Singular Perturbation in the Physical Sciences
- ISBN-10
- 1470425556
- ISBN-13
- 9781470425555
- Category
- Asymptotic expansions
- Pages
- 336
- Language
- English
- Published
- 2015-12-02
- Publisher
- American Mathematical Soc.
- Author
- John C. Neu
Description
This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and phenomena, and the latter emphasizes geometric and physical insight. It will be useful for mathematicians and physicists learning singular perturbation analysis of ODE and PDE boundary value problems as well as the full range of related examples and problems. Prerequisites are basic skills in analysis and a good junior/senior level undergraduate course of mathematical physics.
Get the book
Similar books
-
Selected Papers of F.W.J. Olver
By Frank W. J. OlverFrank W. J. Olver Roderick Wong. 352 F. W. J. OLVER ON 1 Zeros of Y , ( z ) and Y ( z ) when n is half an odd integer If we substitute n = ng + e in ( 8-12 ) , where n , is an integer and 0 < e < 1 , we obtain Y , ( z emai ) = ( - ) mno ...
-
Analysis of Divergence: Control and Management of Divergent Processes
By William O. BrayAnalysis of Divergence: Control and Management of Divergent Processes
-
奇异摄动方程解的渐进展开
By 瓦西里耶娃, 布图佐夫数学天元基金资助项目
-
Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow
By Dan Knopf, Zhou Gang, Israel Michael SigaWhat distinguishes this approach from standard parabolic rescaling (see, e.g., [3] or |2|) is that we do not fix X(t) ... q)0,00+ v *F, (p, q)00 – ayo, with v-dependent coefficients defined with respect to (1.7) a := -\O. A. p = 0, v, ...
-
Concrete Mathematics: A Foundation for Computer Science
By Ronald L. GrahamConcrete Mathematics: A Foundation for Computer Science
-
Analyzable Functions and Applications
Analyzable Functions and Applications
-
Selected Papers of F.W.J. Olver
By Frank W. J. Olver4 A Mathematician and His Mathematical Work Selected Papers of S. S. Chern edited by S. Y. Cheng , P. Li and G. ... 7 Selected Papers of F. W. J. Olver ( in 2 Volumes ) edited by Roderick Wong SELECTED PAPERS OF F.W.J. Olver Part II ...
-
Normal Approximation and Asymptotic Expansions
By Rabindra N. Bhattacharya, Ramaswamy Ranga RaoFor several perspectives and applications of Stein's method, see Barbour (1988), Diaconis and Holmes (2004), Holmes (2004), and Rinott and Rotar (1996). 1(a) The Ornstein—Uhlenbeck Process and Its ... An Application of Stein 's Method.
-
Normal Approximation and Asymptotic Expansions
By Rabindra Nath BhattacharyaThis also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and ...
-
Asymptotic Differential Algebra and Model Theory of Transseries
By Matthias Aschenbrenner, Lou van den Dries, Joris HoevenThe differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms.