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.
Series Preface.- Preface.- Chapter 1: Introduction to Asymptotic Approximations.- Chapter 2: Matched Asymptotic Expansions.- Chapter 3: Multiple Scales.- Chapter 4: The WKB and Related Methods.- Chapter 5: The Method of Homogenization- Chapter 6: Introduction to Bifurcation and Stability.- Appendix A1: Solution and Properties of Transition Layer Equations.- Appendix A2: Asymptotic Approximations of Integrals.- Appendix A3: Numerical Solution of Nonlinear Boundary- Value Problems.- References.- Index.