ISBN: 9783540329022

Our aim is to study ordinary di?erential equations or simply di?erential s- tems in two real variables x ? = P(x,y), (0.1) y? = Q(x,y), r 2 where P and Q are C functions de?ned on an open… More...

Our aim is to study ordinary di?erential equations or simply di?erential s- tems in two real variables x ? = P(x,y), (0.1) y? = Q(x,y), r 2 where P and Q are C functions de?ned on an open subset U of R , with ? r=1,2,...,?,?.AsusualC standsforanalyticity.Weputspecialemphasis onto polynomial di?erential systems, i.e., on systems (0.1) where P and Q are polynomials.Instead of talking about the di?erential system (0.1), we frequently talk about its associated vector ?eld ? ?X = P(x,y) +Q(x,y) (0.2) ?x ?y 2 on U? R . This will enable a coordinate-free approach, which is typical in thetheoryofdynamicalsystems.Anotherwayexpressingthevector?eldisby writingitasX=(P,Q).Infact,wedonotdistinguishbetweenthedi?erential system (0.1) and its vector ?eld (0.2).Almost all the notions and results that we present for two-dimensional di?erential systems can be generalized to higher dimensions and manifolds; but our goal is not to present them in general, we want to develop all these notions and results in dimension 2.We would like this book to be a nice introduction to the qualitative theory of di?erential equations in the plane, providing simultaneously the major part of concepts and ideas for developing a similar theory on more general surfaces and in higher dimensions.Except in very limited cases we do not deal with bifurcations, but focus on the study of individual systems.; PDF; Scientific, Technical and Medical > Mathematics > Calculus & mathematical analysis > Differential ca, Springer Berlin Heidelberg<

ISBN: 9783540329022

This book explores systems of polynomial autonomous ordinary differential equations in two real variables, emphasizing the qualitative without neglecting more algebraic aspects. Late chap… More...

This book explores systems of polynomial autonomous ordinary differential equations in two real variables, emphasizing the qualitative without neglecting more algebraic aspects. Late chapters introduce the performant software tool P4. Provides simple and appropriate proofs, and numerous exercises. MATHEMATICS,Differential Equations,General, eBooks.com<

ISBN: 9783540329022

Qualitative Theory of Planar Differential Systems: ab 79.99 € eBooks > Fachthemen & Wissenschaft > Mathematik Springer-Verlag GmbH eBook als pdf, Springer-Verlag GmbH

2006, ISBN: 9783540329022

[ED: 1], Auflage, eBook Download (PDF), eBooks, [PU: Springer Berlin Heidelberg]

2006, ISBN: 9783540329022

eBooks, eBook Download (PDF), Auflage, [PU: Springer-Verlag], [ED: 1], Springer-Verlag, 2006