Asymptotic Multiple Scale Method In Time Domain PDF Download
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| Author | : Jan Awrejcewicz |
| Publisher | : CRC Press |
| Total Pages | : 506 |
| Release | : 2022-05-10 |
| Genre | : Mathematics |
| ISBN | : 1000581276 |
Download Asymptotic Multiple Scale Method in Time Domain Book in PDF, ePub and Kindle
This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.
| Author | : Jan Awrejcewicz |
| Publisher | : CRC Press |
| Total Pages | : 411 |
| Release | : 2022-05-10 |
| Genre | : Mathematics |
| ISBN | : 100058125X |
Download Asymptotic Multiple Scale Method in Time Domain Book in PDF, ePub and Kindle
This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.
| 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 | : Igor V. Andrianov |
| Publisher | : CRC Press |
| Total Pages | : 409 |
| Release | : 2024-05-20 |
| Genre | : Mathematics |
| ISBN | : 104003277X |
Download Asymptotic Methods for Engineers Book in PDF, ePub and Kindle
Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
| Author | : Ricardo Estrada |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 474 |
| Release | : 2002-02-08 |
| Genre | : Mathematics |
| ISBN | : 9780817641429 |
Download A Distributional Approach to Asymptotics Book in PDF, ePub and Kindle
"...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic
| Author | : Blessing Mudavanhu |
| Publisher | : |
| Total Pages | : 114 |
| Release | : 2002 |
| Genre | : Singular perturbations (Mathematics) |
| ISBN | : |
Download A New Renormalization Method for the Asymptotic Solution of Multiple Scale Singular Perturbation Problems Book in PDF, ePub and Kindle
| Author | : B Vainberg |
| Publisher | : CRC Press |
| Total Pages | : 516 |
| Release | : 1989-02-25 |
| Genre | : Science |
| ISBN | : 9782881246647 |
Download Asymptotic Methods in Equations of Mathematical Physics Book in PDF, ePub and Kindle
Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
| Author | : Jeremiah U. Brackbill |
| Publisher | : |
| Total Pages | : 464 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : |
Download Multiple Time Scales Book in PDF, ePub and Kindle
| 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 | : Alain Bensoussan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 410 |
| Release | : 2011-10-26 |
| Genre | : Mathematics |
| ISBN | : 0821853244 |
Download Asymptotic Analysis for Periodic Structures Book in PDF, ePub and Kindle
This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.
