Abstract
THE work of Euler and Lagrange in the middle of the eighteenth century proved that the essence of theoretical mechanics lay in the calculus of variations, which was itself something that included not only all mechanics but also much else besides. Mechanics is a class of partial differential equations; the calculus of variations corresponds to a similar but bigger class, whose essential properties differ only in detail from those of the former class. Jacobi in particular stressed, in 1836, the intimate relation that subsists between systems of partial differential equations of the first order and equations arising out of the calculus of variations.
Variationsrechnung und partielle Differential-gleichungen erster Ordnung
Von Prof. Constantin Carathéodory. Pp. xi + 407. (Leipzig und Berlin: B. G. Teubner, 1935.) 22 gold marks.
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I., E. Variationsrechnung und partielle Differential-gleichungen erster Ordnung. Nature 136, 814 (1935). https://doi.org/10.1038/136814a0
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DOI: https://doi.org/10.1038/136814a0