Few domains of mathematics are as widely useful as the theory of ordinary differential equations. And while every book on the topic contains at least some material on the behavior of the solutions in the complex domain, this highly regarded graduate-level text is unique in that it was the first book in English to deal exclusively with the subject.
Moreover, Professor Hille's book incorporates much material not available in other treatises and offers full and extensive treatments of existence theorems, representation of solutions by series, representation by integrals, theory of majorants, dominants and minorants, questions of growth, applications of the modern value distribution theory, and more. Included are investigations by Boutroux, Briot-Bouquest, Malmquist, Painlevé, R. Smith, Wittich, and Yosida.
For students not conversant with the required complex analysis, review material has been supplied throughout the text. In addition, each chapter has a list of references to the literature, and there is a bibliography at the end of the book. The exercises at the ends of sections comprise some 675 items.
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