LECTURES ON THE CALCULUS OF VARIATIONS

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1904
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Page 128 - On Doubly Infinite Systems of Directly Similar Convex Arches with Common Base Line...
Page 90 - Leibnitz's rule for the differentiation of a definite integral with respect to a parameter.
Page 218 - Distinction des maxima et des minima dans un probleme isoperimetrique«, Nova acta reg. soc. sc. Upsaliensis Ser. 3. Vol. VII, hervorgehoben und darin zugleich die richtigen Kriterien des Maximums und Minimums für die isoperimetrischen Probleme aufgestellt. Allein abgesehen davon, dass in Folge ungenauen Ausdrucks und zum Theil auch nicht ganz richtiger Formeln seine Schlüsse nur schwer verständlich sind, dürfte es wohl...
Page 128 - BOLZA. The determination of the constants in the problem of the brachistochrone.
Page 46 - ... die entsprechende Frage in der Variations-Rechnung erst verhältnissmässig spät gestellt worden. Sieht man von einem verfehlten Versuch ab, den Laplace 1770 machte (Nova Acta Erud. anni 1772, S. 293), so hat zuerst Legendre die Frage in Angriff genommen in seiner Abhandlung: Memoire sur la maniere de distinguer les maxima des minima dans le calcul des variations (Memoires de Math, et de Phys.
Page x - This treatise is, in substance, a reproduction in considerably extended form of a series of lectures delivered by the author at the Colloquium held in connection with the summer meeting of the American Mathematical Society at Ithaca, NY, in August, 1901. It gives a detailed account of the typical and most important class of problems in the calculus of variations — in which an integral depending upon a plane curve and containing no higher but the first derivatives of the unknown functions is to...
Page 42 - The question of sufficient conditions for one-sided variations has recently been considered by BLISS in a paper read before the Chicago section of the American Mathematical Society. He finds that for a so-called regular problem (§7, c) the arc 23 of the curve...
Page 197 - With this condition imposed upon <I>, the two problems are equivalent; that is, every solution of the one is also a solution of the other.
Page v - Lectures on the Calculus of Variations, by Oskar Bolza, of the Department of Mathmatics.
Page 193 - Hence the partial derivatives of U(x, y] with respect to x and y are, on account of (8) and (9) : Remembering that F...

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