding variety in the mode of demonstration. As my sole object has been to produce a work of utility, I have not hesitated to avail myself of existing elementary. works; of those to which I am chiefly indebted a list is subjoined. My thanks are due to many friends who have taken an interest in the book, and who have favoured me with valuable suggestions and corrections which have relieved it from various imperfections it would otherwise have contained. It was not originally my intention to enter upon the Integral Calculus, but as it was represented to me that without greatly increasing the size of the volume I might give a sufficient account of that subject to meet the demands of many readers, I have enlarged my plan accordingly. At some future opportunity I hope to unite in one volume the higher parts of the Integral Calculus and Differential Equations. St. John's College, I. TODHUNTER. Cournot, Traité élémentaire de la Théorie des Fonctions et du Calcul Infinitésimal, 2 vols. 8vo. Paris, 1841. De Morgan, Differential and Integral Calculus. Lond. 1842. Duhamel, Cours d'Analyse de l'Ecole Polytechnique, 2nd edit., 2 vols. 8vo. Paris, 1847. Moigno, Leçons de Calcul Différentiel et de Calcul Intégral, 2 vols. 8vo. Paris, 1840-44. Navier, Résumé des Leçons d'Analyse données à l'Ecole Polytechnique, 2 vols. 8vo. Paris, 1840. Schlömlich, Handbuch der Differenzial-und Integralrechnung Greifswald. 1847. |