Perturbation Methods for Engineers and Scientists

Content: Cover
 Half Title
 Title Page
 Copyright Page
 Dedication
 Table of Contents
 Preface
 1: Introduction to Perturbation Expansions
 1.1 Model problem. Resisted motion of a particle
 A perturbation expansion
 The exact solution
 1.2 Roots of polynomials
 Regular and singular perturbation expansions
 Exercises
 1.3 Initial value problems
 Exercises
 1.4 Expansions involving the independent variable
 Convergent and divergent series
 Asymptotic series
 Optimum truncation rule
 The error function
 Comparison with a convergent series
 Exercises
 2: Asymptotics
 2.1 Order symbols
 Gauge functions L'Hospital's ruleTaylor's formula with remainder
 Properties of order symbols
 Exercises
 Behavior of logarithmic and exponential functions
 2.2 Asymptotic sequences and expansions
 Exercise
 Uniqueness
 Maclaurin series are asymptotic expansions
 2.3 Uniform and nonuniform expansions
 Region of nonuniformity
 Exercises
 2.4 Sources of nonuniformity
 Infinite domains
 Small parameter multiplying the highest derivative
 3 Strained Coordinates
 3.1 The Lindstedt-Poincare technique
 Model problem
 3.2 Duifing's equation
 The pendulum
 A mass and spring oscillator Solutions of Duffing's equation using the Lindstedt-Poincare techniqueExercise
 3.3 Lighthill's technique
 Renormalization
 Shift in the singularity of a differential equation
 Exercise
 Application to nonlinear oscillators
 An example of the failure of renormalization
 Exercises
 3.4 Flow past an aerofoil
 The complex potential
 The parabolic aerofoil
 Comparison with the exact solution
 The elliptic aerofoil
 Comparison with the exact solution
 4: Multiple Scales
 4.1 Second order systems
 The phase plane
 Nonlinear autonomous systems and limit cycles
 4.2 Limitation of renormalization Perturbations which cause a time-changing amplitude4.3 The method of multiple scales
 Time scales
 Van der Pol oscillator
 Exercises
 4.4 Surface roughness effects in lubricated bearings
 Reynolds equation
 Surface roughness
 Average Reynolds equation
 Effect of roughness on the average pressure distribution
 4.5 The method of averaging: the Krylov-Bogoliubov technique
 5: Boundary layers
 5.1 Model problem
 The stretched variable and inner expansion
 Prandtl's matching condition
 The composite expansion
 5.3 Boundary layer thickness and the principle of least degeneracy A boundary layer of 0{^e)An interior boundary layer
 5.2 Boundary layer location
 The general linear equation
 Exercises
 5.4 Higher order matching
 Exercises
 5.5 Nonlinear examples
 Exercises
 5.6 Practical applications
 Peclet and Reynolds numbers
 Flow between parallel planes with heat transfer
 Heat transfer rate
 The finite difference solution
 Exercise
 Estimation of boundary layer thickness
 The Prandtl number
 Exercise
 A remark on turbulence
 The boundary integral equation method
 Prandtl's momentum boundary layer equations
 The partial differential equation method