A First Look at Perturbation Theory

A First Look at Perturbation Theory
Author :
Publisher : Courier Corporation
Total Pages : 164
Release :
ISBN-10 : 0486675513
ISBN-13 : 9780486675510
Rating : 4/5 (13 Downloads)

Synopsis A First Look at Perturbation Theory by : James G. Simmonds

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.

A First Look at Perturbation Theory

A First Look at Perturbation Theory
Author :
Publisher : Courier Corporation
Total Pages : 162
Release :
ISBN-10 : 9780486315584
ISBN-13 : 0486315584
Rating : 4/5 (84 Downloads)

Synopsis A First Look at Perturbation Theory by : James G. Simmonds

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.

Perturbation theory for linear operators

Perturbation theory for linear operators
Author :
Publisher : Springer Science & Business Media
Total Pages : 610
Release :
ISBN-10 : 9783662126783
ISBN-13 : 3662126788
Rating : 4/5 (83 Downloads)

Synopsis Perturbation theory for linear operators by : Tosio Kato

Perturbation Techniques in Mathematics, Engineering and Physics

Perturbation Techniques in Mathematics, Engineering and Physics
Author :
Publisher : Courier Corporation
Total Pages : 146
Release :
ISBN-10 : 0486432580
ISBN-13 : 9780486432588
Rating : 4/5 (80 Downloads)

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

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.

Introduction to Perturbation Methods

Introduction to Perturbation Methods
Author :
Publisher : Springer Science & Business Media
Total Pages : 344
Release :
ISBN-10 : 9781461253471
ISBN-13 : 1461253470
Rating : 4/5 (71 Downloads)

Synopsis Introduction to Perturbation Methods by : Mark H. Holmes

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.

Advanced Mathematical Methods for Scientists and Engineers I

Advanced Mathematical Methods for Scientists and Engineers I
Author :
Publisher : Springer Science & Business Media
Total Pages : 605
Release :
ISBN-10 : 9781475730692
ISBN-13 : 1475730691
Rating : 4/5 (92 Downloads)

Synopsis Advanced Mathematical Methods for Scientists and Engineers I by : Carl M. Bender

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Symmetry and Perturbation Theory in Nonlinear Dynamics

Symmetry and Perturbation Theory in Nonlinear Dynamics
Author :
Publisher : Springer Science & Business Media
Total Pages : 218
Release :
ISBN-10 : 9783540488743
ISBN-13 : 354048874X
Rating : 4/5 (43 Downloads)

Synopsis Symmetry and Perturbation Theory in Nonlinear Dynamics by : Giampaolo Cicogna

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.

Asymptotic Analysis

Asymptotic Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 172
Release :
ISBN-10 : 9781461211228
ISBN-13 : 1461211220
Rating : 4/5 (28 Downloads)

Synopsis Asymptotic Analysis by : J.D. Murray

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

Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals
Author :
Publisher : Courier Corporation
Total Pages : 453
Release :
ISBN-10 : 9780486650821
ISBN-13 : 0486650820
Rating : 4/5 (21 Downloads)

Synopsis Asymptotic Expansions of Integrals by : Norman Bleistein

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.

A Brief on Tensor Analysis

A Brief on Tensor Analysis
Author :
Publisher : Springer Science & Business Media
Total Pages : 124
Release :
ISBN-10 : 9781441985224
ISBN-13 : 1441985220
Rating : 4/5 (24 Downloads)

Synopsis A Brief on Tensor Analysis by : James G. Simmonds

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.