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.


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.

Perturbation Methods in Applied Mathematics

Author: Jirair Kevorkian
Publisher: Springer Science & Business Media
ISBN: 9781475742138
Release Date: 2013-03-09
Genre: Mathematics

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.

Perturbation Methods for Engineers and Scientists

Author: AlanW. Bush
Publisher: Routledge
ISBN: 9781351425353
Release Date: 2018-05-04
Genre: Mathematics

The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.

Applied Asymptotic Analysis

Author: Peter David Miller
Publisher: American Mathematical Soc.
ISBN: 9780821840788
Release Date: 2006
Genre: Mathematics

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.

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.

Methods of Mathematical Physics

Author: Harold Jeffreys
Publisher: Cambridge University Press
ISBN: 0521664020
Release Date: 1999-11-18
Genre: Mathematics

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

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.

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.

Mathematical Methods for Science Students

Author: Geoffrey Stephenson
Publisher: Prentice Hall
ISBN: 0582444160
Release Date: 1973-01-01
Genre: Calculus

This well-known and widely recommended textbook provides an essential basis of mathematical techniques for engineers, physicists, chemists and management scientists at undergraduate level. The material is suitable for the first two years of a typical University or Polytechnic course, and it is developed assuming only an elementary knowledge of pre-University mathematics. The text includes a large number of worked examples, and there is a selection of unworked problems at the end of each chapter.

Perturbation methods

Author: 欣奇
ISBN: 7506282240
Release Date: 1991
Genre: Perturbation (Mathematics).