Carrier G.F., Pearson C. Ordinary Differential Equations
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SIAM, 1991. - 230 Pages.The material in this book is not a conventional treatment of ordinary differential equations. It does not contain the collection of proofs commonly displayed as the foundations of the subject, nor does it contain the collection of recipes commonly aimed at the scientist or engineer. Rather, in a way which requires little or no previous acquaintance with the subject, it contains a sequence of heuristic arguments, illustrative examples and exercises, which serve to lead the reader towards the invention, generalization, and usage of the techniques by which solutions of differential equations can be constructed. Above all, we hope, the reader can gain a perspective concerning the extent to which methods which lead in principle to the solution of a given problem actually lead to a useful description of that solution.
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