Author : Alan W. Bush
Publisher : CRC-Press
Page : 320 pages
File Size : 49,14 MB
Release : 1992-01-21
Category : Computers
ISBN : 9780849386145
This text provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Computer programs are included to enable students to explore particular ideas, as well as realistic case studies of industrial applications.
Author : Alan W. Bush
Publisher : CRC Press
Page : 326 pages
File Size : 49,14 MB
Release : 1992-02-03
Category : Mathematics
ISBN : 9780849386084
Perturbation Methods for Engineers and Scientists examines the main techniques of perturbation expansions applied to both differential equations and integral expressions. It describes several fluid dynamics applications, including aerofoils, boundary layers in momentum heat, and mass transfer. In addition, it applies the multiple scale technique to the description of surface roughness effects in lubrication. The book's intuitive, rather than formal, approach enables these advanced techniques to be used by scientists and engineers as well as by students.
Author : Reza N. Jazar
Publisher : Springer Nature
Page : 584 pages
File Size : 42,79 MB
Release : 2021-07-12
Category : Technology & Engineering
ISBN : 3030734625
Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.
Author : Carl M. Bender
Publisher : Springer Science & Business Media
Page : 605 pages
File Size : 30,77 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475730691
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 : Anatoli V. Skorokhod
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 14,49 MB
Release : 2007-06-21
Category : Mathematics
ISBN : 0387224467
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.
Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,30 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461253470
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 : J. Kevorkian
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 29,77 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475742134
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.
Author : Ali H. Nayfeh
Publisher : John Wiley & Sons
Page : 437 pages
File Size : 17,37 MB
Release : 2008-09-26
Category : Science
ISBN : 3527617612
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research
Author : Richard Ernest Bellman
Publisher : Courier Corporation
Page : 146 pages
File Size : 14,50 MB
Release : 2003-01-01
Category : Science
ISBN : 9780486432588
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.
Author : AlanW. Bush
Publisher : Routledge
Page : 265 pages
File Size : 40,35 MB
Release : 2018-05-04
Category : Mathematics
ISBN : 1351425358
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.
