Perturbation Methods

Author: E. J. Hinch

Publisher: Cambridge University Press

ISBN: 1139935844

Category: Mathematics

Page: N.A

View: 2570

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.

Mathematische Modellierung

Grundprinzipien in Natur- und Ingenieurwissenschaften

Author: Karl-Heinz Hoffmann,Gabriele Witterstein

Publisher: Springer-Verlag

ISBN: 3034606508

Category: Mathematics

Page: 159

View: 4382

Mathematische Modellbildung und numerische Simulation sind neben Experiment und Theoriebildung zur 3. Säule der naturwissenschaftlichen Forschung geworden. Das Lehrbuch bietet in kompakter Form die Grundlagen, um in Natur-, Ingenieur- und Lebenswissenschaften mathematische Modelle erarbeiten zu können. Fragen zur Dimensionsanalyse, zur asymptotischen Entwicklung und zu Grenzschichten werden behandelt und anhand von Fallbeispielen erläutert. Für das Verständnis sind allgemeine Kenntnisse der Analysis und der linearen Algebra erforderlich.

Beyond Perturbation

Introduction to the Homotopy Analysis Method

Author: Shijun Liao

Publisher: CRC Press

ISBN: 9780203491164

Category: Science

Page: 336

View: 7329

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, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Kármán swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

American Mathematical Society Short Course, January 5-6, 1998, Baltimore, Maryland

Author: Jane Cronin

Publisher: American Mathematical Soc.

ISBN: 0821809296

Category: Mathematics

Page: 187

View: 3997

To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.


proceedings of the Third International Congress on Industrial and Applied Mathematics held in Hamburg, Germany, July 3-7, 1995

Author: K. Kirchgässner,Oskar Mahrenholtz,Reinhard Mennicken

Publisher: Vch Pub


Category: Mathematics

Page: 487

View: 5857


Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 7303

Nonlinear Systems

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 9780521406680

Category: Mathematics

Page: 317

View: 4338

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.

Thinking about Ordinary Differential Equations

Author: Robert E. O'Malley

Publisher: Cambridge University Press

ISBN: 9780521557429

Category: Mathematics

Page: 247

View: 2092

While mastery of these equations is essential, adhering to any one method of solving them is not. This book stresses alternative examples and analyses by means of which students can understand a number of approaches to finding solutions and understanding their behavior. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application.


Author: Klaus-Jürgen Bathe

Publisher: Springer Verlag

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 5499

Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder.