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The book is intended to be an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists and engineers.
The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development of the topic and this usually means examples involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple-scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations.
List of contents
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.
