000			nam a22 4500
999			_c32503 _d32503
008			230901b xxu||||| |||| 00| 0 eng d
020			_a9781800612686
082			_a515.352 _bZOL
100			_aZoladek, Henryk
245			_aQualitative theory of ODEs : an introduction to dynamical systems theory
260			_bWorld Scientific, _c2023 _aNew Jersey :
300			_axiii, 268 p. ; _bill., _c24 cm
365			_b98.00 _cUSD _d85.40
504			_aIncludes bibliographical references and index.
520			_aThe 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.
650			_aDifferential equations
650			_aQualitative theory
650			_aDynamics Mathematical models
700			_aMurillo, Raul
942			_2ddc _cBK