Singular Perturbation In The Physical Sciences
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Singular Perturbation In The Physical Sciences
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Author : John C. Neu
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-02
Singular Perturbation In The Physical Sciences written by John C. Neu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-02 with Mathematics categories.
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.
Singular Perturbation In The Physical Sciences
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Author : John C. Neu
language : en
Publisher:
Release Date : 2015
Singular Perturbation In The Physical Sciences written by John C. Neu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Asymptotic expansions categories.
Cover -- Title page -- Contents -- Acknowledgment -- Introduction -- Chapter 1. What is a singular perturbation? -- Chapter 2. Asymptotic expansions -- Chapter 3. Matched asymptotic expansions -- Chapter 4. Matched asymptotic expansions in PDE -- Chapter 5. Prandtl boundary layer theory -- Chapter 6. Modulated oscillations -- Chapter 7. Modulation theory by transforming variables -- Chapter 8. Nonlinear resonance -- Bibliography -- Index -- Back Cover
Singular Perturbations And Boundary Layers
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Author : Gung-Min Gie
language : en
Publisher: Springer
Release Date : 2018-11-21
Singular Perturbations And Boundary Layers written by Gung-Min Gie and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-21 with Mathematics categories.
Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.
Nonlinear Problems In The Physical Sciences And Biology
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Author : I. Stakgold
language : en
Publisher: Springer
Release Date : 2006-11-15
Nonlinear Problems In The Physical Sciences And Biology written by I. Stakgold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
A Guided Tour Of Mathematical Methods For The Physical Sciences
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Author : Roel Snieder
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-16
A Guided Tour Of Mathematical Methods For The Physical Sciences written by Roel Snieder and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-16 with Mathematics categories.
This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.
Mathematics Applied To Deterministic Problems In The Natural Sciences
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Author : C. C. Lin
language : en
Publisher: SIAM
Release Date : 1988-12-01
Mathematics Applied To Deterministic Problems In The Natural Sciences written by C. C. Lin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-01 with Mathematics categories.
This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.
Singular Perturbation Theory
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Author : Alexander G. Ramm
language : en
Publisher: Kluwer Academic Publishers
Release Date : 2004
Singular Perturbation Theory written by Alexander G. Ramm and has been published by Kluwer Academic Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Inverse problems (Differential equations) categories.
Historical Developments In Singular Perturbations
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Author : Robert E. O'Malley
language : en
Publisher: Springer
Release Date : 2014-11-19
Historical Developments In Singular Perturbations written by Robert E. O'Malley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Recent Studies Inperturbation Theory
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Author : Dimo Uzunov
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-06-14
Recent Studies Inperturbation Theory written by Dimo Uzunov and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-14 with Technology & Engineering categories.
The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y. Takashi), the quantum gravity and its detection and measurement (F. Bulnes), atom-photon interactions (E. G. Thrapsaniotis), treatment of spectra and radiation characteristics by relativistic perturbation theory (A. V. Glushkov et al), and Green's function theory and some applications (Jing Huang). The pure mathematical issues are related to the problem of generalization of the boundary layer function method for bisingularly perturbed differential equations (K. Alymkulov and D. A. Torsunov) and to the development of new homotopy asymptotic methods and some of their applications (Baojian Hong).
Applications Of Nonlinear Analysis In The Physical Sciences
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Author : Herbert Amann
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1981
Applications Of Nonlinear Analysis In The Physical Sciences written by Herbert Amann and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.