Mark H. Holmes (auth.)0387942033, 9780387942032, 3540942033
This book is 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 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. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas. |
Table of contents :
Front Matter….Pages i-xiii
Introduction to Asymptotic Approximations….Pages 1-45
Matched Asymptotic Expansions….Pages 47-104
Multiple Scales….Pages 105-159
The WKB and Related Methods….Pages 161-222
The Method of Homogenization….Pages 223-248
Introduction to Bifurcation and Stability….Pages 249-295
Back Matter….Pages 297-337 |
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