## A First Look at Perturbation TheoryEmphasizing the "why" as well as the "how," this useful and well-written introductory text explains methods for obtaining approximate solutions to mathematical problems by exploiting the presence of small, dimensionless parameters. Geared toward undergraduates in engineering and the physical sciences. Preface. Bibliography. Appendixes. |

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#### LibraryThing Review

User Review - amarcobio - LibraryThingPerturbation theory is another of these wonderful applications of Taylor series expansions, and has a tremendous importance is solving (approximately) non-linear systems. This very short book has ... Read full review

### Contents

Roots of Polynomials | 29 |

Singular Perturbations in Ordinary Differential Equations | 39 |

Periodic Solutions of the Simplest Nonlinear Differential | 45 |

Introduction to the TwoScale Method | 61 |

The WKB Approximation | 71 |

Transition Point Problems and Langers Method of Uni | 81 |

Introduction to Boundary Layer Theory | 91 |

Ancient and Modern Problems | 107 |

Bibliography | 121 |

B Proof that RN+1 O0N+1 | 127 |

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### Common terms and phrases

algebraic analysis apply approximate solution assume asymptotic expansion BC's behavior boundary layer cable calcium calculus change of variable Chapter CHEMISTRY coefficients compute damping DE's determine dimensionless domain Dover drill string equating to zero error Et(z exact solution example Exercise 5.1 exponential exponents Figure finding the roots function graph IC's implies independent variable integral interval Introduction J. P. Den Hartog linear mathematical mechanics membrane non-zero roots Nondimensionalization nonlinear obtain Ordinary Differential Equations pendulum period of oscillation Perturbation Methods perturbation theory physical Poincare's method polynomial proper values protein Pt(z quadratic formula reduces regular expansion Riemann-Lebesgue Lemma right side roots of z2 sequence singular perturbation small parameter solution of 8.83 solve spring-mass system strength of materials Substituting sufficiently small takes the form Theorem of Perturbation thermodynamics tions two-scale method uniformly valid velocity vo(t Watson's Lemma WKB approximation yields