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: 7768

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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.

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: 3500

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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.

Introduction to Perturbation Methods


Author: Mark H. Holmes
Publisher: Springer Science & Business Media
ISBN: 9780387942032
Category: Mathematics
Page: 356
View: 6686

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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.

Perturbation Methods for Engineers and Scientists


Author: Alan W. Bush
Publisher: CRC Press
ISBN: 9780849386145
Category: Mathematics
Page: 320
View: 3464

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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.

Vibration and Coupling of Continuous Systems

Asymptotic Methods
Author: Jacqueline Sanchez Hubert
Publisher: Springer Science & Business Media
ISBN: 364273782X
Category: Science
Page: 421
View: 3219

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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.

A First Look at Perturbation Theory


Author: James G. Simmonds,James E. Mann
Publisher: Courier Corporation
ISBN: 0486315584
Category: Mathematics
Page: 160
View: 8027

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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.

Applied Asymptotic Analysis


Author: Peter David Miller
Publisher: American Mathematical Soc.
ISBN: 0821840789
Category: Mathematics
Page: 467
View: 1383

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"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.

Methods of Mathematical Physics


Author: Harold Jeffreys,Bertha Jeffreys
Publisher: Cambridge University Press
ISBN: 9780521664028
Category: Mathematics
Page: 718
View: 1339

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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.

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: 9961

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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.

Mathematical Methods in Science and Engineering


Author: Selçuk S. Bayin
Publisher: John Wiley & Sons
ISBN: 111942545X
Category: Education
Page: 864
View: 838

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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.

Asymptotic Expansions


Author: E. T. Copson,Edward Thomas Copson
Publisher: Cambridge University Press
ISBN: 9780521604826
Category: Mathematics
Page: 120
View: 2741

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

Introduction to Perturbation Techniques


Author: Ali H. Nayfeh
Publisher: John Wiley & Sons
ISBN: 3527618457
Category: Science
Page: 533
View: 3256

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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.

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: 649

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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.

Asymptotic Analysis of Differential Equations


Author: R. B. White
Publisher: World Scientific
ISBN: 1848166087
Category: Mathematics
Page: 405
View: 5180

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"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.

Ordinary Differential Equations


Author: George F. Carrier,Carl E. Pearson
Publisher: SIAM
ISBN: 9781611971293
Category: Differential equations
Page: 220
View: 8164

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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.

Numerical Partial Differential Equations

Conservation Laws and Elliptic Equations
Author: J.W. Thomas
Publisher: Springer Science & Business Media
ISBN: N.A
Category: Mathematics
Page: 556
View: 6746

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Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation. Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.