This book contains the essentials of the Differential Calculus well arranged for elemental study.
It gives a series of twenty-one easy lessons, showing first the purpose of this interesting branch of mathematics and then its relation to the Integral Calculus.
The main object of the writer is to show the student the real uses of these branches of study, while he is attempting to master elemental principles and methods peculiarly their own, and hold his attention to these things, neglecting as useless, if not hurtful, much of the details which are found in ordinary textbooks.
The author then states and proves the rules for work and applies them to all the topics ordinarily presented in the elementary calculus illustrating each with appropriate exercises, the solutions of which are fully given.
The book is evidently not intended as a textbook, for school or college use, in the sense of furnishing sufficient exercise in the application of the elements of the calculus; but it will be found very useful in review of principles, helpful in the meaning of operations, and instructive in the theories of limits and infinitesimals which so often trouble writers and teachers to explain. We think the author rightly combines the two opposing methods of limits and infinitesimals thereby practically escaping the bald fiction of the one and bridging the dark chasm of the other.