(1) A Course in Mathematical Analysis, Differential Equations (2) Finite Collineation Groups, with an Introduction to the Theory of Groups of Operators and Substitution Groups (3) Introduction to the Calculus of Variations

Abstract

(I) THE American translation of Prof. Gour sat's “Course of Analysis” will be welcome to those who may be unable to read the original oeasily. The present instalment covers ground in which the author is an acknowledged adept, and it illustrates his remarkable power of illuminating obscurities and giving charm to discussions which, although unavoidable, are apt to be dull. Thus his chapter on existence theorems is not only a model of rigour, but actually entertaining as well; § 30, on the Cauchy-Lipschitz method, is most instructive, and illustrates the value of a diagram when properly used—not as a vehicle for a sham “intuitive proof,” but as an image corresponding to a set of analytical odata and deductions. Geometrical imagery of this kind is frequently used throughout f and with the happiest results—especially, tt seems ta us, m the part dealing with partial differential equations of the first order. (1) A Course in Mathematical Analysis, Differential Equations. Being part ii. of vol. ii. By Prof. E. Goursat. Translated by Prof. E. R. Hedrick and Otto Dunkel. Pp. viii + 300. (London: Ginn and Co., n.d.) Price 11s. 6d. net. (2) Finite Collineation Groups, with an Introduction to the Theory of Groups of Operators and Substitution Groups. By Prof. H. F. Blichfeldt. Pp. xi + 194. (Chicago, 111.: University of Chicago Press; London: Cambridge University Press, 1917.) Price 1.50 dollars net, or 6s. net. (3) Introduction to the Calculus of Variations. By Prof. W. E. Byerly. Pp, 48. (Mathematical Tracts for Physicists.) (Cambridge, Mass.: Harvard University Press; London: Oxford University Press, 1917.) Price 3s. 6d. net.