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Asymptotic Solutions Of Certain Ordinary Differential Equations Associated With Multiple Roots Of The Characteristic Equation
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Book Synopsis Asymptotic Solutions of Certain Ordinary Differential Equations Associated with Multiple Roots of the Characteristic Equation by : Hugh L. Turrittin
Download or read book Asymptotic Solutions of Certain Ordinary Differential Equations Associated with Multiple Roots of the Characteristic Equation written by Hugh L. Turrittin and published by . This book was released on 1933 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Solutions of Differential-Difference Equations by : Richard Bellman
Download or read book Asymptotic Behavior of Solutions of Differential-Difference Equations written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1959 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Analysis by : Mikhail V. Fedoryuk
Download or read book Asymptotic Analysis written by Mikhail V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer. This book was released on 2013-11-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call "qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Book Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
Download or read book Asymptotic Behavior and Stability Problems in Ordinary Differential Equations written by Lamberto Cesari and published by Springer. This book was released on 2013-06-29 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call "qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Book Synopsis Asymptotic Expansions for Ordinary Differential Equations by : Wolfgang Wasow
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Book Synopsis Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations by : Ivan Kiguradze
Download or read book Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.
Book Synopsis Singular Perturbation Problems of Ordinary Differential Equations by : Barbara Viola Bentley
Download or read book Singular Perturbation Problems of Ordinary Differential Equations written by Barbara Viola Bentley and published by . This book was released on 1955 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Equations by : Edward Lindsay Ince
Download or read book Ordinary Differential Equations written by Edward Lindsay Ince and published by . This book was released on 1927 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotics of Linear Differential Equations by : M.H. Lantsman
Download or read book Asymptotics of Linear Differential Equations written by M.H. Lantsman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.
Book Synopsis Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems by : George David Birkhoff
Download or read book Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems written by George David Birkhoff and published by . This book was released on 1908 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Asymptotic Solutions of Linear Differential Equations by : Clyde Elton Love
Download or read book On the Asymptotic Solutions of Linear Differential Equations written by Clyde Elton Love and published by . This book was released on 1914 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Difference-Differential Equations by : Edmund Pinney
Download or read book Ordinary Difference-Differential Equations written by Edmund Pinney and published by Univ of California Press. This book was released on with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotics and Special Functions by : Frank Olver
Download or read book Asymptotics and Special Functions written by Frank Olver and published by CRC Press. This book was released on 1997-01-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
Book Synopsis Lectures on Asymptotic Solutions of Ordinary Linear Differential Equations by : Arthur Erdélyi
Download or read book Lectures on Asymptotic Solutions of Ordinary Linear Differential Equations written by Arthur Erdélyi and published by . This book was released on 1961 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Analysis Of Differential Equations (Revised Edition) by : White Roscoe B
Download or read book Asymptotic Analysis Of Differential Equations (Revised Edition) written by White Roscoe B and published by World Scientific. This book was released on 2010-08-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Solutions of Certain Linear Differential Equations in which the Coefficient of the Parameter May Have a Zero by : Henry Scheffé
Download or read book Asymptotic Solutions of Certain Linear Differential Equations in which the Coefficient of the Parameter May Have a Zero written by Henry Scheffé and published by . This book was released on 1935 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
