Asymptotic Methods In Mechanics
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Introduction To Asymptotic Methods
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Author : David Y. Gao
language : en
Publisher: CRC Press
Release Date : 2006-05-03
Introduction To Asymptotic Methods written by David Y. Gao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-03 with Mathematics categories.
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
Asymptotic Methods In Mechanics
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Author : Rmi Vaillancourt
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-12-21
Asymptotic Methods In Mechanics written by Rmi Vaillancourt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-21 with Technology & Engineering categories.
Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
Applied Asymptotic Methods In Nonlinear Oscillations
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Author : Yuri A. Mitropolsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Applied Asymptotic Methods In Nonlinear Oscillations written by Yuri A. Mitropolsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Technology & Engineering categories.
Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.
Asymptotic Analysis And Boundary Layers
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Author : Jean Cousteix
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-22
Asymptotic Analysis And Boundary Layers written by Jean Cousteix and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-22 with Science categories.
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.
Asymptotic Methods In Fluid Mechanics Survey And Recent Advances
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Author : Herbert Steinrück
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-29
Asymptotic Methods In Fluid Mechanics Survey And Recent Advances written by Herbert Steinrück and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-29 with Technology & Engineering categories.
A survey of asymptotic methods in fluid mechanics and applications is given including high Reynolds number flows (interacting boundary layers, marginal separation, turbulence asymptotics) and low Reynolds number flows as an example of hybrid methods, waves as an example of exponential asymptotics and multiple scales methods in meteorology.
Asymptotic Analysis Of Differential Equations
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Author : Roscoe B. White
language : en
Publisher: World Scientific
Release Date : 2005
Asymptotic Analysis Of Differential Equations written by Roscoe B. White and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Advanced Mathematical Methods For Scientists And Engineers I
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Author : Carl M. Bender
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Advanced Mathematical Methods For Scientists And Engineers I written by Carl M. Bender and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.
Asymptotic Methods For Integrals
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Author : Nico M. Temme
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015
Asymptotic Methods For Integrals written by Nico M. Temme and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Differential equations categories.
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.
Perturbation Methods In Fluid Mechanics
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Author : Milton Van Dyke
language : en
Publisher: Parabolic Press, Incorporated
Release Date : 1975
Perturbation Methods In Fluid Mechanics written by Milton Van Dyke and has been published by Parabolic Press, Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Science categories.