Asymptotic Integration Of Differential And Difference Equations
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Asymptotic Integration Of Differential And Difference Equations
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Author : Sigrun Bodine
language : en
Publisher: Springer
Release Date : 2015-05-26
Asymptotic Integration Of Differential And Difference Equations written by Sigrun Bodine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Colloquium On Differential And Difference Equations Cdde 2006
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Author : Ondřej Došlý
language : en
Publisher:
Release Date : 2007
Colloquium On Differential And Difference Equations Cdde 2006 written by Ondřej Došlý and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Difference equations categories.
Asymptotic Behavior Of Solutions Of Differential Difference Equations
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Author : Richard Bellman
language : en
Publisher: American Mathematical Soc.
Release Date : 1959
Asymptotic Behavior Of Solutions Of Differential Difference Equations written by Richard Bellman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Difference equations categories.
Asymptotics Of Analytic Difference Equations
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Author : G. K. Immink
language : en
Publisher: Springer
Release Date : 2006-12-08
Asymptotics Of Analytic Difference Equations written by G. K. Immink and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Differential Difference Equations
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Author : Bellman
language : en
Publisher: Academic Press
Release Date : 1963-01-01
Differential Difference Equations written by Bellman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963-01-01 with Mathematics categories.
Differential-Difference Equations
Selected Papers Of Norman Levinson
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Author : J.A. Nohel
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-12-18
Selected Papers Of Norman Levinson written by J.A. Nohel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-18 with Mathematics categories.
The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.
Asymptotic Analysis And Perturbation Theory
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Author : William Paulsen
language : en
Publisher: CRC Press
Release Date : 2013-07-18
Asymptotic Analysis And Perturbation Theory written by William Paulsen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-18 with Mathematics categories.
Beneficial to both beginning students and researchers, Asymptotic Analysis and Perturbation Theory immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Suitable for those who have completed the standard calculus sequence, the book assumes no prior knowledge of differential equations. It explains the exact solution of only the simplest differential equations, such as first-order linear and separable equations. With varying levels of problems in each section, this self-contained text makes the difficult subject of asymptotics easy to comprehend. Along the way, it explores the properties of some important functions in applied mathematics. Although the book emphasizes problem solving, some proofs are scattered throughout to give readers a justification for the methods used.
Equadiff 82
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Author : H. W. Knobloch
language : en
Publisher: Springer
Release Date : 2007-01-05
Equadiff 82 written by H. W. Knobloch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
Asymptotic Behavior Of Solutions Of Differential Difference Equations
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Author :
language : en
Publisher:
Release Date : 1958
Asymptotic Behavior Of Solutions Of Differential Difference Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with categories.
In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the problem is considerably more complicated than the corresponding problem for ordinary differential equations, by means of a sequence of transformations the problem was reduced to a form where the standard techniques of ordinary differential equation theory could be employed. The differential-difference equation was transformed into an integral equation which was trans formed into an integro-differential equation. At this point the Liouville transformation plays a vital role. Although the guiding ideas were simple, the analysis became formidable. For this reason, only some of the more immediate aspects of the problem were considered.
Integral And Discrete Inequalities And Their Applications
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Author : Yuming Qin
language : en
Publisher: Birkhäuser
Release Date : 2016-10-06
Integral And Discrete Inequalities And Their Applications written by Yuming Qin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-06 with Mathematics categories.
This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities. It complements the author’s book on linear inequalities and serves as an essential tool for researchers interested in differential (ODE and PDE), difference, and integral equations. The present volume is part 2 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.