A History of the Progress of the Calculus of Variations During the Nineteenth Century |
Other editions - View all
Common terms and phrases
1+p² arbitrary constants axis Calculus of Variations catenary chapter condition considered curvature curve d²f Delaunay denote determined Differential Calculus differential equation double integral ds ds ds² dv dv dx dx dx dy dz dx dz dx² dy dx dy dy dy dy² dz dx dz dy dz dz Euler exact differential coefficient example expression formula geodesic gives indefinitely small independent variable Integral Calculus integral sign investigation involves Jacobi's Jacobi's theorem Lacroix Lagrange maxima and minima maximum or minimum memoir method minimum value notation obtain occupies pages Ostrogradsky partial differential equation plane Poisson problem quantities remarks respect result Sarrus second order shew solution Stegmann Strauch suppose surface theorem tion treatise triple integral UNIV vanish volume Y₁ zero бу
Popular passages
Page 40 - Find an expression for the area of a triangle in terms of the coordinates of its angular points.
Page 229 - ... nor a minimum exists. We have already intimated in Art. 5, that Legendre had arrived at some results on these points, and that Lagrange had shewn that further investigations were required in order to ensure the accuracy of Legendre's conclusions. The requisite investigations were supplied by Jacobi in 1837, and the memoir which Jacobi then published has given rise to an extensive series of commentaries and developments. Before however we proceed to Jacobi's investigations, we will give an analysis...