---

＜電子ブック＞
Advanced Mathematical Methods for Scientists and Engineers I : Asymptotic Methods and Perturbation Theory / by Carl M. Bender, Steven A. Orszag

版	1st ed. 1999.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1999
本文言語	英語
大きさ	XIV, 593 p : online resource
著者標目	*Bender, Carl M author Orszag, Steven A author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Mathematical physics FREE:Analysis FREE:Mathematical and Computational Engineering Applications FREE:Mathematical Methods in Physics FREE:Theoretical, Mathematical and Computational Physics
一般注記	I Fundamentals -- 1 Ordinary Differential Equations -- 2 Difference Equations -- II Local Analysis -- 3 Approximate Solution of Linear Differential Equations -- 4 Approximate Solution of Nonlinear Differential Equations -- 5 Approximate Solution of Difference Equations -- 6 Asymptotic Expansion of Integrals -- III Perturbation Methods -- 7 Perturbation Series -- 8 Summation of Series -- IV Global Analysis -- 9 Boundary Layer Theory -- 10 WKB Theory -- 11 Multiple-Scale Analysis The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as­ asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus HTTP:URL=https://doi.org/10.1007/978-1-4757-3069-2

 類似資料