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About this book :-
Perturbation Method for Engineers and Scientist written by
Alan W. Bush .
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. In some areas such as boundary layers it provides the essential ideas of scaling of regions of rapid change which must be understood before an appropriate discretization can be constructed. The book is aimed at students in applied mathematics, engineering, industrial mathematics, fluid mechanics and computational mechanics.
The purpose of this book is to describe the application of perturbation expansion techniques to the solution of differential equations and the approximation of integrals. Approximate expressions are generated in the form of asymptotic series. These may not and often do not converge but, in a truncated form of only two or three terms, provide a useful approximation to the original problem.
The techniques, being analytical rather than numerical, provide an alternative to a direct computer solution. An awareness of the perturbation approach is sometimes essential even when a direct numerical approach is adopted. An example of this occurs in boundary layer problems where there are regions of rapid change of quantities such as fluid velocity, temperature or concentration. Appropriate scaling of the boundary layer dimension is required before a numerical solution can be generated which will capture the behavior in the rapidly changing region.
The material is based on lectures given at Teesside Polytechnic as part of the Master’s Degree in Applicable Mathematics. The main techniques with some of the applications are taught in a course of sixty hours duration. The book can be used at advanced undergraduate or postgraduate level.
Students, teachers and researchers in applied and engineering mathematics should find this book of help in gaining an understanding of most of the powerful perturbation techniques along with their applications. The essential prerequisite knowledge is usually gained by the end of the first year mathematical methods course in an engineering or mathematics degree. Specifically the reader is assumed to be familiar with the elementary techniques for solving first order differential equations and second order constant coefficient equations.
The perturbation methods for differential equations are explained using simple ‘model’ ordinary differential equations. The motivation for developing the methods is the need to deal with more complicated, often nonlinear, ordinary and partial differential equations. Applications to these problems are presented. To fully appreciate some of the partial differential equation examples a knowledge of the governing equations of fluid mechanics and heat transport are required. Readers unfamiliar with these subjects may either take the formulation of the problems for granted and follow the mathematical techniques, or the material may be omitted without impeding their understanding of later material.
Book Detail :-
Title: Perturbation Method for Engineers and Scientist
Edition:
Author(s): Alan W. Bush
Publisher: CRC Press;Routledge
Series:
Year: 2017
Pages: 316
Type: PDF
Language: English
ISBN: 9780849386084,084938608X,9781351425360,1351425366
Country: UK
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About Author :-
Alan W. Bush, is from the School of Computing and Mathematics, Teesside Polytechnic, Middlesbrough, U.K.
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Perturbation Method for Engineers and Scientist written by
Alan W. Bush
cover the following topics.
Introduction to Perturbation Expansions
Set Theory
Asymptotics
Strained Coordinates
Multiple Scales
Boundary layers
The dominant balance and WKB Methods
the Asymptotic Approximation of intagrals
Refrences
Bibiliography
Index
Note:-
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