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This manual was written with a double purpose. The first, and most important, provide students with a degree (now grade) in mathematics of a good study material on differential equations, including rigorous and detailed tests of theorems, varied examples and sufficient exercises. On the other hand, thinking of a teaching potential, perhaps inexperienced, which would like to use it as a textbook, a gradation of the contents according to its relevance is proposed, distinguishing between the essential opinions and those that could be omitted without impairment for the goodStudent preparation. Unlike other similar profile books, the present includes a wide battery of applications of differential equations to applied sciences, chemistry to ecology, from astronomy to engineering, which are presented without presupposing in readers more knowledge more knowledgeof these disciplines that the elementals.

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