Introduction to Asymptotic Methods
Title | Introduction to Asymptotic Methods PDF eBook |
Author | David Y. Gao |
Publisher | CRC Press |
Pages | 270 |
Release | 2006-05-03 |
Genre | Mathematics |
ISBN | 1420011731 |
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
Title | Asymptotic Methods in Mechanics PDF eBook |
Author | Rmi Vaillancourt |
Publisher | American Mathematical Soc. |
Pages | 308 |
Release | 1993-12-21 |
Genre | Technology & Engineering |
ISBN | 9780821870266 |
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
Title | Applied Asymptotic Methods in Nonlinear Oscillations PDF eBook |
Author | Yuri A. Mitropolsky |
Publisher | Springer Science & Business Media |
Pages | 352 |
Release | 2013-03-09 |
Genre | Technology & Engineering |
ISBN | 9401588473 |
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 Methods in Fluid Mechanics: Survey and Recent Advances
Title | Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances PDF eBook |
Author | Herbert Steinrück |
Publisher | Springer Science & Business Media |
Pages | 426 |
Release | 2012-01-29 |
Genre | Technology & Engineering |
ISBN | 3709104084 |
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 Methods in Quantum Mechanics
Title | Asymptotic Methods in Quantum Mechanics PDF eBook |
Author | S.H. Patil |
Publisher | Springer Science & Business Media |
Pages | 194 |
Release | 2000-04-26 |
Genre | History |
ISBN | 9783540672401 |
This book describes some general properties of wave functions, with an emphasis on their asymptotic behaviour. The asymptotic region is particularly important since it is the wave function in the outer region of an atom, a molecule or a nucleus, which is sensitive to external interaction. An analysis of these properties helps in constructing simple and compact wave functions and in developing a broad understanding of different aspects of the quantum mechanics of many-particle systems. As applications, wave functions with correct asymptotic forms are used to generate a large data base for susceptibilities, polarizabilities, interatomic potentials, and nuclear densities.
Asymptotic methods in mechanics of solids
Title | Asymptotic methods in mechanics of solids PDF eBook |
Author | Svetlana M. Bauer |
Publisher | Birkhäuser |
Pages | 342 |
Release | 2015-05-30 |
Genre | Mathematics |
ISBN | 3319183117 |
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic.
Asymptotical Mechanics of Thin-Walled Structures
Title | Asymptotical Mechanics of Thin-Walled Structures PDF eBook |
Author | Igor V. Andrianov |
Publisher | Springer Science & Business Media |
Pages | 527 |
Release | 2013-06-29 |
Genre | Science |
ISBN | 354045246X |
In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.