## Perturbation methods in applied mathematics |

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### Contents

Twovariable expansion procedures | 79 |

Applications to partial differential equations | 120 |

Derivation of approximate equations Several parameters | 222 |

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amplitude approximate equations assumed asymptotic expansion asymptotic sequence behavior body boundary condition Equation boundary layer boundary-layer equations boundary-value problem characteristic coefficients consider const constants of integration constructed coordinates corresponding curl curl curl curves decay dimensionless discussed distinguished limit dx dx elasticity equation Equation exact solution example expansion Equation expansion procedure expansion valid exponential exponential decay expressed Figure fixed fluid functions ideas initial conditions inner and outer inner expansion integral of Equation intermediate limit inviscid limit cycle limit process method motion Navier-Stokes equations nonlinear obtained ordinary differential equations outer expansion outer solution partial differential equations periodic solution perturbation phase plane piston potential flow pressure result right-hand side satisfy the boundary Section shock waves side of Equation singular Singular perturbation small parameter solution of Equation subcharacteristic suitable surface theory tion transcendentally small transonic uniformly valid upstream infinity variables viscous vorticity zero