Abstract
IN reviewing the first volume of this book (NATURE, vol. Ixiii. p. 390) it was pointed out that owing to the great advances in mathematical physics which have taken place in the forty years since Riemann's time, Prof. Weber had found it necessary, instead of merely issuing a revised edition of the well-known “Partielle Differential-gleichungen,” to write practically an entirely new book. The present volume, which is written much on the same general lines as the first, is divided into five parts. The first contains the more important properties of hypergeometric series and their application to the theory of linear differential equations. The second part, dealing with conduction of heat, is much after the lines of Riemann's original treatment, and treats mainly of conduction in one dimension and conduction in a sphere. The third part is devoted to theory of elasticity and vibrations, the torsion problem being included in the former subject, and vibrations of strings and membranes in the latter. Electrical oscillations come next in order, and the last part consists of hydrodynamics and propagation of plane and spherical sound-waves, including Riemann's own theory of sound-waves of finite amplitude.
Die Partiellen Differential-gleichungen der mathematischen Physik.
By Heinrich Weber, based on Riemann's lectures. Vol. ii. Pp. 527. (Brunswick: Fried. Vieweg and Son, 1901.)
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B., G. Die Partiellen Differential-gleichungen der mathematischen Physik . Nature 65, 30 (1901). https://doi.org/10.1038/065030a0
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DOI: https://doi.org/10.1038/065030a0