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Présentation de l'éditeur:
These two volumes, now published asP art IV of the present work, are my final contribution towards the fulfihiient of a promise made twenty-one years ago. They are devoted to the theory of partial differential equations. Though the work thus is completed, no claim is made that every topic of importance has been discussed. In the earlier volumes, indications of omissions from other portions of the whole subject were given and need not now be repeated: here also, there have been definite omissions. Nothing, for instance, is said concerning the researches of Picard and Dini on the method of successive approximations for the construction of an integral which obeys assigned conditions ;these investigations limit the variables to real values, and throughout the treatise I have dealt with variables having complex values. Formal questions, such as those wdiich arise out of the application of the theory of groups, are hardly mentioned; here, as in the preceding volumes, I have concerned myself with organic properties, given by applications of the theory of functions, rather than with formal properties.
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