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Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory

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Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory Cover

 

Synopses & Reviews

Publisher Comments:

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain 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 and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader 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.

Synopsis:

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and pertubation theory for obtaining approximate analytical solutions to differential and difference equations. The presentation provides insights that will be useful approaching new problems.

Synopsis:

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.

Table of Contents

1. Asymptotic methods and perturbation theory

Product Details

ISBN:
9780387989310
Author:
Bender, Carl M.
Author:
Orszag, Steven A.
Author:
Bender, C. M.
Publisher:
Springer
Location:
New York, NY
Subject:
Science
Subject:
Physics
Subject:
Differential Equations
Subject:
Applied
Subject:
Engineering mathematics
Subject:
Difference equations
Subject:
Analysis
Subject:
Science -- Mathematics.
Subject:
Mathematical Analysis
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
mathematical methods in physics
Subject:
Numerical and Computational Physics
Subject:
Mathematics-Differential Equations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Subject:
Mathematical Physics
Copyright:
Edition Description:
Book
Series Volume:
29
Publication Date:
19991029
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
607
Dimensions:
235 x 155 mm 2270 gr

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Related Subjects

» Engineering » Engineering » Mathematics
» Reference » Science Reference » Technology
» Science and Mathematics » Mathematics » Analysis General
» Science and Mathematics » Mathematics » Applied
» Science and Mathematics » Mathematics » Differential Equations
» Science and Mathematics » Mathematics » General
» Science and Mathematics » Physics » General
» Science and Mathematics » Physics » Math

Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory New Hardcover
0 stars - 0 reviews
$108.50 In Stock
Product details 607 pages Springer - English 9780387989310 Reviews:
"Synopsis" by , This book gives a clear, practical and self-contained presentation of the methods of asymptotics and pertubation theory for obtaining approximate analytical solutions to differential and difference equations. The presentation provides insights that will be useful approaching new problems.
"Synopsis" by , 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.
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