A History of the Progress of the Calculus of Variations During the Nineteenth Century

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Macmillan and Company, 1861 - Calculus of variations - 532 pages

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Page 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...
Page 37 - Sed quum calculus variationum integralium duplicium pro casu ubi etiam limites tanquam variabiles spectari debent, hactenus parum excultus sit, hanc disquisitionem subtilem paullo profundius petere oportet.

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