Ordinary Differential Equations And Stability Theory

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Ordinary Differential Equations And Stability Theory
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Author : David A. Sanchez
language : en
Publisher: Courier Dover Publications
Release Date : 2019-09-18
Ordinary Differential Equations And Stability Theory written by David A. Sanchez and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Mathematics categories.
This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.
Ordinary Differential Equations
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Author : Nicolas Rouche
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1980
Ordinary Differential Equations written by Nicolas Rouche and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Stability Theory Of Differential Equations
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Author : Richard Bellman
language : en
Publisher: Courier Corporation
Release Date : 2013-02-20
Stability Theory Of Differential Equations written by Richard Bellman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
Hyers Ulam Stability Of Ordinary Differential Equations
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Author : Arun Kumar Tripathy
language : en
Publisher: CRC Press
Release Date : 2021-05-24
Hyers Ulam Stability Of Ordinary Differential Equations written by Arun Kumar Tripathy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Mathematics categories.
Hyers-Ulam Stability of Ordinary Differential Equations undertakes an interdisciplinary, integrative overview of a kind of stability problem unlike the existing so called stability problem for Differential equations and Difference Equations. In 1940, S. M. Ulam posed the problem: When can we assert that approximate solution of a functional equation can be approximated by a solution of the corresponding equation before the audience at the University of Wisconsin which was first answered by D. H. Hyers on Banach space in 1941. Thereafter, T. Aoki, D. H. Bourgin and Th. M. Rassias improved the result of Hyers. After that many researchers have extended the Ulam's stability problems to other functional equations and generalized Hyer's result in various directions. Last three decades, this topic is very well known as Hyers-Ulam Stability or sometimes it is referred Hyers-Ulam-Rassias Stability. This book synthesizes interdisciplinary theory, definitions and examples of Ordinary Differential and Difference Equations dealing with stability problems. The purpose of this book is to display the new kind of stability problem to global audience and accessible to a broader interdisciplinary readership for e.g those are working in Mathematical Biology Modeling, bending beam problems of mechanical engineering also, some kind of models in population dynamics. This book may be a starting point for those associated in such research and covers the methods needed to explore the analysis. Features: The state-of-art is pure analysis with background functional analysis. A rich, unique synthesis of interdisciplinary findings and insights on resources. As we understand that the real world problem is heavily involved with Differential and Difference equations, the cited problems of this book may be useful in a greater sense as long as application point of view of this Hyers-Ulam Stability theory is concerned. Information presented in an accessible way for students, researchers, scientists and engineers.
A Short Course In Ordinary Differential Equations
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Author : Qingkai Kong
language : en
Publisher: Springer
Release Date : 2014-10-21
A Short Course In Ordinary Differential Equations written by Qingkai Kong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-21 with Mathematics categories.
This text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré—Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm—Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : en
Publisher: Springer
Release Date : 2013-06-29
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Ordinary Differential Equations And Stability
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Author : David Alan Sánchez
language : en
Publisher:
Release Date : 1968
Ordinary Differential Equations And Stability written by David Alan Sánchez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Stability By Fixed Point Theory For Functional Differential Equations
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Author : T. A. Burton
language : en
Publisher: Courier Corporation
Release Date : 2013-04-16
Stability By Fixed Point Theory For Functional Differential Equations written by T. A. Burton and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-16 with Mathematics categories.
The first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques, this text is suitable for advanced undergraduates and graduate students. 2006 edition.
Stability Theory By Liapunov S Direct Method
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Author : Nicolas Rouche
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stability Theory By Liapunov S Direct Method written by Nicolas Rouche 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 2012-12-06 with Mathematics categories.
This monograph is a collective work. The names appear ing on the front cover are those of the people who worked on every chapter. But the contributions of others were also very important: C. Risito for Chapters I, II and IV, K. Peiffer for III, IV, VI, IX R. J. Ballieu for I and IX, Dang Chau Phien for VI and IX, J. L. Corne for VII and VIII. The idea of writing this book originated in a seminar held at the University of Louvain during the academic year 1971-72. Two years later, a first draft was completed. However, it was unsatisfactory mainly because it was ex ce~sively abstract and lacked examples. It was then decided to write it again, taking advantage of -some remarks of the students to whom it had been partly addressed. The actual text is this second version. The subject matter is stability theory in the general setting of ordinary differential equations using what is known as Liapunov's direct or second method. We concentrate our efforts on this method, not because we underrate those which appear more powerful in some circumstances, but because it is important enough, along with its modern developments, to justify the writing of an up-to-date monograph. Also excellent books exist concerning the other methods, as for example R. Bellman [1953] and W. A. Coppel [1965].