A First Look at Perturbation Theory / Edition 2

A First Look at Perturbation Theory / Edition 2

by James G. Simmonds, Physics
     
 

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ISBN-10: 0486675513

ISBN-13: 9780486675510

Pub. Date: 07/10/1997

Publisher: Dover Publications

Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the

Overview

Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way.
The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume.
Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.

Product Details

ISBN-13:
9780486675510
Publisher:
Dover Publications
Publication date:
07/10/1997
Series:
Dover Books on Physics Series
Edition description:
REVISED
Pages:
160
Product dimensions:
5.41(w) x 8.45(h) x 0.33(d)

Table of Contents

Contents

Preface,
1 Introduction and Overview,
2 Roots of Polynomials,
3 Singular Perturbations in Ordinary Differential Equations,
4 Periodic Solutions of the Simplest Nonlinear Differential Equations. Poincaré's Method,
5 Introduction to the Two-Scale Method,
6 The WKB Approximation,
7 Transition Point Problems and Langer's Method of Uniform Approximation,
8 Introduction to Boundary Layer Theory,
9 Cables and Cells: Ancient and Modern Problems,
Bibliography,
A Roots of T[member of](z)and T0(z),
B Proof that RN+1 = O(βN+1),
C Approximate Evaluation of Integrals,

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