In its expanded new edition, this book covers boundary layers, multiple scales, homogenisation, slender body theory, symbolic computing, discrete equations and more. Includes exercises derived from current research, drawn from a range of application areas.

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten 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 such traditional topics as boundary layers and multiple scales. However, 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.

One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

Lots of examples and exercises Class test for over 20 years Includes delay equations Includes supplementary material: sn.pub/extras

Autorentext

Mark Holmes is a Professor at Rensselaer Polytechnic Institute, and is currently the Director of the Center for Modeling, Optimization and Computational Analysis. His research interests involve problems integrating modeling and computational analysis. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.

Inhalt
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.