文档介绍：To Jenny, for giving me the gift of page intentionallyleftblankPrefaceThis book is based on a two-semester course in ordinary di?erential equa-tions that I have taught to graduate students for two decades at the Uni-versity of Missouri. The scope of the narrative evolved over time froman embryonic collection of supplementary notes, through many classroomtested revisions, to a treatment of the subject that is suitable for a year (ormore) of graduate it is true that students of di?erential equations give away their point ofview by the way they denote the derivative with respect to the independentvariable, then the initiated reader can turn to Chapter 1, note that I write˙x,notx?, and thus correctly deduce that this book is written with an eyetoward dynamical systems. Indeed, this book contains a thorough intro-duction to the basic properties of di?erential equations that are needed toapproach the modern theory of (nonlinear) dynamical systems. However,this is not the whole story. The book is also a product of my desire todemonstrate to my students that di?erential equations is the least insularof mathematical subjects, that it is strongly connected to almost all areasof mathematics, and it is an essential element of applied I teach this course, I use the ?rst part of the ?rst semester to pro-vide a rapid, student-friendly survey of the standard topics encountered inan introductory course of ordinary di?erential equations (ODE): existencetheory, ?ows, invariant manifolds, linearization, omega limit sets, phaseplane analysis, and stability. These topics, covered in Sections – ofChapter 1 of this book, are introduced, together with some of their im-portant andinterestingapplications, so that the power and beauty of thesubject is immediately apparent. This is followed by a discussion of linearviii Prefacesystems theory and the proofs of the basic theorems on linearized stabil-ity in Chapter 2. Then, I conclude the ?rst semester