Introduction to Perturbation Techniques,9780471310136

Introduction to Perturbation Techniques

by
Edition: 1st
ISBN13: 9780471310136
ISBN10: 0471310131
Format: Paperback
Pub. Date: 1993-08-20
Publisher(s): Wiley-VCH
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Summary

Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.

Author Biography

Ali H. Nayfeh received his BS in engineering science and his MS and PhD in aeronautics and astronautics from Stanford University. He holds honorary doctorates from Marine Technical University, Russia, Technical University of Munich, Germany, and Politechnika Szczecinska, Poland. He is currently University Distinguished Professor of Engineering at Virginia Tech. He is the Editor of the Wiley Series in Nonlinear Science and Editor in Chief of Nonlinear Dynamics and the Journal of Vibration and Control.

Table of Contents

Introduction
1(27)
Dimensional Analysis
1(9)
Expansions
10(2)
Gauge Functions
12(5)
Order Symbols
17(1)
Asymptotic Series
18(4)
Asymptotic Expansions and Sequences
22(1)
Convergent Versus Asymptotic Series
23(1)
Elementary Operations on Asymptotic Expansions
24(4)
Exercises
24(4)
Algebraic Equations
28(23)
Quadratic Equations
28(11)
Cubic Equations
39(4)
Higher-Order Equations
43(2)
Transcendental Equations
45(6)
Exercises
48(3)
Integrals
51(56)
Expansion of Integrands
52(4)
Integration by Parts
56(9)
Laplace's Method
65(14)
The Method of Stationary Phase
79(9)
The Method of Steepest Descent
88(19)
Exercises
101(6)
The Duffing Equation
107(27)
The Straightforward Expansion
109(4)
Exact Solution
113(5)
The Lindstedt-Poincare Technique
118(3)
The Method of Renormalization
121(1)
The Method of Multiple Scales
122(5)
Variation of Parameters
127(2)
The Method of Averaging
129(5)
Exercises
131(3)
The Linear Damped Oscillator
134(13)
The Straightforward Expansion
135(1)
Exact Solution
136(3)
The Lindstedt-Poincare Technique
139(3)
The Method of Multiple Scales
142(2)
The Method of Averaging
144(3)
Exercises
146(1)
Self-Excited Oscillators
147(12)
The Straightforward Expansion
148(3)
The Method of Renormalization
151(1)
The Method of Multiple Scales
152(3)
The Method of Averaging
155(4)
Exercises
157(2)
Systems with Quadratic and Cubic Nonlinearities
159(18)
The Straightforward Expansion
160(2)
The Method of Renormalization
162(2)
The Lindstedt-Poincare Technique
164(2)
The Method of Multiple Scales
166(2)
The Method of Averaging
168(1)
The Generalized Method of Averaging
169(4)
The Krylov-Bogoliubov-Mitropolsky Technique
173(4)
Exercises
175(2)
General Weakly Nonlinear Systems
177(13)
The Straightforward Expansion
177(2)
The Method of Renormalization
179(2)
The Method of Multiple Scales
181(1)
The Method of Averaging
182(2)
Applications
184(6)
Exercises
188(2)
Forced Oscillations of the Duffing Equation
190(26)
The Straightforward Expansion
191(2)
The Method of Multiple Scales
193(16)
Secondary Resonances
193(12)
Primary Resonance
205(4)
The Method of Averaging
209(7)
Secondary Resonances
209(3)
Primary Resonance
212(1)
Exercises
213(3)
Multifrequency Excitations
216(18)
The Straightforward Expansion
216(3)
The Method of Multiple Scales
219(7)
The Case ω2 + ω1 ≈ 1
220(2)
The Case ω2 - ω1 ≈ 1 and ω1 ≈ 2
222(4)
The Method of Averaging
226(8)
The Case ω1 + ω2 ≈ 1
230(1)
The Case ω2 - ω1 ≈ 1 and ω1 ω2
230(1)
Exercises
230(4)
The Mathieu Equation
234(23)
The Straightforward Expansion
235(1)
The Floquet Theory
236(7)
The Method of Strained Parameters
243(4)
Whittaker's Method
247(2)
The Method of Multiple Scales
249(4)
The Method of Averaging
253(4)
Exercises
254(3)
Boundary-Layer Problems
257(68)
A Simple Example
257(11)
The Method of Multiple Scales
268(2)
The Method of Matched Asymptotic Expansions
270(9)
Higher Approximations
279(5)
Equations with Variable Coefficients
284(12)
Problems with Two Boundary Layers
296(8)
Multiple Decks
304(3)
Nonlinear Problems
307(18)
Exercises
320(5)
Linear Equations with Variable Coefficients
325(35)
First-Order Scalar Equations
326(3)
Second-Order Equations
329(2)
Solutions Near Regular Singular Points
331(11)
Singularity at Infinity
342(2)
Solutions Near an Irregular Singular Point
344(16)
Exercises
355(5)
Differential Equations with a Large Parameter
360(28)
The WKB Approximation
361(3)
The Liouville-Green Transformation
364(2)
Eigenvalue Problems
366(3)
Equations with Slowly Varying Coefficients
369(1)
Turning-Point Problems
370(5)
The Langer Transformation
375(4)
Eigenvalue Problems with Turning Points
379(9)
Exercises
383(5)
Solvability Conditions
388(84)
Algebraic Equations
389(5)
Nonlinear Vibrations of Two-Degree-of-Freedom Gyroscopic Systems
394(3)
Parametrically Excited Gyroscopic Systems
397(4)
Second-Order Differential Systems
401(5)
General Boundary Conditions
406(6)
A Simple Eigenvalue Problem
412(2)
A Degenerate Eigenvalue Problem
414(4)
Acoustic Waves in a Duct with Sinusoidal Walls
418(8)
Vibrations of Nearly Circular Membranes
426(6)
A Fourth-Order Differential System
432(6)
General Fourth-Order Differential Systems
438(3)
A Fourth-Order Eigenvalue Problem
441(4)
A Differential System of Equations
445(2)
General Differential Systems of First-Order Equations
447(5)
Differential Systems with Interfacial Boundary Conditions
452(2)
Integral Equations
454(4)
Partial-Differential Equations
458(14)
Exercises
462(10)
Appendix A Trigonometric Identities 472(8)
Appendix B Linear Ordinary-Differential Equations 480(21)
Bibliography 501(6)
Index 507

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