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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Qualitative Theory Of Odes: An Introduction To Dynamical Systems Theory (Hardcover)
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Qualitative Theory Of Odes: An Introduction To Dynamical Systems Theory (Hardcover)
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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 Raul Murillo's translation of Henryk Zoladek's lecture notes,
which were in Polish and edited in the portal Matematyka Stosowana
(Applied Mathematics) in the University of Warsaw.
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