## Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation TheoryThis book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

II | 3 |

III | 5 |

IV | 7 |

V | 11 |

VI | 14 |

VII | 20 |

VIII | 24 |

IX | 27 |

XLV | 276 |

XLVI | 280 |

XLVII | 302 |

XLVIII | 306 |

XLIX | 319 |

L | 324 |

LI | 330 |

LII | 335 |

X | 29 |

XI | 30 |

XII | 36 |

XIII | 37 |

XIV | 40 |

XV | 49 |

XVI | 53 |

XVIII | 61 |

XIX | 62 |

XX | 66 |

XXI | 68 |

XXII | 76 |

XXIII | 88 |

XXIV | 103 |

XXV | 107 |

XXVI | 118 |

XXVII | 136 |

XXVIII | 146 |

XXIX | 148 |

XXX | 152 |

XXXI | 171 |

XXXII | 185 |

XXXIII | 196 |

XXXIV | 205 |

XXXV | 206 |

XXXVI | 214 |

XXXVII | 218 |

XXXVIII | 227 |

XXXIX | 233 |

XL | 240 |

XLI | 247 |

XLII | 249 |

XLIII | 252 |

XLIV | 261 |

### Other editions - View all

### Common terms and phrases

analysis analytic approach approximation assume asymptotic approximation asymptotic behavior asymptotic expansion asymptotic series becomes boundary conditions boundary layer Clue coefficients compared complex compute consider constant continuous contour convergence correct critical point curves defined derive determine difference equation differential equation discussion eigenvalues error exact solution Example exists exponentially expression factor Figure finite formula function given gives homogeneous independent initial inner integral irregular singular point leading behavior limit linear local analysis matching method nonlinear Note Observe obtain origin Padé approximants parameter perturbation plane plot poles positive possible Prob problem prove radius of convergence region regular relation replace representation require result roots satisfies sequence Show simple solve Substituting Table Taylor series theory tion trajectories transformation valid values vanishes verify