Asymptotic Methods For Engineers

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Asymptotic Methods for Engineers

Igor V. Andrianov,Jan Awrejcewicz
Asymptotic Methods for Engineers Book PDF

Author : Igor V. Andrianov,Jan Awrejcewicz
Publisher : CRC Press
Page : 265 pages
File Size : 51,7 Mb
Release : 2024-05-16
Category : Mathematics
ISBN : 9781040032718

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Asymptotic Methods for Engineers by Igor V. Andrianov,Jan Awrejcewicz Pdf

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.).

Advanced Mathematical Methods for Scientists and Engineers I

Carl M. Bender,Steven A. Orszag
Advanced Mathematical Methods for Scientists and Engineers I Book PDF

Author : Carl M. Bender,Steven A. Orszag
Publisher : Springer Science & Business Media
Page : 605 pages
File Size : 43,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475730692

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Advanced Mathematical Methods for Scientists and Engineers I by Carl M. Bender,Steven A. Orszag Pdf

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.

Asymptotic Methods in Electromagnetics

Daniel Bouche,Frederic Molinet,Raj Mittra
Asymptotic Methods in Electromagnetics Book PDF

Author : Daniel Bouche,Frederic Molinet,Raj Mittra
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642605178

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Asymptotic Methods in Electromagnetics by Daniel Bouche,Frederic Molinet,Raj Mittra Pdf

Numerically rigorous techniques for the computation of electromagnetic fields diffracted by an object become computationally intensive, if not impractical to handle, at high frequencies and one must resort to asymptotic methods to solve the scattering problem at short wavelengths. The asymptotic methods provide closed form expansions for the diffracted fields and are also useful for eliciting physical interpretations of the various diffraction phenomena. One of the principal objectives of this book is to discuss the different asymptotic methods in a unified manner. Although the book contains explicit formulas for computing the field diffracted by conducting or dielectric-coated objects, it also provides the mathematical foundations of the different methods and explains how they are interrelated.

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions

Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov
Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions Book PDF

Author : Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov
Publisher : John Wiley & Sons
Page : 281 pages
File Size : 48,9 Mb
Release : 2014-02-06
Category : Science
ISBN : 9781118725146

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Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions by Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov Pdf

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary value problems • Introduces modern asymptotic and summation procedures • Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates • Covers statics, dynamics and stability of plates with mixed boundary conditions • Explains links between the Adomian and homotopy perturbation approaches Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.

Asymptotic Analysis and Boundary Layers

Jean Cousteix,Jacques Mauss
Asymptotic Analysis and Boundary Layers Book PDF

Author : Jean Cousteix,Jacques Mauss
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 52,9 Mb
Release : 2007-03-22
Category : Science
ISBN : 9783540464891

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Asymptotic Analysis and Boundary Layers by Jean Cousteix,Jacques Mauss Pdf

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 Multiple Scale Method in Time Domain

Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska
Asymptotic Multiple Scale Method in Time Domain Book PDF

Author : Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska
Publisher : CRC Press
Page : 506 pages
File Size : 53,7 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 9781000581270

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Asymptotic Multiple Scale Method in Time Domain by Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska Pdf

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.

Asymptotic Analysis Of Differential Equations (Revised Edition)

White Roscoe B
Asymptotic Analysis Of Differential Equations Revised Edition Book PDF

Author : White Roscoe B
Publisher : World Scientific
Page : 432 pages
File Size : 55,8 Mb
Release : 2010-08-16
Category : Mathematics
ISBN : 9781911298595

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Asymptotic Analysis Of Differential Equations (Revised Edition) by White Roscoe B Pdf

The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.

Techniques of Asymptotic Analysis

Lawrence Sirovich
Techniques of Asymptotic Analysis Book PDF

Author : Lawrence Sirovich
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 47,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461264026

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Techniques of Asymptotic Analysis by Lawrence Sirovich Pdf

These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. In the hope that these notes might prove useful for reference purposes several additional sections have been included and also a table of contents and index. Although asymptotic analysis is now enjoying a period of great vitality, these notes do not reflect a research oriented course. The course is aimed toward people in applied mathematics, physics, engineering, etc., who have a need for asymptotic analysis in their work. The choice of subjects has been largely dictated by the likelihood of application. Also abstraction and generality have not been pursued. Technique and computation are given equal prominence with theory. Both rigorous and formal theory is presented --very often in tandem. In practice, the means for a rigorous analysis are not always available. For this reason a goal has been the cultivation of mature formal reasoning. Therefore, during the course of lectures formal presentations gradually eclipse rigorous presentations. When this occurs, rigorous proofs are given as exercises or in the case of lengthy proofs, reference is made to the Reading List at the end.

Asymptotic Methods in Mechanics

Rémi Vaillancourt,Andrei L. Smirnov
Asymptotic Methods in Mechanics Book PDF

Author : Rémi Vaillancourt,Andrei L. Smirnov
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 42,8 Mb
Release : 1993
Category : Technology & Engineering
ISBN : 0821869930

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Asymptotic Methods in Mechanics by Rémi Vaillancourt,Andrei L. Smirnov Pdf

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.

Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances

Herbert Steinrück
Asymptotic Methods in Fluid Mechanics Survey and Recent Advances Book PDF

Author : Herbert Steinrück
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 41,9 Mb
Release : 2012-01-29
Category : Technology & Engineering
ISBN : 9783709104088

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Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances by Herbert Steinrück Pdf

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.

Asymptotical Mechanics of Thin-Walled Structures

Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch
Asymptotical Mechanics of Thin Walled Structures Book PDF

Author : Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 49,6 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783540452461

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Asymptotical Mechanics of Thin-Walled Structures by Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch Pdf

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.

Asymptotic Expansions of Integrals

Norman Bleistein,Richard A. Handelsman
Asymptotic Expansions of Integrals Book PDF

Author : Norman Bleistein,Richard A. Handelsman
Publisher : Courier Corporation
Page : 453 pages
File Size : 53,9 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 9780486650821

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Asymptotic Expansions of Integrals by Norman Bleistein,Richard A. Handelsman Pdf

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.

Applied Asymptotic Analysis

Peter David Miller
Applied Asymptotic Analysis Book PDF

Author : Peter David Miller
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 50,6 Mb
Release : 2006
Category : Approximation theory
ISBN : 9780821840788

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Applied Asymptotic Analysis by Peter David Miller Pdf

This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entirenonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary. The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and appliedmathematics 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. The book is ideally suited to the needs of a graduate student who, on the one hand, wants to learn basic applied mathematics, and on the other, wants to understand what is needed to make the various arguments rigorous. Down here in the Village, this is knownas the Courant point of view!! --Percy Deift, Courant Institute, New York Peter D. Miller is an associate professor of mathematics at the University of Michigan at Ann Arbor. He earned a Ph.D. in Applied Mathematics from the University of Arizona and has held positions at the Australian NationalUniversity (Canberra) and Monash University (Melbourne). His current research interests lie in singular limits for integrable systems.

Advanced Mathematical Methods for Scientists and Engineers I

Carl M. Bender,Steven A. Orszag
Advanced Mathematical Methods for Scientists and Engineers I Book PDF

Author : Carl M. Bender,Steven A. Orszag
Publisher : Springer
Page : 593 pages
File Size : 53,6 Mb
Release : 1999-10-29
Category : Mathematics
ISBN : 0387989315

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Advanced Mathematical Methods for Scientists and Engineers I by Carl M. Bender,Steven A. Orszag Pdf

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.

Mathematical Methods for Engineers and Scientists 2

Kwong-Tin Tang
Mathematical Methods for Engineers and Scientists 2 Book PDF

Author : Kwong-Tin Tang
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 54,5 Mb
Release : 2006-11-30
Category : Science
ISBN : 9783540302681

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Mathematical Methods for Engineers and Scientists 2 by Kwong-Tin Tang Pdf

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.