A First Course in the Differential and Integral Calculus (Classic Reprint)

The treatment of tlie calculus that here follows is based on the courses which I have given in this subject inH arvard College for a number of years and corresponds in its main outlines to the course as given by Professor B. 0. Peirce in the early eighties. The introduction of the integral as the limit of a sum at an early stage is due toP rofessor Byerly, who made this important change more than a dozen years ago. Professor Byerly, moreover, was a pioneer in this country in teaching the calculus by means of problems, his work in this direction dating from the seventies. The chief characteristics of the treatment are the close touch between the calculus and those problems of physics, including geometry, to which it owed its origin; and the simplicity and directness with which the principles of the calculus are set forth. It is important that the formal side of the calculus should be thoroughly taught in a first course, and great stress has been laid on this side. But nowhere do the ideas that underlie the calculus come out more clearly than in its applications to curve tracing and the study of curves and surfaces, in definite integrals with their varied applications to physics and geometry, and in mechanics. Por this reason these subjects have been taken up at an early stage and illustrated by many examples not usually found in American text-books. It is exceedingly difficult to cover in a first course in the calculus all the subjects that claim a place there. Some teachers will wish to see a fuller treatment of the geometry of special Professor Campbell sbook: The Elements of theD ifferential and Integral Calculus, Macmillan, 1904, in its excellent treatment of the integral as the limit of a sum, is a notable exception.
(Typographical errors above are due to OCR software and don't occur in the book.)

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