Introduction to Perturbation Methods

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapt

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapt

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the lif

Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordin

Perturbation methods are one of the fundamental tools used by all applied mathematicians and theoretical physicists. In this book, the author has managed to present the theory and techniques underlying such methods in a manner which will give the text wide appeal to students from a broad range of disciplines. Asymptotic expansions, strained coordinates and multiple scales are illustrated by copious use of examples drawn from all areas of applied mathematics and theoretical physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather to give a physical understanding of the subtle balances in a complex problem.

This book presents the basic methods of regular perturbation theory of Hamiltonian systems in an accessible fashion. It discusses all main aspects of the basic modern theory of perturbed Hamiltonian s

This book presents an introduction to singular-perturbation problems, problems which depend on a parameter in such a way that solutions behave non-uniformly as the parameter tends toward some limiting value of interest. The author considers and solves a variety of problems, mostly for ordinary differential equations. He constructs (approximate) solutions for oscillation problems, using the methods of averaging and of multiple scales. For problems of the nonoscillatory type, where solutions exhibit 'fast dynamics' in a thin initial layer, he derives solutions using the O'Malley/Hoppensteadt method and the method of matched expansions. He obtains solutions for boundary-value problems, where solutions exhibit rapid variation in thin layers, using a multivariable method. After a suitable approximate solution is constructed, the author linearizes the problem about the proposed approximate solution, and, emphasizing the use of the Banach/Picard fixed-point theorem, presents a study of the li

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, a

Perturbation Methods for Engineers and Scientists examines the main techniques of perturbation expansions applied to both differential equations and integral expressions. It describes several fluid d

This book presents an introduction to singular-perturbation problems, problems which depend on a parameter in such a way that solutions behave non-uniformly as the parameter tends toward some limiting value of interest. The author considers and solves a variety of problems, mostly for ordinary differential equations. He constructs (approximate) solutions for oscillation problems, using the methods of averaging and of multiple scales. For problems of the nonoscillatory type, where solutions exhibit 'fast dynamics' in a thin initial layer, he derives solutions using the O'Malley/Hoppensteadt method and the method of matched expansions. He obtains solutions for boundary-value problems, where solutions exhibit rapid variation in thin layers, using a multivariable method. After a suitable approximate solution is constructed, the author linearizes the problem about the proposed approximate solution, and, emphasizing the use of the Banach/Picard fixed-point theorem, presents a study of the li

Extensively tested in both academic and corporate settings, this is the ideal instructional resource for everyone new to agile development: students, software practitioners, and managers. Drawing on e

"An Introduction to Philosophical Methods is a timely, comprehensive, and accessible introduction to `metaphilosophy': the study of the nature of philosophy itself. Daly's concern is with the methods

"In combination with EEG and MR-based cortical reconstruction, MEG has considerably improved in the past ten years to become very close to the brain imager's long-awaited ideal---a non-invasive method

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.

From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena has been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyse and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another. Suitable as an upper-undergraduate textbook for mathematics students or as a fascinating, engaging, and fully illustrated resource for readers in physics and biology, Rebecca Hoyle's book, using a non-partisan approach, unifies a range of techniques used by active researchers in this growing field.

This book has been awarded the Ferran Sunyer i Balaguer 2005 prize.The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbativ

Describes numerical continuation methods that have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. These methods may be used not only t

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.