Gives an introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductions on the subject, this work distinguishes between formal and rigorous asymptotic validity. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method, are covered, and the asymptotic validity (in the rigorous sense) of each method is proved. Coverage encompasses both perturbation and geometrical results. Includes chapter exercises and appendices on prerequisite mathematics. Can be used before or after a traditional graduate course in ordinary differential equations. This is a paperback reprint of a work that was first published in 1991. The author is professor of mathematics at Iowa State University. Annotation c. Book News, Inc., Portland, OR (booknews.com)