This is a companion volume to Professor Lodge's Differential Calculus for Beginners. In that volume the student was prepared to practice retracing his steps, and thus, without the use of the integral notation, to perform the operation of integration or anti-differentiation in simple cases. Hence the author is in a position to commence this volume by exhibiting an integral as the limit of a sum; and that no time is wasted in getting to business is evidenced by the fact that the centre of gravity of a parabolic area is ...
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This is a companion volume to Professor Lodge's Differential Calculus for Beginners. In that volume the student was prepared to practice retracing his steps, and thus, without the use of the integral notation, to perform the operation of integration or anti-differentiation in simple cases. Hence the author is in a position to commence this volume by exhibiting an integral as the limit of a sum; and that no time is wasted in getting to business is evidenced by the fact that the centre of gravity of a parabolic area is worked out at p. 9. The standard methods of integration are clearly explained and illustrated in the first five chapters. The most novel feature of the book is perhaps the seventh chapter dealing with approximate methods of integration. Here, after the well-known rules of Simpson and Weddle, approximate formulae, recently devised by Mr. R. W. K. Edwards and Professor Lodge himself, are given, for dealing with the case in which the curvilinear boundary of a required area cuts the axis at right angles; a case for which, as is well known, rules of the Simpson type are not well fitted. Interesting approximate formulae for the elliptic integrals are also given. A chapter on Moments of Inertia is very welcome, and the book concludes with a chapter on the Gamma functions and with chapters on the differential equations, other than partial, of most frequent occurrence. The suggestion may be submitted for consideration in a future edition that, while doubtless the theory of Amster's planimeter is too difficult for a first book on the Integral Calculus, yet some of the earlier instruments described in Professor Henrici's British Association report (1894) perform the process of summing up ydx in an obvious manner; and the Integraphs of Professors Boys and Abdank Abakanowicz are also exceedingly interesting concrete embodiments of Integration, viewed as the converse of differentiation. Professor Lodge's book is likely to maintain the position which his book on the Differential Calculus has won. - The Mathematical Gazette.
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New. Trade paperback (US). Glued binding. 246 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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