| 書目名稱 | Ordinary Differential Equations with Applications | | 編輯 | Carmen Chicone | | 視頻video | http://file.papertrans.cn/704/703683/703683.mp4 | | 概述 | Provides a thorough introduction to all standard topics for a graduate level course in ordinary differential equations.Contains concise introductions to continuation, calculus of variations, optimizat | | 叢書名稱 | Texts in Applied Mathematics | | 圖書封面 |  | | 描述 | This book, developed during 20 years of the author teaching differential equations courses at his home university, is designed to serve as a text for a graduate level course focused on the central theory of the subject with attention paid to applications and connections to other advanced topics in mathematics. Core theory includes local existence and uniqueness, the phase plane, Poincaré-Bendixson theory, Lyapunov and linearized stability, linear systems, Floquet theory, the Grobman–Hartman theorem, persistence of rest points and periodic orbits, the stable and center manifold theorems, and bifurcation theory. This edition includes expanded treatment of deterministic chaos, perturbation theory for periodic solutions, boundary value problems, optimization, and a wide range of their applications. In addition, it contains a formulation and new proof of a theorem on instability of rest points in the presence of an eigenvalue with positive real part, and new proofs of differential inequalities and Lyapunov’s center theorem. New sections present discussions of global bifurcation, the Crandall–Rabinowitz theorem, and Alekseev’s formula. Of particular note is a new chapter on basic control | | 出版日期 | Textbook 2024Latest edition | | 關(guān)鍵詞 | Derivative; Implicit function; Smooth function; differential equation; ordinary differential equation | | 版次 | 3 | | doi | https://doi.org/10.1007/978-3-031-51652-8 | | isbn_softcover | 978-3-031-51654-2 | | isbn_ebook | 978-3-031-51652-8Series ISSN 0939-2475 Series E-ISSN 2196-9949 | | issn_series | 0939-2475 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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