singular perturbation theory - math and analyt technique w. appl to engineering - r. johnson

[...]... mechanics; the theory of nonlinear oscillations; control theory; the theory of semiconductors All these, and many others, have helped to develop the mathematical study of singular perturbation theory, which has, from the mid-1960s, been supported and made popular by a range of excellent text books and research papers The subject is now quite familiar to postgraduate students in applied mathematics (and related... applied mathematics (and related areas) and, to some extent, to undergraduate students who specialise in applied mathematics Indeed, it is an essential tool of the modern applied mathematician, physicist and engineer This book is based on material that has been taught, mainly by the author, to MSc and research students in applied mathematics and engineering mathematics, at the University of Newcastle... (such as Mathieu’s equation) and then, as an extension of some of the ideas already developed, the method of strained coordinates is presented One of the most general and most powerful techniques in the armoury of singular perturbation theory is the method of multiple scales This is introduced, explained and developed in Chapter 4, and then applied to a wide variety of problems These include linear and. .. is big-oh of g as or simply ‘ f is order g as As examples, we offer but also 12 1 Mathematical preliminaries finally but (Little-oh and big-oh–o and O—are usually called the Landau symbols.) (c) Asymptotically equal to or behaves like Finally, we write if the limit L, in (1.31), is precisely L = 1; then we say that ‘ f is asymptotically equal to g as or ‘ f behaves like g as Some examples are and then... these analytical approaches and techniques Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and. .. upon Tyne United Kingdom PREFACE The theory of singular perturbations has been with us, in one form or another, for a little over a century (although the term singular perturbation dates from the 1940s) The subject, and the techniques associated with it, have evolved over this period as a response to the need to find approximate solutions (in an analytical form) to complex problems Typically, such... importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful... wish to explore this aspect of mathematical analysis; there are many good texts that describe methods for solving (standard) ordinary and partial differential equations However, if the reader can accept the given solution, it will enable the main theme of singular perturbation theory to progress more smoothly Chapter 1 introduces all the mathematical preliminaries that are required for the study of singular. .. in applied mathematics or mathematical physics Thus we look at nonlinear wave propagation, supersonic flow past a thin aerofoil, solutions of Laplace’s equation, heat transfer to a fluid flowing through a pipe and an example taken from gas dynamics All these are classical problems, at some level, and are intended to show the efficacy of these techniques The chapter concludes with some applications to. .. identification and emergence of the study of inverse problems, new analytical approaches have stimulated the development of numerical techniques for the solution of this major class of practical problems Such work divides naturally into two parts, the first being the identification and formulation of inverse problems, the theory of ill-posed problems and the class of one-dimensional inverse problems, and the . x0 y0 w0 h0" alt="" SINGULAR PERTURBATION THEORY MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING Alan. Online at: http://www.springeronline.com To Ros, who still, after nearly 40 years, sometimes listens when I extol the wonders of singular perturbation theory, fluid mechanics or water waves —usually. PERTURBATION THEORY MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING R. S. JOHNSON Springer eBook ISBN: 0-3 8 7-2 321 7-6 Print ISBN: 0-3 8 7-2 320 0-1 Print ©2005 Springer Science