Elements of the Differential and Integral Calculus, by a new Method, founded on the True System of Sir Isaac Newton, without the Use of Infinitesimals or Limits Elements of the Infinitesimal Calculus, with Numerous Examples and Applications to Analysis and Geometry On a New Method of Obtaining the Differentials of Functions with Especial Reference to the Newtonian Conception of Rates

Abstract

AN American writer who had exceptional opportunities of contrasting the methods of mathematical teaching adopted in his own country with those which obtained at Cambridge twenty-five years ago, strongly condemns the Transatlantic system, and leads his readers to infer that the attainments of the ordinary graduate in this particular branch of study were only on a par with those of a fairly trained schoolboy here. It may be supposed, then, that not many of the students ventured upon the difficulties of the calculus. Indeed, he writes that “at Yale where the course used to be thought a very difficult and thorough one, the Differential was among the optional studies at the end of the third year.” (Bristed: “Five Years at an English University,” vol. ii., pp. 94, &c., 1852.) Elements of the Differential and Integral Calculus, by a new Method, founded on the True System of Sir Isaac Newton, without the Use of Infinitesimals or Limits. By C. P. Buckingham. (Chicago: S. C. Griggs and Co., 1875. 343 pp.) Elements of the Infinitesimal Calculus, with Numerous Examples and Applications to Analysis and Geometry. By James G. Clark (Ray Series. New York: Wilson, Hinkle, and Co., 1875. 441 pp.) On a New Method of Obtaining the Differentials of Functions with Especial Reference to the Newtonian Conception of Rates or Velocities. By J. Minot Rice W. Woolsey Johnson. (New York: D. van Nosbrand, 1875. 32 pp.)