Share

Perturbations

1999-01-01 Mathematics
Download Perturbations PDF Online Free

Author :
Release : 1999-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 095/5 ( reviews)

GET EBOOK


Book Synopsis Perturbations by : James A. Murdock

Download or read book Perturbations written by James A. Murdock. This book was released on 1999-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

A First Look at Perturbation Theory

2013-07-04 Mathematics
Download A First Look at Perturbation Theory PDF Online Free

Author :
Release : 2013-07-04
Genre : Mathematics
Kind : eBook
Book Rating : 584/5 ( reviews)

GET EBOOK


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

Download or read book A First Look at Perturbation Theory written by James G. Simmonds. This book was released on 2013-07-04. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Theory of Singular Perturbations

1996-11-08 Mathematics
Download The Theory of Singular Perturbations PDF Online Free

Author :
Release : 1996-11-08
Genre : Mathematics
Kind : eBook
Book Rating : 751/5 ( reviews)

GET EBOOK


Book Synopsis The Theory of Singular Perturbations by : E.M. de Jager

Download or read book The Theory of Singular Perturbations written by E.M. de Jager. This book was released on 1996-11-08. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.

Singular Perturbations I

1990-08-16 Mathematics
Download Singular Perturbations I PDF Online Free

Author :
Release : 1990-08-16
Genre : Mathematics
Kind : eBook
Book Rating : 440/5 ( reviews)

GET EBOOK


Book Synopsis Singular Perturbations I by : L.S. Frank

Download or read book Singular Perturbations I written by L.S. Frank. This book was released on 1990-08-16. Available in PDF, EPUB and Kindle. Book excerpt: Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.

Random Perturbations of Dynamical Systems

2012-12-06 Mathematics
Download Random Perturbations of Dynamical Systems PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 769/5 ( reviews)

GET EBOOK


Book Synopsis Random Perturbations of Dynamical Systems by : M. I. Freidlin

Download or read book Random Perturbations of Dynamical Systems written by M. I. Freidlin. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.

You may also like...