Ordinary Differential Equations with ApplicationsSpringer Science & Business Media, 23. sep. 2006 - 636 síður Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden New York, New York L. Sirovich College Park, Maryland S.S. Antman Preface This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. |
Efni
1 | |
Linear Systems and Stability of Nonlinear Systems | 145 |
Applications | 225 |
Hyperbolic Theory | 323 |
Continuation of Periodic Solutions | 367 |
Homoclinic Orbits Melnikovs Method and Chaos | 449 |
Averaging 511 | 510 |
Local Bifurcation | 545 |
603 | |
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apply approximation Banach space bifurcation bifurcation theory boundary bounded called complete compute consider constant contained continuous coordinates corresponding curve defined definition denote derivative determine differential equation direction discuss displacement dynamical eigenvalues equivalent example Exercise existence fact Figure Find fixed flow formula function fundamental given Hamiltonian hyperbolic identity important initial condition integral interval invariant invertible limit cycle linear linear system manifold matrix method Moreover motion multipliers norm obtain operator origin oscillator parameter partial particular periodic orbit periodic solution perturbed phase portrait plane Poincaré map positive proof Proposition prove resonance respect rest point result simple smooth solution space stable subset Suppose tangent term theorem theory tion transformation unique unperturbed unstable variables vector field zero