A First Look At Perturbation Theory

Author: James G. Simmonds
Publisher: Courier Corporation
ISBN: 0486315584
Size: 65.95 MB
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This introductory text explains methods for obtaining approximate solutions to mathematical problems by exploiting the presence of small, dimensionless parameters. For engineering and physical science undergraduates.

Introduction To Perturbation Theory In Quantum Mechanics

Author: Francisco M. Fernandez
Publisher: CRC Press
ISBN: 1420039644
Size: 64.92 MB
Format: PDF, Kindle
View: 5565
Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation Introduction to Perturbation Theory in Quantum Mechanics does. It collects into a single source most of the techniques for applying the theory to the solution of particular problems. Concentrating on problems that allow exact analytical solutions of the perturbation equations, the book resorts to numerical results only when necessary to illustrate and complement important features of the theory. The author also compares different methods by applying them to the same models so that readers clearly understand why one technique may be preferred over another. Demonstrating the application of similar techniques in quantum and classical mechanics, Introduction to Perturbation Theory in Quantum Mechanics reveals the underlying mathematics in seemingly different problems. It includes many illustrative examples that facilitate the understanding of theoretical concepts, and provides a source of ideas for many original research projects.

Advanced Mathematical Methods For Scientists And Engineers I

Author: Carl M. Bender
Publisher: Springer Science & Business Media
ISBN: 1475730691
Size: 75.16 MB
Format: PDF, Mobi
View: 7746
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 A. Murdock
Publisher: SIAM
ISBN: 9781611971095
Size: 74.54 MB
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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.

Perturbation Techniques In Mathematics Engineering And Physics

Author: Richard Ernest Bellman
Publisher: Courier Corporation
ISBN: 9780486432588
Size: 13.50 MB
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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

Author: Mark H. Holmes
Publisher: Springer Science & Business Media
ISBN: 1461454778
Size: 12.73 MB
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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. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

Wave Phenomena

Author: Dudley H. Towne
Publisher: Courier Dover Publications
ISBN: 0486145158
Size: 30.86 MB
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View: 2896
Brilliantly written undergraduate-level text emphasizes optics, acoustics; covers transverse waves on a string, acoustic plane waves, boundary-value problems, much more. Numerous problems (half with solutions).

Quantum Mechanics For Applied Physics And Engineering

Author: Albert T. Fromhold
Publisher: Courier Corporation
ISBN: 0486164691
Size: 73.17 MB
Format: PDF, ePub, Mobi
View: 550
For upper-level undergraduates and graduate students: an introduction to the fundamentals of quantum mechanics, emphasizing aspects essential to an understanding of solid-state theory. Numerous problems (and selected answers), projects, exercises.

Perturbation Methods In Applied Mathematics

Author: Jirair Kevorkian
Publisher: Springer Science & Business Media
ISBN: 1475742134
Size: 51.20 MB
Format: PDF, Docs
View: 7699
This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate level course on the subject. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.