Abstract
THIS little book is founded on a course of lectures, given by the author at Rome in 1930–31, on the theory of characteristics of partial differential equations and their applications (following the methods originated by L'Hugoniot and developed by Hadamard) to wave motion in acoustics, elasticity, optics, electromagnetism and other branches of physics. It opens by recalling some existence theorems concerning partial differential equations. The characteristics are introduced as the loci of singular points where these theorems break down. We then pass on to the consideration of wave motion, and wave surfaces prove to be closely connected with characteristics. The most interesting part of the book is the concluding section, which deals with the wave-particle dualism of modern physics according to de Broglie. An account is given of the recent dynamical-optical work of Persico, which aims at making Schrödinger's wave equation plausible, and a tantalisingly brief reference is added concerning Racah's use (in 1931) of the principles expounded in this book to obtain a justification of Heisenberg's principle of indeterminacy. Most readers will probably wish for a fuller account of the new developments so briefly mentioned here.
Caratteristiche dei sistemi differenziali e propagazione ondosa.
Tullio
Levi-Civita
Per. Lezioni raccolte dal Dott. G. Lampariello. (Attualità Scientifiche, N. 41.) Pp. vii + 110. (Bologna: Nicola Zanichelli, 1931.) 15 lire.
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P., H. Caratteristiche dei sistemi differenziali e propagazione ondosa . Nature 131, 45 (1933). https://doi.org/10.1038/131045a0
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DOI: https://doi.org/10.1038/131045a0
