Introduction to Perturbation MethodsSpringer Science & Business Media, 19 jun 1998 - 356 páginas 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. |
Índice
Series Preface | 1 |
Accuracy versus Convergence of an Asymptotic | 12 |
Multiple Scales | 105 |
The WKB and Related Methods | 161 |
The Method of Homogenization | 223 |
Introduction to Bifurcation and Stability | 249 |
Solution and Properties of Transition | 297 |
Asymptotic Approximations of Integrals | 305 |
References | 313 |
| 331 | |
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Términos y frases comunes
amplitude appropriate expansion assumed asymptotic approximation asymptotic expansion asymptotic solution asymptotically stable bifurcation diagram bifurcation point boundary conditions boundary layer coefficients composite expansion coordinate curve depends derive determine difference equation eigenvalue eikonal equation exact solution example Exercise Ə² Find a first-term Find a two-term first-term approximation first-term expansion following problem function given homogenized Hopf bifurcation initial conditions integral interval linear matched asymptotic expansions Math Mathematical multiple scales multiple-scale nonlinear nonzero numerical solution obtain ordinary differential equation oscillator outer expansion parameter partial differential equations positive constant propagation region result satisfies second term secular terms shown in Fig small ɛ smooth solve steady Suppose t₁ t₂ Taylor's theorem tion traveling wave turning point two-term expansion u₁ uo(x valid for large values variable WKB approximation WKB method y₁
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Wave Propagation and Time Reversal in Randomly Layered Media Jean-Pierre Fouque,Josselin Garnier,G. Papanicolaou,Knut Solna No hay ninguna vista previa disponible - 2007 |