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

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arbitrary constants arbitrary functions axis brachistochrone Calculus of Variations catenary Cauchy chapter co-ordinates condition considered contains curvature d*Du dDu dDu Delaunay Delaunay's denote determined Differential Calculus differential equation double integral dx dx dx dy dz dx dz dxdy dy dx dy dy dz dz Euler exact differential coefficient example expression formula given in Art gives Hence indefinitely small independent variables Integral Calculus integral sign integration with respect investigation involves Jacobi's Jacobi's theorem Lacroix Lagrange limiting values maxima and minima maximum or minimum memoir method minimum area minimum value multiple integral notation obtain occupies pages occur ordinary Ostrogradsky partial differential coefficients partial differential equation plane Poisson problem quantities remarks result Sarrus satisfy second order shew solution Stegmann Strauch suppose tangent theorem tion transform treatise triple integral vanish volume zero

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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 539 - SNOWBALL — THE ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY; with the Construction and Use of Tables of Logarithms. By JC SNOWBALL, MA New Edition.

Page 548 - ... which can be altered only by the changes of entire units or integral multiples of units in the fundamental conditions of the problem ; the other concerning those chances which have respect to insensible gradations in the value of the element measured), the present tract has been drawn up.

Page 548 - ... to chances which can be altered only by the changes of entire units or integral multiples of units in the fundamental conditions of the problem ; the other concerning those chances which have respect to insensible gradations in the value...

Page 548 - It is of importance that those who wish to cultivate any subject may be able to ascertain what results have already been obtained, and thus reserve their strength for difficulties which have not yet been conquered. The Author has endeavoured in this work to ascertain distinctly what has been effected in the Progress of the Calculus, and to form some estimate of the manner in which it has been effected.

Page 556 - The author has endeavoured to connect the history of the New Testament Canon with the growth and consolidation of the Church, and to point out the relation existing between the amount of evidence for the authenticity of its component parts, and the whole mass of Christian literature. Such a method of inquiry will convey both the truest notion of the connection of the written Word with the living Body of Christ, and the surest conviction of its divine authority.

Page 542 - ... the want of a work on a subject of great importance and high interest— La Place's Coefficients and Functions and the calculation of the Figure of the Earth by means of his remarkable analysis. No student of the higher branches of Physical Astronomy should be ignorant of La Place's analysis and its result — " a calculus," says Airy, " the most singular in its nature and the most powerful in its application that has ever appeared.

Page 542 - Mechanics. For the use of the Junior Classes at the University, and the Higher Classes in Schools. "With a copious Collection of Examples. Crown Svo. cloth, 9s. 6it. 2. A Treatise on Optics. Crown Svo. cloth, 10*.

Page 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.

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.