Asymptotic Analysis and Perturbation Theory PDF Download

Author: William Paulsen
Publisher: CRC Press
ISBN: 1466515120
Category : Mathematics
Languages : en
Pages : 550

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Book Description
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: Lindsay A. Skinner
Publisher: Springer Science & Business Media
ISBN: 1441999582
Category : Mathematics
Languages : en
Pages : 85

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Book Description
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: Carl M. Bender
Publisher: Springer Science & Business Media
ISBN: 1475730691
Category : Mathematics
Languages : en
Pages : 605

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Book Description
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: 0486315584
Category : Mathematics
Languages : en
Pages : 164

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Book Description
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: J.D. Murray
Publisher: Springer Science & Business Media
ISBN: 1461211220
Category : Mathematics
Languages : en
Pages : 172

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Book Description
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: Michael Borinsky
Publisher: Springer
ISBN: 3030035417
Category : Science
Languages : en
Pages : 173

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Book Description
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: Jean Cousteix
Publisher: Springer Science & Business Media
ISBN: 3540464891
Category : Science
Languages : en
Pages : 437

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Book Description
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: W. Eckhaus
Publisher: Elsevier
ISBN: 9780080875309
Category : Mathematics
Languages : en
Pages : 286

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Book Description
Asymptotic Analysis of Singular Perturbations

Author: S. A. Lomov
Publisher: American Mathematical Soc.
ISBN: 9780821897416
Category : Mathematics
Languages : en
Pages : 402

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Book Description
This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.

Author: Takahiro Kawai
Publisher: American Mathematical Soc.
ISBN: 9780821835470
Category : Mathematics
Languages : en
Pages : 148

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Book Description
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.