ELEMENTS OF THE DIFFERENTIAL AND INTEGRAL CALCULUS, WITH EXAMPLES AND APPLICATIONS. BY JAMES M. TAYLOR, PROFESSOR OF MATHEMATICS, MADISON UNIVERSITY. BOSTON: PUBLISHED BY GINN, HEATH, & CO. Edue + 188. 34, 819 こ HARVARD COLLEGE LIBRARY By exchange from OBERLIN COLLEGE LIBRARY Jan. 30, 1926 Entered according to Act of Congress, in the year 1884, by in the Office of the Librarian of Congress, at Washington. J. S. CUSHING & Co., PRINTERS, 115 HIGH STREET, BOSTON. PREFACE. THE THE object of the following treatise is to present simply and concisely the fundamental problems of the Calculus, their solution, and more common applications. Since variables are its characteristic quantities, the first fundamental problem of the Calculus is, To find the ratio of the rates of change of related variables. To enable the learner most clearly to comprehend this problem, the author has employed the conception of rates, which affords finite differentials and the simplest demonstration of many principles. The problem of Differentiation having been clearly presented, a general method of its solution is obtained by the use of limits. This order of 0 development avoids the use of the indeterminate form and secures all the advantages of the differential notation. Many principles are proved, both by the method of rates and that of limits, and thus each is made to throw light upon the other. In a final chapter, the method of infinitesimals is briefly presented; its underlying principles having been previously established. The chapter on Differentiation is followed by one on Integration; and in each, as throughout the work, there |