Asymptotic Methods in Analysis

Author: N. G. de Bruijn

Publisher: Courier Corporation

ISBN: 0486150798

Category: Mathematics

Page: 224

View: 3439

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This pioneering study/textbook in a crucial area of pure and applied mathematics features worked examples instead of the formulation of general theorems. Extensive coverage of saddle-point method, iteration, and more. 1958 edition.
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Asymptotic Methods in Resonance Analytical Dynamics

Author: Eugeniu Grebenikov,Yu. A. Mitropolsky,Y.A. Ryabov

Publisher: CRC Press

ISBN: 9780203409831

Category: Mathematics

Page: 278

View: 473

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Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.
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Asymptotic Methods for Integrals

Author: Nico M Temme

Publisher: World Scientific

ISBN: 9814612170

Category: Mathematics

Page: 628

View: 8404

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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. Contents:Basic Methods for IntegralsBasic Methods: Examples for Special FunctionsOther Methods for IntegralsUniform Methods for IntegralsUniform Methods for Laplace-Type IntegralsUniform Examples for Special FunctionsA Class of Cumulative Distribution Functions Readership: Researchers in applied mathematics, engineering, physics, mathematical statistics, probability theory and biology. The introductory parts and examples will be useful for post-graduate students in mathematics. Key Features:The book gives a complete overview of the classical asymptotic methods for integralsThe many examples give insight in the behavior of the well-known special functionsThe detailed explanations on how to obtain the coefficients in the expansions make the results useful for numerical applications, in particular, for computing special functionsThe many results on asymptotic representations of special functions supplement and extend those in the NIST Handbook of Mathematical FunctionsKeywords:Asymptotic Analysis;Approximation of Integrals;Asymptotic Approximations;Asymptotic Expansions;Steepest Descent Methods;Saddle Point Methods;Stationary Phase Method;Special Functions;Numerical Approximation of Special Functions;Cumulative Distribution FunctionsReviews: “The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt MATH
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Asymptotic Methods in the Theory of Gaussian Processes and Fields

Author: Vladimir I. Piterbarg

Publisher: American Mathematical Soc.

ISBN: 0821883313

Category: Mathematics

Page: 206

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This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.
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Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances

Author: Herbert Steinrück

Publisher: Springer Science & Business Media

ISBN: 3709104084

Category: Technology & Engineering

Page: 420

View: 1440

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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.
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Asymptotic Methods in Mechanics

Author: RŽmi Vaillancourt,Andrei L. Smirnov

Publisher: American Mathematical Soc.

ISBN: 9780821870266

Category: Technology & Engineering

Page: 282

View: 1053

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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.
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Analysis I

Integral Representations and Asymptotic Methods

Author: R.V. Gamkrelidze

Publisher: Springer

ISBN: 9783540170082

Category: Mathematics

Page: 238

View: 9927

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Infinite series, and their analogues-integral representations, became funda mental tools in mathematical analysis, starting in the second half of the seven teenth century. They have provided the means for introducing into analysis all o( the so-called transcendental functions, including those which are now called elementary (the logarithm, exponential and trigonometric functions). With their help the solutions of many differential equations, both ordinary and partial, have been found. In fact the whole development of mathematical analysis from Newton up to the end of the nineteenth century was in the closest way connected with the development of the apparatus of series and integral representations. Moreover, many abstract divisions of mathematics (for example, functional analysis) arose and were developed in order to study series. In the development of the theory of series two basic directions can be singled out. One is the justification of operations with infmite series, the other is the creation oftechniques for using series in the solution of mathematical and applied problems. Both directions have developed in parallel Initially progress in the first direction was significantly smaller, but, in the end, progress in the second direction has always turned out to be of greater difficulty.
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Asymptotic Methods in the Theory of Non-linear Oscillations

Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov,Николай Николаевич Боголюбов,Iurii Alekseevich Mitropol'skii,Юрий Алексеевич Митропольский,Jurij A. Mitropolʹskij,Y. A. Mitropolsky

Publisher: CRC Press

ISBN: 9780677200507

Category: Technology & Engineering

Page: 537

View: 1987

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