Elements of the Differential and Integral Calculus (Classic Reprint)

Ul PREFACE. The present work is intended to contain aboirt as mnch of the Calculus as an undergraduate student either in Arts orS cience can be expected to master during his regular course. He may find more exercises than he has time to work out; in this case it is suggested that he only work enough to show that he understands the principles they are designed to elucidate. The most difficult question which arises in treating the subject is how the first principles should be presented to the mind of the beginner. The author has deemed it best to begin by laying down the logical basis on which the whole superstructure must ultimately rest. It is now well understood that the method of limits forms the only rigorous basis for the infinitesimal calculus and that infinitesimals can be used with logical rigor only when based on this method, that is when considered as quantities approaching zero as their limit. When thus defined, no logical difficulty arises in their use; they flow naturally from the conception of limits, and they are therefore introduced at an early stage in the present work. The fundamental principles on which the use of infinitesimals is based are laid down in the second chapter.
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