Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 1475730691

Category: Mathematics

Page: 593

View: 8417

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 at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Posted in Mathematics

Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 9780387989310

Category: Mathematics

Page: 593

View: 8400

This book gives 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. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form. The presentation provides insights that will be useful in approaching new problems.
Posted in Mathematics

Introduction to Perturbation Methods

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

ISBN: 9780387942032

Category: Mathematics

Page: 356

View: 5989

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.
Posted in Mathematics

Perturbation Methods for Engineers and Scientists

Author: Alan W. Bush

Publisher: CRC Press

ISBN: 9780849386145

Category: Mathematics

Page: 320

View: 8982

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.
Posted in Mathematics

Vibration and Coupling of Continuous Systems

Asymptotic Methods

Author: Jacqueline Sanchez Hubert

Publisher: Springer Science & Business Media

ISBN: 364273782X

Category: Science

Page: 421

View: 7330

Real problems concerning vibrations of elastic structures are among the most fascinating topics in mathematical and physical research as well as in applications in the engineering sciences. This book addresses the student familiar with the elementary mechanics of continua along with specialists. The authors start with an outline of the basic methods and lead the reader to research problems of current interest. An exposition of the method of spectra, asymptotic methods and perturbation is followed by applications to linear problems where elastic structures are coupled to fluids in bounded and unbounded domains, to radiation of immersed bodies, to local vibrations, to thermal effects and many more.
Posted in Science

A First Look at Perturbation Theory

Author: James G. Simmonds,James E. Mann

Publisher: Courier Corporation

ISBN: 0486315584

Category: Mathematics

Page: 160

View: 3506

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.
Posted in Mathematics

Applied Asymptotic Analysis

Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 0821840789

Category: Mathematics

Page: 467

View: 8355

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.
Posted in Mathematics

Methods of Mathematical Physics

Author: Harold Jeffreys,Bertha Jeffreys

Publisher: Cambridge University Press

ISBN: 9780521664028

Category: Mathematics

Page: 718

View: 2589

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.
Posted in Mathematics

Worked Problems in Applied Mathematics

Author: Nikola-I Nikolaevich and Lebedev,I. P. Skal?skai?a?,I?A?kov Solomonovich Ufli?a?nd

Publisher: Courier Corporation

ISBN: 9780486637303

Category: Mathematics

Page: 429

View: 439

These 566 problems plus answers cover a wide range of topics in an accessible manner, including steady-state harmonic oscillations, Fourier method, integral transforms, curvilinear coordinates, integral equations, and more. 1965 edition.
Posted in Mathematics

Asymptotic Expansions of Integrals

Author: Norman Bleistein,Richard A. Handelsman

Publisher: Courier Corporation

ISBN: 0486650820

Category: Mathematics

Page: 425

View: 3432

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Posted in Mathematics

Asymptotic Expansions

Author: E. T. Copson,Edward Thomas Copson

Publisher: Cambridge University Press

ISBN: 9780521604826

Category: Mathematics

Page: 120

View: 8818

Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
Posted in Mathematics

Mathematical Methods in Science and Engineering

Author: Selçuk S. Bayin

Publisher: John Wiley & Sons

ISBN: 111942545X

Category: Education

Page: 864

View: 4889

A Practical, Interdisciplinary Guide to Advanced Mathematical Methods for Scientists and Engineers Mathematical Methods in Science and Engineering, Second Edition, provides students and scientists with a detailed mathematical reference for advanced analysis and computational methodologies. Making complex tools accessible, this invaluable resource is designed for both the classroom and the practitioners; the modular format allows flexibility of coverage, while the text itself is formatted to provide essential information without detailed study. Highly practical discussion focuses on the “how-to” aspect of each topic presented, yet provides enough theory to reinforce central processes and mechanisms. Recent growing interest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance to expand advanced mathematical methods beyond theoretical physics. This book is written with this multi-disciplinary group in mind, emphasizing practical solutions for diverse applications and the development of a new interdisciplinary science. Revised and expanded for increased utility, this new Second Edition: Includes over 60 new sections and subsections more useful to a multidisciplinary audience Contains new examples, new figures, new problems, and more fluid arguments Presents a detailed discussion on the most frequently encountered special functions in science and engineering Provides a systematic treatment of special functions in terms of the Sturm-Liouville theory Approaches second-order differential equations of physics and engineering from the factorization perspective Includes extensive discussion of coordinate transformations and tensors, complex analysis, fractional calculus, integral transforms, Green's functions, path integrals, and more Extensively reworked to provide increased utility to a broader audience, this book provides a self-contained three-semester course for curriculum, self-study, or reference. As more scientific disciplines begin to lean more heavily on advanced mathematical analysis, this resource will prove to be an invaluable addition to any bookshelf.
Posted in Education

Introduction to Perturbation Techniques

Author: Ali H. Nayfeh

Publisher: John Wiley & Sons

ISBN: 3527618457

Category: Science

Page: 533

View: 7810

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.
Posted in Science

Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems

Author: Randall J. LeVeque

Publisher: SIAM

ISBN: 9780898717839

Category: Differential equations

Page: 339

View: 2645

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Posted in Differential equations

Asymptotic Analysis of Differential Equations

Author: R. B. White

Publisher: World Scientific

ISBN: 1848166087

Category: Mathematics

Page: 405

View: 4898

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Posted in Mathematics

Ordinary Differential Equations

Author: George F. Carrier,Carl E. Pearson

Publisher: SIAM

ISBN: 9781611971293

Category: Differential equations

Page: 220

View: 9270

Offers an alternative to the "rote" approach of presenting standard categories of differential equations accompanied by routine problem sets. The exercises presented amplify and provide perspective for the material, often giving readers opportunity for ingenuity. Little or no previous acquaintance with the subject is required to learn usage of techniques for constructing solutions of differential equations in this reprint volume.
Posted in Differential equations