A First Look At Perturbation Theory

Author : James G. Simmonds,James E. Mann
Publisher : Courier Corporation
Page : 164 pages
File Size : 55,5 Mb
Release : 2013-07-04
Category : Mathematics
ISBN : 9780486315584

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A First Look at Perturbation Theory by James G. Simmonds,James E. Mann Pdf

Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.

Author : Richard Ernest Bellman
Publisher : Courier Corporation
Page : 146 pages
File Size : 49,5 Mb
Release : 2003-01-01
Category : Science
ISBN : 0486432580

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Perturbation Techniques in Mathematics, Engineering and Physics by Richard Ernest Bellman Pdf

Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces scientifically significant problems and indicates useful solutions. 1966 edition.

Author : Giampaolo Cicogna,Guiseppe Gaeta
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 51,9 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540488743

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Symmetry and Perturbation Theory in Nonlinear Dynamics by Giampaolo Cicogna,Guiseppe Gaeta Pdf

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to a equations increasingly popular applied of the of the book Olver This by variety problems (following appearance [2621). with is and deals of nature theory deeply geometrical symmetries general (pro vided that described i.e. in this context there is are vector no they by fields), to limit attention to linear reason symmetries. In this look the basic tools of i.e. normal book we at perturbation theory, introduced Poincar6 about and their inter a forms (first by century ago) study action with with no limitation to linear ones. We focus on the most symmetries, basic fixed the and i.e. a setting, systems having point (at origin) perturbative around thus is local.

Author : Gilvan A Alves,Oscar J P Eboli,Victor O Rivelles
Publisher : World Scientific
Page : 672 pages
File Size : 40,6 Mb
Release : 2002-11-05
Category : Science
ISBN : 9789814488426

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Particles and Fields by Gilvan A Alves,Oscar J P Eboli,Victor O Rivelles Pdf

The Jorge André Swieca Summer School is a traditional school in Latin America well known for the high level of its courses and lecturers. This book contains lectures on forefront areas of high energy physics, such as collider physics, neutrino phenomenology, noncommutative field theory, string theory and branes. Contents:Noncommutative Field Theories and (Super) String Field Theories (I Ya Aref'eva et al.)Introduction to Superstring Theory (N Berkovits)Selected Topics in Integrable Models (A Das)Monte Carlo Simulation: A Road from Theoretical Models to Experimental Observables (R Z Funchal)Renormalization in Noncommutative Field Theory (M Gomes)What is behind the Tricks of Data Analysis in High Energy Physics (P Gouffon)The Physics of Hadron Colliders (D Green)Lectures on Noncommutative Theories (S Minwalla)Introduction to Perturbative QCD (P Nason)High Energy Cosmic Rays (R C Shellard)Brane Solutions in Supergravity (K S Stelle)Introductory Lectures on D-Branes (I V Vancea)Physics at Hadron Colliders (J Womersley) Readership: Graduate students and researchers in high energy physics. Keywords:

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 40,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253471

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Introduction to Perturbation Methods by Mark H. Holmes Pdf

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

Author : W. W. Sawyer
Publisher : Courier Dover Publications
Page : 210 pages
File Size : 50,7 Mb
Release : 2010-12-22
Category : Mathematics
ISBN : 9780486478821

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A First Look at Numerical Functional Analysis by W. W. Sawyer Pdf

Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis. Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence of an iteration, and Rall's ideas of polynomial and quadratic operators. Numerous examples appear throughout the text.

Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 47,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662126783

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Perturbation theory for linear operators by Tosio Kato Pdf

Author : James G. Simmonds
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 55,7 Mb
Release : 2012-10-31
Category : Mathematics
ISBN : 9781441985224

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A Brief on Tensor Analysis by James G. Simmonds Pdf

In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.

Author : T.S.L Radhika,T. Iyengar,T. Rani
Publisher : CRC Press
Page : 200 pages
File Size : 43,7 Mb
Release : 2014-11-21
Category : Mathematics
ISBN : 9781466588165

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Approximate Analytical Methods for Solving Ordinary Differential Equations by T.S.L Radhika,T. Iyengar,T. Rani Pdf

Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solut

Author : E. J. Hinch
Publisher : Cambridge University Press
Page : 178 pages
File Size : 43,8 Mb
Release : 1991-10-25
Category : Mathematics
ISBN : 0521378974

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Perturbation Methods by E. J. Hinch Pdf

A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

Author : Elena Shchepakina,Vladimir Sobolev,Michael P. Mortell
Publisher : Springer
Page : 212 pages
File Size : 45,7 Mb
Release : 2014-10-06
Category : Mathematics
ISBN : 9783319095707

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Singular Perturbations by Elena Shchepakina,Vladimir Sobolev,Michael P. Mortell Pdf

These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.

Author : James A. Murdock
Publisher : SIAM
Page : 513 pages
File Size : 47,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 9780898714432

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Perturbations by James A. Murdock Pdf

This book gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations.

Author : Zhen Hua,Roderick Wong
Publisher : World Scientific
Page : 390 pages
File Size : 45,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9812702393

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Differential Equations & Asymptotic Theory in Mathematical Physics by Zhen Hua,Roderick Wong Pdf

This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."

Author : Robert Watts
Publisher : Springer Nature
Page : 185 pages
File Size : 47,8 Mb
Release : 2022-05-31
Category : Mathematics
ISBN : 9783031024047

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Essentials of Applied Mathematics for Engineers and Scientists, Second Edition by Robert Watts Pdf

The Second Edition of this popular book on practical mathematics for engineers includes new and expanded chapters on perturbation methods and theory. This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering fields as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, fluid flow and mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms. This second edition includes two new and revised chapters on perturbation methods, and singular perturbation theory of differential equations. Table of Contents: Partial Differential Equations in Engineering / The Fourier Method: Separation of Variables / Orthogonal Sets of Functions / Series Solutions of Ordinary Differential Equations / Solutions Using Fourier Series and Integrals / Integral Transforms: The Laplace Transform / Complex Variables and the Laplace Inversion Integral / Solutions with Laplace Transforms / Sturm-Liouville Transforms / Introduction to Perturbation Methods / Singular Perturbation Theory of Differential Equations / Appendix A: The Roots of Certain Transcendental Equations

Author : Ronald E. Mickens
Publisher : World Scientific
Page : 261 pages
File Size : 52,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814291651

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Truly Nonlinear Oscillations by Ronald E. Mickens Pdf

This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of "truly nonlinear" (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply this technique to the field of nonlinear oscillations.