Advanced Mathematical Methods for Scientists and Engineers I

Author: Carl M. Bender
Publisher: Springer Science & Business Media
ISBN: 9781475730692
Release Date: 2013-03-09
Genre: Mathematics

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.

Advanced Mathematical Methods for Scientists and Engineers I

Author: Carl M. Bender
Publisher: Springer Science & Business Media
ISBN: 0387989315
Release Date: 1999-10-29
Genre: Mathematics

This book gives 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. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form. The presentation provides insights that will be useful in approaching new problems.

Introduction to Perturbation Methods

Author: Mark H. Holmes
Publisher: Springer Science & Business Media
ISBN: 0387942033
Release Date: 1998-06-19
Genre: Mathematics

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.

A First Look at Perturbation Theory

Author: James G. Simmonds
Publisher: Courier Corporation
ISBN: 9780486315584
Release Date: 2013-07-04
Genre: Mathematics

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.


Author: James A. Murdock
Publisher: SIAM
ISBN: 1611971098
Release Date: 1999-01-01
Genre: Perturbation

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.

Asymptotic Expansions of Integrals

Author: Norman Bleistein
Publisher: Courier Corporation
ISBN: 9780486650821
Release Date: 1975
Genre: Mathematics

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.

Asymptotic Analysis of Differential Equations

Author: R. B. White
Publisher: World Scientific
ISBN: 9781848166080
Release Date: 2010
Genre: Mathematics

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

Mathematics Applied to Deterministic Problems in the Natural Sciences

Author: C. C. Lin
Publisher: SIAM
ISBN: 1611971349
Release Date: 1988
Genre: Mathematics

Addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences. The authors' case studies approach leads to excitement in teaching realistic problems. The many problems and exercises reinforce, test and extend the reader's understanding. This reprint volume may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers working on fluid mechanics, elasticity, perturbation methods, dimensional analysis, numerical analysis, continuum mechanics and differential equations.

Asymptotic Analysis

Author: J.D. Murray
Publisher: Springer Science & Business Media
ISBN: 9781461211228
Release Date: 2012-12-06
Genre: Mathematics

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

Worked Problems in Applied Mathematics

Author: Nikola-I Nikolaevich and Lebedev
Publisher: Courier Corporation
ISBN: 0486637301
Release Date: 1979
Genre: Mathematics

These 566 problems plus answers cover a wide range of topics in an accessible manner, including steady-state harmonic oscillations, Fourier method, integral transforms, curvilinear coordinates, integral equations, and more. 1965 edition.

Asymptotic Approximations of Integrals

Author: R. Wong
Publisher: Academic Press
ISBN: 9781483220710
Release Date: 2014-05-10
Genre: Mathematics

Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

Boundary Value Problems of Mathematical Physics

Author: Ivar Stakgold
Publisher: SIAM
ISBN: 9781611972382
Release Date: 2000-06-30

For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.

Asymptotic Methods in Mechanics

Author: RŽmi Vaillancourt
Publisher: American Mathematical Soc.
ISBN: 0821870262
Release Date: 1993-12-21
Genre: Technology & Engineering

Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.

Perturbation Techniques in Mathematics Engineering and Physics

Author: Richard Ernest Bellman
Publisher: Courier Corporation
ISBN: 0486432580
Release Date: 2003
Genre: Science

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.