Asymptotic Analysis And Perturbation Theory

Author : William Paulsen
Publisher : CRC Press
ISBN 13 : 1466515120
Total Pages : 546 pages
Book Rating : 4.23/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Analysis and Perturbation Theory written by William Paulsen and published by CRC Press. This book was released on 2013-07-18 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge o

Author : Carl M. Bender
Publisher : Springer Science & Business Media
ISBN 13 : 1475730691
Total Pages : 605 pages
Book Rating : 4.92/5 ( download)

DOWNLOAD NOW!

Download or read book Advanced Mathematical Methods for Scientists and Engineers I written by Carl M. Bender and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : James G. Simmonds
Publisher : Courier Corporation
ISBN 13 : 0486315584
Total Pages : 162 pages
Book Rating : 4.84/5 ( download)

DOWNLOAD NOW!

Download or read book A First Look at Perturbation Theory written by James G. Simmonds and published by Courier Corporation. This book was released on 2013-07-04 with total page 162 pages. 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.

Author : Lindsay A. Skinner
Publisher : Springer Science & Business Media
ISBN 13 : 1441999582
Total Pages : 95 pages
Book Rating : 4.80/5 ( download)

DOWNLOAD NOW!

Download or read book Singular Perturbation Theory written by Lindsay A. Skinner and published by Springer Science & Business Media. This book was released on 2011-05-11 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.

Author : J.D. Murray
Publisher : Springer Science & Business Media
ISBN 13 : 1461211220
Total Pages : 172 pages
Book Rating : 4.28/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Analysis written by J.D. Murray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Tosio Kato
Publisher : Springer Science & Business Media
ISBN 13 : 3662126788
Total Pages : 610 pages
Book Rating : 4.83/5 ( download)

DOWNLOAD NOW!

Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Takahiro Kawai
Publisher : American Mathematical Soc.
ISBN 13 : 9780821835470
Total Pages : 148 pages
Book Rating : 4.75/5 ( download)

DOWNLOAD NOW!

Download or read book Algebraic Analysis of Singular Perturbation Theory written by Takahiro Kawai and published by American Mathematical Soc.. This book was released on 2005 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This volume is suitable for graduate students and researchers interested in differential equations and special functions.

Author : Jean Cousteix
Publisher : Springer Science & Business Media
ISBN 13 : 3540464891
Total Pages : 437 pages
Book Rating : 4.91/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Analysis and Boundary Layers written by Jean Cousteix and published by Springer Science & Business Media. This book was released on 2007-03-22 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael Borinsky
Publisher : Springer
ISBN 13 : 3030035417
Total Pages : 173 pages
Book Rating : 4.19/5 ( download)

DOWNLOAD NOW!

Download or read book Graphs in Perturbation Theory written by Michael Borinsky and published by Springer. This book was released on 2018-11-04 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.

Author : White Roscoe B
Publisher : World Scientific
ISBN 13 : 1911298593
Total Pages : 432 pages
Book Rating : 4.95/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Analysis Of Differential Equations (Revised Edition) written by White Roscoe B and published by World Scientific. This book was released on 2010-08-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.