عنوان

Asymptotic analysis and perturbation theory

1466515112

1466515120

9781466515116

9781466515123

b551467

Asymptotic analysis and perturbation theory

[Book]

William Paulsen.

Boca Raton

CRC Press

2014

Introduction to Asymptotics Basic DefinitionsLimits via Asymptotics Asymptotic Series Inverse Functions Dominant Balance Asymptotics of Integrals Integrating Taylor Series Repeated Integration by Parts Laplace's MethodReview of Complex NumbersMethod of Stationary Phase Method of Steepest DescentsSpeeding Up Convergence Shanks Transformation Richardson Extrapolation Euler Summation Borel Summation Continued Fractions Pade ApproximantsDifferential Equations Classification of Differential EquationsFirst Order EquationsTaylor Series Solutions Frobenius Method Asymptotic Series Solutions for Differential Equations Behavior for Irregular Singular Points Full Asymptotic Expansion Local Analysis of Inhomogeneous Equations Local Analysis for Nonlinear EquationsDifference Equations Classification of Difference EquationsFirst Order Linear EquationsAnalysis of Linear Difference EquationsThe Euler-Maclaurin FormulaTaylor-Like and Frobenius-Like Series ExpansionsPerturbation Theory Introduction to Perturbation Theory Regular Perturbation for Differential Equations Singular Perturbation for Differential Equations Asymptotic MatchingWKBJ Theory The Exponential Approximation Region of Validity Turning PointsMultiple-Scale Analysis Strained Coordinates Method (Poincare-Lindstedt) The Multiple-Scale Procedure Two-Variable Expansion Method Appendix: Guide to the Special Functions Answers to Odd-Numbered Problems Bibliography Index

Differential equations -- Asymptotic theory -- Textbooks.

Differential equations -- Asymptotic theory.

Perturbation (Mathematics) -- Textbooks.

William Paulsen.

William Paulsen

[Book]

Y