Introduction to perturbation methods

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last twenty or so years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover more advanced topics such as systems and partial differential equations. Moreover, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. For this new edition every section has been updated throughout, many only in minor ways, while others have been completely rewritten. New material has also been added. This includes approximations for weakly coupled oscillators, analysis of problems that involve transcendentally small terms, an expanded discussion of Kummer functions, and metastability. Two appendices have been added, one on solving difference equations and another on delay equations. Additional exercises have been included throughout. Review of first edition:"Those familiar with earlier expositions of singular perturbations for ordinary and partial differential equations will find many traditional gems freshly presented, as well as many new topics. Much of the excitement lies in the examples and the more than 250 exercises, which are guaranteed to provoke and challenge readers and learners with various backgrounds and levels of expertise."(SIAM Review, 1996 ) Read more... Introduction to Asymptotic Approximations -- Matched Asymptotic Expansions -- Multiple Scales -- The WKB and Related Methods -- The Method of Homogenization -- Introduction to Bifurcation and Stability. Preface -- Preface to Second Edition -- Introduction to Asymptotic Approximations -- Matched Asymptotic Expansions -- Multiple Scales -- The WKB and Related Methods -- The Method of Homogenization- Introduction to Bifurcation and Stability -- References -- Index