A First Course in Infinitesimal Calculus (Classic Reprint)

Excerpt from Differential and Integral Calculus

This book has been written for beginners in calculus. Its purpose is to provide an introductory course for those who are entering upon that study either to prepare themselves for elementary work in applied science or to gratify and develop their interest in mathematics. This purpose has determined the choice and the arrangement of the topics and the mode of presentation. Little more has been discussed than what may be regarded as the essentials of a primary course in calculus. An attempt is made to describe and emphasise the fundamental principles of the subject in such a way that, as much as may reasonably be expected, they may be clearly understood, firmly grasped, and intelligently applied by young students. There has also been kept in view the development in them of the ability to read mathematics and to prosecute its study by themselves.

Excepting in a few instances, only real functions of real variables are considered. Simple, practical applications of the more elementary notions are introduced as early as possible; and, subject to the requirements of a logically connected development of the study, the more difficult and abstract discussions appear later. In accordance with this plan, the time-honoured division into differential calculus and integral calculus has not been made, and, to mention one instance in particular, following the example set by Professors Lamb, Gibson, and others, the development of functions in series is taken up in the latter, instead of in the earlier, part of the course. The book, however, can be divided easily into differential and integral sections, and thus can be adapted, in this respect at least, for use in cases in which such a division is deemed necessary.

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