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already appears application arbitrary constants axis becomes Calculus of Variations chapter complete condition considered consists constant contains curve Delaunay denote dependent determined differential coefficients differential equation discussed double integral dx dy dy dz equal examine example expression extends fact fixed formula function given gives Hence hold independent indicate integral integral sign involves Jacobi's known Lacroix Lagrange length limits manner maxima and minima maximum or minimum means memoir method minima values namely necessary notation observed obtain occur ordinary original plane Poisson positive preceding present principles problem proposed proved published quantities question refers relation remains remarks respect result Sarrus satisfied says second order shews solution Strauch suppose surface theorem theory third tion transformed treatise usual vanish variable volume zero
Seite 140 - In fact this integral resembles the integral fVdydz ... and may be treated in the same way. We have merely indicated the transformations which must be applied to the portion JDUdxdydz ... of the variation SF; because since these transformations reduce to integration by parts they belong to the Integral Calculus rather than to the method of variations. It is true that one of the fundamental principles of this method consists in removing as much as possible the differential coefficients of the variations...
Seite 540 - An excellent Introductory Book. The definitions are very clear; the descriptions and explanations are sufliciently full and intelligible ; the investigations are simple and scientific. The examples greatly enhance its value.