Qualitative theory of ODEs : an introduction to dynamical systems theory /
Żołądek, Henryk, 1953-
Qualitative theory of ODEs : an introduction to dynamical systems theory / Henryk Żołądek, Raul Murillo. - Singapore : World Scientific, 2022. - 1 online resource (284 p.).
Includes bibliographical references and index.
Singular points of vector fields -- Phase portraits of vector fields -- Bifurcation theory -- Equations with a small parameter -- Irregular dynamics in differential equations -- Appendix: Basic concepts and theorems of the theory of ODEs.
"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"--
Mode of access: World Wide Web.
System requirements: Adobe Acrobat reader.
9781800612693 1800612699
2022021010
GBC2E5604 bnb
020716184 Uk
Differential equations--Qualitative theory.
Dynamics--Mathematical models.
Electronic books.
QA372 / .Z64
515.352
Qualitative theory of ODEs : an introduction to dynamical systems theory / Henryk Żołądek, Raul Murillo. - Singapore : World Scientific, 2022. - 1 online resource (284 p.).
Includes bibliographical references and index.
Singular points of vector fields -- Phase portraits of vector fields -- Bifurcation theory -- Equations with a small parameter -- Irregular dynamics in differential equations -- Appendix: Basic concepts and theorems of the theory of ODEs.
"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"--
Mode of access: World Wide Web.
System requirements: Adobe Acrobat reader.
9781800612693 1800612699
2022021010
GBC2E5604 bnb
020716184 Uk
Differential equations--Qualitative theory.
Dynamics--Mathematical models.
Electronic books.
QA372 / .Z64
515.352