The Construction Of Related Equations For The Asymptotic Theory Of Linear Ordinary Differential Equations About A Turning Point PDF Download
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Author | : RUDOLPH E. LANGER |
Publisher | : |
Total Pages | : 1 |
Release | : 1962 |
Genre | : Differential equations |
ISBN | : |
Download The Construction of Related Equations for the Asymptotic Theory of Linear Ordinary Differential Equations about a Turning Point Book in PDF, ePub and Kindle
Fully developed theory is extant, and can justifiably be referred to as classical, for the determination of the asymptotic forms of the solutions of a differential equation over any closed zregion which completely excludes turning-points. This theory applies, of course, irrespective of the region, to all equations with constant coefficients. The state of the theory is very different, namely quite fragmentary, when a turningpoint is lodged within the region. For this reason, and also because modern physical theories require it, the stdy of the solution forms of an equation in a region about a turning-point is of emminent contemporary interest. The classical algorithms fail irretrievably in such a region, a fact which has been shown to be inevitable by results otherwise obtained, because the forms yielded by those algorithms lak adequacy to reflect the intricate functional metamorphoses which characterize the solutions of the differential equation in a turning-point neighborhood. The origin is in this case a turning point, and bout this point the solutions undergo transitions between oscillatory and exponential function types. (Author).
Author | : Wolfgang Wasow |
Publisher | : Courier Dover Publications |
Total Pages | : 385 |
Release | : 2018-03-21 |
Genre | : Mathematics |
ISBN | : 0486824586 |
Download Asymptotic Expansions for Ordinary Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Walter Charles Strodt |
Publisher | : American Mathematical Soc. |
Total Pages | : 86 |
Release | : 1954 |
Genre | : Difference equations |
ISBN | : 0821812130 |
Download Contributions to the Asymptotic Theory of Ordinary Differential Equations in the Complex Domain Book in PDF, ePub and Kindle
Author | : Mikhail Vasilʹevich Fedori︠u︡k |
Publisher | : Springer |
Total Pages | : 428 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : |
Download Asymptotic Analysis Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 944 |
Release | : 1962 |
Genre | : Science |
ISBN | : |
Download U.S. Government Research Reports Book in PDF, ePub and Kindle
Author | : R. V. Gamkrelidze |
Publisher | : Springer Science & Business Media |
Total Pages | : 223 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468433032 |
Download Mathematical Analysis Book in PDF, ePub and Kindle
This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V. F. Butuzov, A. B. Vasil'eva, and M. V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A. L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S. A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 1962-1967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters also deals with the problem of the convergence of positive operators, inasmuch as the ideas and methods of this theory are close to those of the theory of best ap proximation. The survey covers the literature of the decade 1958-1967. The third article is devoted to a comparatively new and rapid ly growing branch of mathematics which is closely related to many classical and modern mathematical disciplines. A survey is given of results in entropy theory, classical dynamic systems, ergodic theorems, etc. The results surveyed were primarily published during the period 1956-1967.
Author | : Rudolph Ernest Langer |
Publisher | : |
Total Pages | : 44 |
Release | : 1954 |
Genre | : Differential equations, Linear |
ISBN | : |
Download On the Asymptotic Solutions of Ordinary Linear Differential Equations about a Turning Point Book in PDF, ePub and Kindle
Author | : Frank Olver |
Publisher | : CRC Press |
Total Pages | : 591 |
Release | : 1997-01-24 |
Genre | : Mathematics |
ISBN | : 1439864543 |
Download Asymptotics and Special Functions Book in PDF, ePub and Kindle
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.
Author | : White Roscoe B |
Publisher | : World Scientific |
Total Pages | : 432 |
Release | : 2010-08-16 |
Genre | : Mathematics |
ISBN | : 1911298593 |
Download Asymptotic Analysis Of Differential Equations (Revised Edition) Book in PDF, ePub and Kindle
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.
Author | : Defense Documentation Center (U.S.) |
Publisher | : |
Total Pages | : 824 |
Release | : 1963 |
Genre | : Science |
ISBN | : |
Download Technical Abstract Bulletin Book in PDF, ePub and Kindle