Ordinary Differential Equations And Stability PDF Download
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Author | : David A. Sanchez |
Publisher | : Courier Dover Publications |
Total Pages | : 179 |
Release | : 2019-09-18 |
Genre | : Mathematics |
ISBN | : 0486837599 |
Download Ordinary Differential Equations and Stability Theory: Book in PDF, ePub and Kindle
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.
Author | : Richard Bellman |
Publisher | : Courier Corporation |
Total Pages | : 178 |
Release | : 2013-02-20 |
Genre | : Mathematics |
ISBN | : 0486150135 |
Download Stability Theory of Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Lamberto Cesari |
Publisher | : Springer |
Total Pages | : 278 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662015293 |
Download Asymptotic Behavior and Stability Problems in Ordinary Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Nicolas Rouche |
Publisher | : Pitman Advanced Publishing Program |
Total Pages | : 280 |
Release | : 1980 |
Genre | : Differential equations |
ISBN | : |
Download Ordinary Differential Equations Book in PDF, ePub and Kindle
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.
Author | : T. A. Burton |
Publisher | : Courier Corporation |
Total Pages | : 366 |
Release | : 2013-04-16 |
Genre | : Mathematics |
ISBN | : 0486153320 |
Download Stability by Fixed Point Theory for Functional Differential Equations Book in PDF, ePub and Kindle
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.
Author | : T. A. Burton |
Publisher | : Courier Corporation |
Total Pages | : 370 |
Release | : 2014-06-24 |
Genre | : Mathematics |
ISBN | : 0486150453 |
Download Stability & Periodic Solutions of Ordinary & Functional Differential Equations Book in PDF, ePub and Kindle
This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.
Author | : K. Gopalsamy |
Publisher | : Springer Science & Business Media |
Total Pages | : 514 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401579202 |
Download Stability and Oscillations in Delay Differential Equations of Population Dynamics Book in PDF, ePub and Kindle
This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.
Author | : Luis Barreira |
Publisher | : Springer |
Total Pages | : 291 |
Release | : 2007-09-26 |
Genre | : Mathematics |
ISBN | : 3540747753 |
Download Stability of Nonautonomous Differential Equations Book in PDF, ePub and Kindle
This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Author | : Sadashiv G. Deo |
Publisher | : |
Total Pages | : 260 |
Release | : 1980 |
Genre | : Differential equations |
ISBN | : |
Download Ordinary Differential Equations and Stability Theory Book in PDF, ePub and Kindle
Author | : Arun Kumar Tripathy |
Publisher | : |
Total Pages | : |
Release | : 2021 |
Genre | : Differential equations |
ISBN | : 9780367636685 |
Download Hyers-Ulam Stability of Ordinary Differential Equations Book in PDF, ePub and Kindle