The authors' aim is to provide the reader with the very basic knowledge necessary to begin research on differential equations with professional ability. The selection of topics should provide the reader with methods and results which are applicable in a variety of different fields. Each chapter begins with a brief discussion of its contents and history and ends with a number of problems and exercises.

Review

"This book in pure mathematics will guide the reader on a newly marked path through classic and awesome terrain---first so well described by Coddington and Levinson---toward research in the important and useful areas of power series solutions and asymptotics. The path not taken would be marked by at least one explicit mention of a Poincaré map, a resonance in celestial mechanics, an average, a traveling wave, or a transversal intersection of separatrices."--MATHEMATICAL REVIEWS

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