Abstract
THIS small book contains a fair amount of the calculus put together in a clears and readable form. It merely touches the subject, but appears to contain enough to meet the wants of a South Kensington examinee. “It assumes a knowledge of elementary algebra and trigonometry as far as the properties of plane triangles.” The student is supposed to be unacquainted with analytical geometry, but as he is credited with a knowledge of the exponential and binomial theorems, with “indeterminate coefficients” and a few other matters, it will be seen that elementary includes a fair grasp of the two subjects named. Six chapters are devoted to the elements, successive differentiation, the theorems of Leibnitz, Taylor, and Maclaurin, maxima and minima values of a function of one variable, and the evaluation of indeterminate expressions; the remaining four chapters are devoted to elementary integration, formulæ of reduction, rational fractions, and a few applications of the integral calculus. We presume that the miscellaneous examples are taken from South Kensington papers; those in the text are old friends which figure in Todhunter's works. In the text, the following slips occur: p. 4, 1. 15, for f(x) read f'(.r); p. 18 (6), read exx; p. 37 (3), for x6 720 we get x6; p. 40 (3),? (a - b)2;2la for the maximum; p. 41, 1. 4 up, for 2^+3^, read 3^ + 2^; p. 42 (i), read cos3 6 and 3 \f$d2/i6; p. 62 (4),? last connecting sign (read -); p. 71 (4), for TT read 7T2; p. 80 (24). in first place read (i+^r2)2. In the answers, we differ from the author in (i), (20), (74), and (88). We prefer to work (84) from f (i +/a)V/, where t stands for tan x.
An Introduction to the Differential and Integral Calculus.
By T. Hugh Miller. (London: Percival and Co., 1891.)
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[Book Reviews]. Nature 45, 52 (1891). https://doi.org/10.1038/045052a0
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DOI: https://doi.org/10.1038/045052a0