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The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.
(source: Nielsen Book Data)

• Preface--
• 1. Introduction and motivation-- Part I. Finite Dimensional Perturbations:
• 2. Inversion of analytically perturbed matrices--
• 3. Perturbation of null spaces, eigenvectors, and generalized inverses--
• 4. Polynomial perturbation of algebraic nonlinear systems-- Part II. Applications to Optimization and Markov Process:
• 5. Applications to optimization--
• 6. Applications to Markov chains--
• 7. Applications to Markov decision processes-- Part III. Infinite Dimensional Perturbations:
• 8. Analytic perturbation of linear operators--
• 9. Background on Hilbert spaces and Fourier analysis-- Bibliography-- Index.
• (source: Nielsen Book Data)

Mathematical models, vital to our understanding of complex phenomena, typically depend on parameters that are assigned nominal values based on current understanding of the system in question. As these values are usually estimates, it is important to know how even small perturbations of them affect the behavior of the model. This book considers systems that can be disturbed to varying degrees by changing the value of a single perturbation parameter. It includes comprehensive treatment of analytic perturbations of matrices and linear operators, particularly the singular perturbation of inverses, generalized inverses, and polynomial systems. It also presents original applications to topics that include Markov decision processes, optimisation, search engine rankings, and the Hamiltonian cycle problem. This text is appropriate for pure and applied mathematicians and engineers interested in systems and control. Every chapter includes a problem section, making it suitable for a graduate course in perturbation theory.
(source: Nielsen Book Data)

• Introduction. General survey Part I.Asymptotic integration of various problems for ordinary differential euqaitons:: The method of regularization of singular perturbations Asymptotic integratin of a boundary value problem Asymptotic integration of linear integro-differential equations-- Some problems with rapidly oscillating coefficients Problems with an unstable spectrum Singularly perturbed problems for nonlinear equations Part II.Singularly perturbed partial differential equations:: Asymptotic integration of linear parabolic equations Application of the regularization method to some elliptic problems in a cylindrical domain Asymptotic integration of some singularly perturbed evolution equations.
• (source: Nielsen Book Data)

This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects, and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.
(source: Nielsen Book Data)

• INTRODUCTION TO PERTURBATION EXPANSIONS Model Problem. Resisted Motion of a Particle Roots of Polynomials Initial Value Problems Expansions Involving the Independent Variable ASYMPTOTICS Order Symbols Asymptotic Sequences and Expansions Uniform and Non-Uniform Expansions Sources of Non-Uniformity STRAINED CO-ORDINATES The Lindstedt-Poincare Technique Duffing's Equation Lighthill's Technique Flow Past an Aerofoil. MULTIPLE SCALES Second Order Systems Limitation of Renormalization The Method of Multiple Scales Surface Roughness Effects in Lubricated Bearings The Method of Averaging: the Krylov-Bogoliubov Technique. BOUNDARY LAYERS Model Problem Boundary Layer Location Boundary Layer Thickness and the Principle of Least Degeneracy Higher Order Matching Non-Linear Examples. Practical Applications THE DOMINANT BALANCE AND WKB METHODS Frobenius Series The Method of Dominant Balance The WKB Method Eigenvalue Problems Turning Points THE ASYMPTOTIC APPROXIMATION OF INTEGRALS The Region of Dominant Contribution Watson's Lemma Extensions of Watson's Lemma Laplace's Method The Reimann-Lebesque Lemma The Method of Stationary Phase Bessel and Airy Functions REFERENCES BIBLIOGRAPHY INDEX Catalog no. 8608 1992, 320 pp., ISBN: 0-8493-8608-X $104.95 / GBP65.99 Short TOC.
• (source: Nielsen Book Data)

• Introduction to perturbation expansions-- asymptotics-- strained coordinates-- multiple scales-- boundary layers-- the dominant balance and WKB methods-- asymptotic approximation of integrals.
• (source: Nielsen Book Data)

"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 dynamics applications, including aerofoils, boundary layers in momentum heat, and mass transfer. In addition, it applies the multiple scale technique to the description of surface roughness effects in lubrication. The book's intuitive, rather than formal, approach enables these advanced techniques to be used by scientists and engineers as well as by students.
(source: Nielsen Book Data)
The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.
(source: Nielsen Book Data)

• Preface--
• 1. Algebraic equations--
• 2. Asymptotic expansions--
• 3. Integrals--
• 4. Regular problems in PDEs--
• 5. Matched asymptotic expansions--
• 6. Method of strained coordinates--
• 7. Method of multiple scales--
• 8. Improved convergence-- Bibliography-- Index.
• (source: Nielsen Book Data)

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.
(source: Nielsen Book Data)

• INTRODUCTION TO PERTURBATION THEORY-- Root Finding-- Regular Perturbations-- Direct Error Estimation-- OSCILLATORY PHENOMENA-- Periodic Solutions and Lindstedt Series-- Multiple Scales-- Averaging-- TRANSITION LAYERS-- Initial Layers-- Boundary Layers-- Methods of the WKB Type-- Appendices-- Symbol Index-- Index.
• (source: Nielsen Book Data)

This is a course in perturbation theory for the solution of algebraic and differential equations, especially ordinary differential equations. It covers all of the methods commonly used in both regular and singular perturbations: Taylor series, Lindstedt series, strained parameters, multiple scales, averaging, matching and WKB methods. The text pays great attention to understanding the meaning of the results, as it is extremely easy to make mistakes and draw invalid conclusions from a perturbation analysis.
(source: Nielsen Book Data)

• Introduction.- Basic Facts from Functional Analysis and Banach Lattices.- An Overview of Semigroup Theory.- Some Classical Perturbation Results.- Positive Perturbations of Positive Semigroups.- Substochastic Semigroups and Generator Characterization.- Applications to Birth-and-Death Problems.- Applications to Pure Fragmentation Problems.- Fragmentation with Growth and Decay.- Applications to Kinetic Theory.- Singularly Perturbed Inelastic Collision Models.- Index.- References.
• (source: Nielsen Book Data)

This book is devoted predominantly to one particular way of looking at the evolution of the system in which we describe time changes as transitions from one state to another. This leads in a natural way to the semigroup theory that has been developed in the last fifty years. There are many applications coming from kinetic theory, fragmentation theory, mathematical biology and many other fields, where the assumptions of standard perturbation theory are not satisfied. In this book the authors concentrate on perturbation results that take advantage of the fact that in many applications the operators involved are positive (as only nonnegative data and solutions make sense) and dissipative. The main part of the book is devoted to linking the properties of the generator with the properties of the semigroup, that are important in applications. In the final part of the book the authors discuss applications of the developed theory to a variety of problems ranging from the classical birth-and-death type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models. The authors also discuss a few miscellaneous applications that do not fit into their theory exactly but nevertheless their treatment draws substantially from it.
(source: Nielsen Book Data)
"Perturbations of Positive Semigroups with Applications" is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book presents a survey of the results that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material. The second part then deals with the application of the developed theory to a variety of problems ranging from the classical birth-and-death type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models. The only prerequisites are a basic knowledge of functional analysis and measure theory. This is an essential one-stop reference for graduate and postgraduate students and researchers in applied analysis and mathematical physics who are interested in the application of functional analytic techniques to concrete problems arising in physics, biology and engineering.
(source: Nielsen Book Data)

• Preliminaries. Norms and Metrics. Linear Systems and Least Squares Problems. The Perturbation of Eigenvalues. Invariant Subspaces. Generalized Eigenvalue Problems.
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This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms.
(source: Nielsen Book Data)