IN an introductory course on the Differential and Integral Calculus the subject of Infinite Series forms an important topic. The presentation of this subject should have in view first to make the beginner acquainted with the nature and use of infinite series and secondly to introduce him to the theory of these series in such a way that he sees at each step precisely what the question at issue is and never enters on the proof of a theorem till he feels that the theorem actually requires proof. Aids to the attainment of these ends are: (a) a variety of illustrations, taken from the cases that actually arise in practice, of the application of series to computation both in pure and applied mathematics; (b) a full and careful exposition of the meaning and scope of the more difficult theorems; (c) the use of diagrams and graphical illustrations in the proofs.
The pamphlet that follows is designed to give a presentation of the kind here indicated. The references are to Byerly's "Differential Calculus, Integral Calculus," and "Problems in Differential Calculus; and to B. O. Peirce's "Short Table of Integrals;" all published by Ginn & Co., Boston.