Introduction To Asymptotic Methods PDF Download
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| Author | : David Y. Gao |
| Publisher | : CRC Press |
| Total Pages | : 270 |
| Release | : 2006-05-03 |
| Genre | : Mathematics |
| ISBN | : 1420011731 |
Download Introduction to Asymptotic Methods Book in PDF, ePub and Kindle
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
| Author | : Norman Bleistein |
| Publisher | : Courier Corporation |
| Total Pages | : 453 |
| Release | : 1986-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486650820 |
Download Asymptotic Expansions of Integrals Book in PDF, ePub and Kindle
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.
| Author | : Carl M. Bender |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 605 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475730691 |
Download Advanced Mathematical Methods for Scientists and Engineers I Book in PDF, ePub and Kindle
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.
| Author | : Douglas Samuel Jones |
| Publisher | : World Scientific |
| Total Pages | : 184 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9789810229153 |
Download Introduction to Asymptotics Book in PDF, ePub and Kindle
"A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999
| Author | : Mark H. Holmes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461253470 |
Download Introduction to Perturbation Methods Book in PDF, ePub and Kindle
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.
| Author | : Douglas S Jones |
| Publisher | : World Scientific |
| Total Pages | : 177 |
| Release | : 1997-01-16 |
| Genre | : |
| ISBN | : 9814497967 |
Download Introduction To Asymptotics - A Treatment Using Nonstandard Analysis Book in PDF, ePub and Kindle
Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hyperasymptotics as well as uniform asymptotics. There are many numerical examples to illustrate the relation between theory and practice. Exercises in the chapters enable the book to be used as a text for an introductory course.
| Author | : J.D. Murray |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 172 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461211220 |
Download Asymptotic Analysis Book in PDF, ePub and Kindle
From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) #Choice Sept. 1984#1
| Author | : Nico M. Temme |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : Differential equations |
| ISBN | : 9789814612159 |
Download Asymptotic Methods for Integrals Book in PDF, ePub and Kindle
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
| Author | : R. B. White |
| Publisher | : World Scientific |
| Total Pages | : 430 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 1848166079 |
Download Asymptotic Analysis of Differential Equations Book in PDF, ePub and Kindle
"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.
| Author | : Johan Grasman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 229 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461210569 |
Download Asymptotic Methods for Relaxation Oscillations and Applications Book in PDF, ePub and Kindle
In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
