Abstract
THIS interesting and well-written book shows that the ideas of Sophus Lie are at last bearing fruit, even in elementary text-books. There are three chapters dealing respectively with ordinary differential equations of the first order, with similar equations of higher order and systems of such equations, and with partial differential equations of the first order with two independent variables. Besides this, there is an introductory chapter dealing mainly with existence-theorems, and a concluding one on-partial differential equations of the second order. The examples are numerous, and admit of geometrical interpretation; many of them illustrate the theory of tangential transformations, which, happily, receives a good deal of attention. The articles on existence-theorems appear to be sound, so far as they go, and are unusually readable. Altogether, Dr. Liebmann's book may be recommended as a useful introduction to the modern treatment of the vast subject with which he deals.
Lehrbuch der Differentialgleichungen.
Von Dr. H. Liebmann. Pp. vi + 226. (Leipzig: Veit and Co., 1901.)
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M. Lehrbuch der Differentialgleichungen . Nature 65, 389–390 (1902). https://doi.org/10.1038/065389b0
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DOI: https://doi.org/10.1038/065389b0
