Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients PDF Download

Author: Erugin
Publisher: Academic Press
ISBN: 0080955355
Category : Computers
Languages : en
Pages : 295

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Linear Systems of Ordinary Differential Equations, with Periodic and Quasi-Periodic Coefficients

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9400959885
Category : Mathematics
Languages : en
Pages : 540

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Book Description
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author: Harris
Publisher: Academic Press
ISBN: 0080956610
Category : Computers
Languages : en
Pages : 247

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Stability of Linear Systems: Some Aspects of Kinematic Similarity

Author: V. I. Arnol_d
Publisher: American Mathematical Soc.
ISBN: 9780821896518
Category :
Languages : en
Pages : 278

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Author: A.M. Fink
Publisher: Springer
ISBN: 3540383077
Category : Mathematics
Languages : en
Pages : 345

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Author: Lev Semenovich Pontri︠a︡gin
Publisher: Pergamon
ISBN:
Category : Mathematics
Languages : en
Pages : 312

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Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

Author: M. Hazewinkel
Publisher: Springer
ISBN: 1489937919
Category : Mathematics
Languages : en
Pages : 932

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 424

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Author: Zhensheng Lin
Publisher: World Scientific
ISBN: 9789810242831
Category : Mathematics
Languages : en
Pages : 222

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Book Description
Historically, the theory of stability is based on linear differential systems, which are simple and important systems in ordinary differential equations. The research on differential equations and on the theory of stability will, to a certain extent, be influenced by the research on linear differential systems. For differential linear equation systems, there are still many historical open questions attracting mathematicians. This book deals with the theory of linear differential systems developed around the notion of exponential dichotomies. The authors advance the theory of stability through their research in this field. Several new important results on linear differential systems are presented. They concern exponential dichotomy and the structure of the sets of hyperbolic points. The book has five chapters: Chapter 1 introduces some necessary classical results on the linear differential systems, and the following chapters discuss exponential dichotomy, spectra of almost periodic linear systems, the Floquet theory for quasi periodic linear systems and the structure of sets of hyperbolic points. This book is a very useful reference in the area of the stability theory of ordinary differential equations and the theory of dynamic systems.

Author: Gerald Teschl
Publisher: American Mathematical Society
ISBN: 147047641X
Category : Mathematics
Languages : en
Pages : 370

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Book Description
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.