Forsyth A.R. Theory Of Differential Equations. Part 3: Ordinary Linear Equations. Volume 4

Cambridge: At the University Press, 1902. — 275 P.The present volume, constituting Part III of this work, deals with the theory of ordinary linear differential equations. The "whole range of that theory is too vast to be covered by a single volume ; and it contains several distinct regions that have no organic relation with one another. Accordingly, I have limited the discussion to the single region specially occupied by applications of the theory of functions ; in imposing this limitation, my wish has been to secure a uniform presentation of the subject.As a natural consequence, much is omitted that "would have been included, had my decision permitted the devotion of greater space to the subject. Thus the formal theory, in its various shapes, is not expounded, save as to a few topics that arise incidentally in the functional theory. The association with homogeneous forms is indicated only slightly. The discussion of combinations of the coefficients, which are invariantive under all transformations that leave the equation linear, of the associated equations that are covariantive under these transformations, and of the significance of these invariants and covariants, is completely omitted. Nor is any appliication of the theory of groups, save in a single functional investigation, given here. The student, who wishes to consider these subjects, and others that have been passed by, will find them in Schlesinger's Handbuch der Theorie der linearen Differentialgleichungen, in treatises such as Picard's Cours d' Analyse, and in many of the memoirs quoted in the present volume.