Description
Taylor & Francis Asymptotic Analysis and Perturbation Theory 2013 Edition by William Paulsen
Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge of differential equations. It explains the exact solution of only the simplest differential equations, such as first-order linear and separable equations. With varying levels of problems in each section, this self-contained text makes the difficult subject of asymptotics easy to comprehend. Along the way, it explores the properties of some important functions in applied mathematics. Although the book emphasizes problem solving, some proofs are scattered throughout to give readers a justification for the methods used. Table of contents :- 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