Introduction To Perturbation Methods

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Introduction To Perturbation Methods

Author : Mark H. Holmes
ISBN : 9781461454779
Genre : Mathematics
File Size : 48.75 MB
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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 chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
Category: Mathematics

Introduction To Perturbation Methods

Author : Mark H. Holmes
ISBN : 9781461253471
Genre : Mathematics
File Size : 83.87 MB
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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 chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
Category: Mathematics

Introduction To Perturbation Techniques

Author : Ali H. Nayfeh
ISBN : 9783527618453
Genre : Science
File Size : 57.60 MB
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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 ordinary differential equations. Each chapter contains a number of exercises.
Category: Science

Perturbation Methods

Author : E. J. Hinch
ISBN : 0521378974
Genre : Mathematics
File Size : 89.64 MB
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A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.
Category: Mathematics

Perturbation Methods Bifurcation Theory And Computer Algebra

Author : Richard H. Rand
ISBN : 9781461210603
Genre : Mathematics
File Size : 84.56 MB
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Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.
Category: Mathematics

Perturbation Methods For Differential Equations

Author : Bhimsen Shivamoggi
ISBN : 0817641890
Genre : Mathematics
File Size : 37.83 MB
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Perturbation methods are widely used in the study of physically significant differential equations, which arise in Applied Mathematics, Physics and Engineering.; Background material is provided in each chapter along with illustrative examples, problems, and solutions.; A comprehensive bibliography and index complete the work.; Covers an important field of solutions for engineering and the physical sciences.; To allow an interdisciplinary readership, the book focuses almost exclusively on the procedures and the underlying ideas and soft pedal the proofs; Dr. Bhimsen K. Shivamoggi has authored seven successful books for various publishers like John Wiley & Sons and Kluwer Academic Publishers.
Category: Mathematics

Perturbations

Author : James A. Murdock
ISBN : 1611971098
Genre : Perturbation
File Size : 71.89 MB
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Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.
Category: Perturbation

Introduction To Perturbation Theory In Quantum Mechanics

Author : Francisco M. Fernandez
ISBN : 9781420039641
Genre : Science
File Size : 74.15 MB
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Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation
Category: Science

Singular Perturbation Methods In Control

Author : Petar Kokotovic
ISBN : 9780898714449
Genre : Mathematics
File Size : 79.30 MB
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This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications.
Category: Mathematics

Introduction To The Foundations Of Applied Mathematics

Author : Mark H. Holmes
ISBN : 9780387877655
Genre : Mathematics
File Size : 80.5 MB
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FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.
Category: Mathematics

A First Look At Perturbation Theory

Author : James G. Simmonds
ISBN : 9780486315584
Genre : Mathematics
File Size : 43.57 MB
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This introductory text explains methods for obtaining approximate solutions to mathematical problems by exploiting the presence of small, dimensionless parameters. For engineering and physical science undergraduates.
Category: Mathematics

Introduction To Asymptotic Methods

Author : David Y. Gao
ISBN : 1420011731
Genre : Mathematics
File Size : 38.94 MB
Format : PDF
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Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Category: Mathematics

Perturbation Methods For Engineers And Scientists

Author : Alan W. Bush
ISBN : 084938608X
Genre : Mathematics
File Size : 52.15 MB
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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.
Category: Mathematics

Singular Perturbation Methods For Ordinary Differential Equations

Author : Robert E., Jr. O'Malley
ISBN : 9781461209775
Genre : Mathematics
File Size : 89.68 MB
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This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.
Category: Mathematics

Singular Perturbation Theory

Author : Donald R. Smith
ISBN : 0521300428
Genre : Mathematics
File Size : 84.76 MB
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Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.
Category: Mathematics

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

Author : Jane Cronin
ISBN : 082186761X
Genre : Mathematics
File Size : 59.95 MB
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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.
Category: Mathematics

Introduction To Scientific Computing And Data Analysis

Author : Mark H. Holmes
ISBN : 9783319302560
Genre : Computers
File Size : 80.56 MB
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This textbook provides and introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The MATLAB codes used to produce most of the figures and data tables in the text are available on the author’s website and SpringerLink.
Category: Computers

Applied Mathematics In Hydraulic Engineering

Author : Kazumasa Mizumura
ISBN : 9789814299558
Genre : Technology & Engineering
File Size : 73.95 MB
Format : PDF
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This is a teaching guide and reference to treating nonlinear mathematical problems in hydraulic, hydrologic and coastal engineering--
Category: Technology & Engineering

Nonlinear Ordinary Differential Equations

Author : Dominic William Jordan
ISBN : 0198565623
Genre : Mathematics
File Size : 67.51 MB
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The text of this edition has been revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. It is directed towards practical applications of the theory with examples and problems.
Category: Mathematics