Techniques of Asymptotic Analysis

Techniques of Asymptotic Analysis

These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown.

Author: Lawrence Sirovich

Publisher: Springer Science & Business Media

ISBN: 9781461264026

Category: Mathematics

Page: 306

View: 895

These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. In the hope that these notes might prove useful for reference purposes several additional sections have been included and also a table of contents and index. Although asymptotic analysis is now enjoying a period of great vitality, these notes do not reflect a research oriented course. The course is aimed toward people in applied mathematics, physics, engineering, etc., who have a need for asymptotic analysis in their work. The choice of subjects has been largely dictated by the likelihood of application. Also abstraction and generality have not been pursued. Technique and computation are given equal prominence with theory. Both rigorous and formal theory is presented --very often in tandem. In practice, the means for a rigorous analysis are not always available. For this reason a goal has been the cultivation of mature formal reasoning. Therefore, during the course of lectures formal presentations gradually eclipse rigorous presentations. When this occurs, rigorous proofs are given as exercises or in the case of lengthy proofs, reference is made to the Reading List at the end.
Categories: Mathematics

Asymptotic Methods in Analysis

Asymptotic Methods in Analysis

This pioneering study/textbook in a crucial area of pure and applied mathematics features worked examples instead of the formulation of general theorems. Extensive coverage of saddle-point method, iteration, and more. 1958 edition.

Author: N. G. de Bruijn

Publisher: Courier Corporation

ISBN: 9780486150796

Category: Mathematics

Page: 224

View: 271

This pioneering study/textbook in a crucial area of pure and applied mathematics features worked examples instead of the formulation of general theorems. Extensive coverage of saddle-point method, iteration, and more. 1958 edition.
Categories: Mathematics

Asymptotic Analysis of Differential Equations

Asymptotic Analysis of Differential Equations

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

Author: R. B. White

Publisher: World Scientific

ISBN: 9781848166080

Category: Mathematics

Page: 405

View: 294

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Categories: Mathematics

Asymptotic Analysis

Asymptotic Analysis

In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives.

Author: Mikhail V. Fedoryuk

Publisher: Springer Science & Business Media

ISBN: 9783642580161

Category: Mathematics

Page: 363

View: 447

In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Categories: Mathematics

Asymptotic Analysis

Asymptotic Analysis

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics.

Author: James Dickson Murray

Publisher: Oxford University Press, USA

ISBN: UCSD:31822012789053

Category: Approximation theory

Page: 140

View: 452

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's "Asymptotic" "Expansions" or N.G. de Bruijn's "Asymptotic Methods in" "Analysis" (1958), any academic library would do well to have this excellent introduction." ("S. Puckette, University of" "the South") #"Choice Sept. 1984"#1
Categories: Approximation theory

Techniques of Asymptotic Analysis

Techniques of Asymptotic Analysis

"In this second part of Willie Sugg's history of Cambridgeshire cricket the author focuses on the first documented period of sustained success for a Cambridgeshire club - that of the Cambridge Cricket Club." (back cover) Part two of three.

Author: Lawrence Sirovich

Publisher:

ISBN: 3540900225

Category: Analyse fonctionnelle

Page: 306

View: 474

Categories: Analyse fonctionnelle

Mathematics for the Analysis of Algorithms

Mathematics for the Analysis of Algorithms

The book is very well written. The style and the mathematical exposition make the book pleasant to read.

Author: Daniel H. Greene

Publisher: Springer Science & Business Media

ISBN: 9780817647292

Category: Computers

Page: 132

View: 792

This monograph collects some fundamental mathematical techniques that are required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is concise enough for easy reference yet detailed enough for those with little background with the material.
Categories: Computers

Applied Asymptotic Analysis

Applied Asymptotic Analysis

This book is a survey of asymptotic methods set in the current applied research context of wave propagation.

Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 9780821840788

Category: Mathematics

Page: 467

View: 921

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.
Categories: Mathematics

Asymptotic Analysis

Asymptotic Analysis

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics.

Author: J.D. Murray

Publisher: Springer Science & Business Media

ISBN: 9781461211228

Category: Mathematics

Page: 165

View: 372

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) #Choice Sept. 1984#1
Categories: Mathematics

Asymptotic Analysis

Asymptotic Analysis

Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus.

Author: Ricardo Estrada

Publisher: Springer Science & Business Media

ISBN: 9781468400298

Category: Mathematics

Page: 258

View: 353

Asymptotic analysis is an old subject that has found applications in vari ous fields of pure and applied mathematics, physics and engineering. For instance, asymptotic techniques are used to approximate very complicated integral expressions that result from transform analysis. Similarly, the so lutions of differential equations can often be computed with great accuracy by taking the sum of a few terms of the divergent series obtained by the asymptotic calculus. In view of the importance of these methods, many excellent books on this subject are available [19], [21], [27], [67], [90], [91], [102], [113]. An important feature of the theory of asymptotic expansions is that experience and intuition play an important part in it because particular problems are rather individual in nature. Our aim is to present a sys tematic and simplified approach to this theory by the use of distributions (generalized functions). The theory of distributions is another important area of applied mathematics, that has also found many applications in mathematics, physics and engineering. It is only recently, however, that the close ties between asymptotic analysis and the theory of distributions have been studied in detail [15], [43], [44], [84], [92], [112]. As it turns out, generalized functions provide a very appropriate framework for asymptotic analysis, where many analytical operations can be performed, and also pro vide a systematic procedure to assign values to the divergent integrals that often appear in the literature.
Categories: Mathematics

Partial Differential Equations I

Partial Differential Equations I

Sirovich : Techniques of Asymptotic Analysis . 3. Hale : Theory of Functional Differential ... Giacoglia : Perturbation Methods in Non - linear Systems . 9. ... Bluman / Cole : Similarity Methods for Differential Equations . 14.

Author: Michael Eugene Taylor

Publisher: Springer Science & Business Media

ISBN: 0387946535

Category: Mathematics

Page: 563

View: 435

This book is intended to be a comprehensive introduction to the subject of partial differential equations. It should be useful to graduate students at all levels beyond that of a basic course in measure theory. It should also be of interest to professional mathematicians in analysis, mathematical physics, and differential geometry. This work will be divided into three volumes, the first of which focuses on the theory of ordinary differential equations and a survey of basic linear PDEs.
Categories: Mathematics

Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations

Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations.This work focuses on the approach to stochastic equations from the perspective of ordinary ...

Author: Anatoliy M Samoilenko

Publisher: World Scientific

ISBN: 9789814462396

Category: Mathematics

Page: 324

View: 827

Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed. Contents:Differential Equations with Random Right-Hand Sides and Impulsive EffectsInvariant Sets for Systems with Random PerturbationsLinear and Quasilinear Stochastic Ito SystemsExtensions of Ito Systems on a TorusThe Averaging Method for Equations with Random Perturbations Readership: Graduate students and researchers in mathematics and physics. Keywords:Stochastic Systems;Invariant Manifold;Invariant Torus;Lyapunov Function;Stability;Periodic Solutions;Reduction PrincipleKey Features:Develops new methods of studying the stochastic differential equations; contrary to the existing purely probabilistic methods, these methods are based on the differential equations approachStudies new classes of stochastic systems, for instance, the stochastic expansions of dynamical systems on the torus, enabling the study of general oscillatory systems subject to the influences of random factorsBridges the gap between the stochastic differential equations and ordinary differential equations, namely, it describes which properties of the ordinary differential equations remain unchanged, and which new properties appear in the stochastic caseReviews: "This book is well written and readable. Most results included in the book are by the authors. All chapters contain a final section with comments and references, where the authors make a detailed description of the origin of the results. This is a helpful point for all readers, especially for researchers in the field." Mathematical Reviews "This monograph collects a great variety of stimulating results concerning random perturbation theory always deeply rooted in the classical theory of ordinary differential equations and celestial mechanics. Despite its technical content the text is written in a clear and accessible way, with many insightful explanations. The fact that each chapter closes with a detailed review on the current literature and the historic development of the theory is highly appreciated." Zentralblatt MATH
Categories: Mathematics

Asymptotic Analysis

Asymptotic Analysis

ASYMPTOTICS In this section we shall study the solution of (1.4) with f as sketched * f (s) x a., ( t ) in figure 2, ... the application of standard techniques of asymptotic analysis of singular perturbations as treated in, for example, ...

Author: F. Verhulst

Publisher: Springer

ISBN: 9783540353324

Category: Mathematics

Page: 248

View: 951

Categories: Mathematics

Asymptotic Analysis of Differential Equations

Asymptotic Analysis of Differential Equations

Methods of asymptotic analysis covered include dominant balance, the use of divergent asymptotic series, phase-integral methods, asymptotic evaluation of integrals, and boundary layer analysis. The construction of integral solutions and ...

Author: R. B. White

Publisher: World Scientific

ISBN: 9781848166073

Category: Mathematics

Page: 405

View: 638

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Categories: Mathematics

Differential Equations Asymptotic Analysis and Mathematical Physics

Differential Equations  Asymptotic Analysis  and Mathematical Physics

This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996.

Author: Michael Demuth

Publisher: John Wiley & Sons

ISBN: 3055017692

Category: Asymptotic expansions

Page: 424

View: 381

This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.
Categories: Asymptotic expansions

Asymptotic Analysis and Boundary Layers

Asymptotic Analysis and Boundary Layers

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM).

Author: Jean Cousteix

Publisher: Springer Science & Business Media

ISBN: 9783540464891

Category: Science

Page: 434

View: 503

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.
Categories: Science

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

Asymptotic-Induced Numerical Methods for Conservation Laws Marc Garbey Université Claude Bernard Lyon1 LAN, 69622 Villeurbanne cedex ... 1 Introduction The combination of asymptotic and numerical analyses provides improved accuracy for ...

Author: Hans G. Kaper

Publisher: CRC Press

ISBN: 9781482277067

Category: Mathematics

Page: 286

View: 951

Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Categories: Mathematics

Plates Laminates and Shells

Plates  Laminates  and Shells

This book gives a systematic and comprehensive presentation of the results concerning effective behavior of elastic and plastic plates with periodic or quasiperiodic structure.

Author: T. Lewi?ski

Publisher: World Scientific

ISBN: 9810232063

Category: Mathematics

Page: 739

View: 903

This book gives a systematic and comprehensive presentation of the results concerning effective behavior of elastic and plastic plates with periodic or quasiperiodic structure. One of the chapters covers the hitherto available results concerning the averaging problems in the linear and nonlinear shell models.A unified approach to the problems studied is based on modern variational and asymptotic methods, including the methods of variational inequalities as well as homogenization techniques. Duality arguments are also exploited. A significant part of the book deals with problems important for engineering practice, such as: statical analysis of highly nonhomogeneous plates and shells for which common discretization techniques fail to be efficient, assessing stiffness reduction of cracked 0n/900m]s laminates, and assessing ultimate loads for perfectly plastic plates and shells composed of repeated segments. When possible, the homogenization formulas are cast in closed form expressions. The formulas presented in this manner are then used in constructing regularized formulations of the fundamental optimization problems for plates and shells, since the regularization concepts are based on introducing the composite regions for which microstructural properties play the role of new design variables.
Categories: Mathematics

Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals

Asymptotic analysis is that branch of mathematics devoted to the study of the behavior of functions in particular limits of interest. This book is concerned with the theory and technique of asymptotic expansions of functions defined by ...

Author: Norman Bleistein

Publisher: Courier Corporation

ISBN: 9780486650821

Category: Mathematics

Page: 425

View: 932

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Categories: Mathematics