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题名/责任者:

Qualitative theory of ODEs : an introduction to dynamical systems theory / Henryk Zotadek, Raul Murillo.

出版发行项:

New Jersey : World Scientific, 2023.

ISBN:

9781800612686:

载体形态项:

xiii, 268 pages ; 24 cm

个人责任者:

Zootadek, Henryk, 1953- author.

附加个人名称:

Murillo, Raul, author.

论题主题:

Differential equations-Qualitative theory.

论题主题:

Dynamics-Mathematical models.

中图法分类号:

O175.12

书目附注:

Includes bibliographical references (pages 263-264) and index.

摘要附注:

"The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods. The main idea of the qualitative analysis of differential equations is to be able to say something about the behavior of solutions of the equations, without solving them explicitly. Therefore, in the first place such properties like the stability of solutions stand out. It is the stability with respect to changes in the initial conditions of the problem. Note that, even with the numerical approach to differential equations, all calculations are subject to a certain inevitable error. Therefore, it is desirable that the asymptotic behavior of the solutions is insensitive to perturbations of the initial state. Each chapter contains a series of problems (with varying degrees of difficulty) and a self-respecting student should solve them. This book is based on the first author's translation of lecture notes in Polish by the second author, edited in the portal Matematyka Stosowana (Applied Mathematics) at the University of Warsaw"--

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