Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining appro ximate analytical solutions to differential and difference equations. These methods allow one to analyze problems that are encountered in ph ysics and engineering that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutio ns. The presentation is aimed at teaching the insights that are most u seful in approaching new problems; it avoids special methods and trick s that work only for particular problems, such as the traditional tran scendental functions.