Introduction to perturbation methods / Mark H. Holmes

Bibliogr. p. 421-432. Index

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. (Source : Springer)