04382nam a22006255i 4500 978-3-031-51652-8 DE-He213 20251030112048.0 cr nn 008mamaa 240519s2024 sz | s |||| 0|eng d 9783031516528 978-3-031-51652-8 10.1007/978-3-031-51652-8 doi QA299.6-433 QA299.6-433 PBK bicssc PBK bicssc MAT034000 bisacsh PBK thema PBK thema Chicone, Carmen. author. aut http://id.loc.gov/vocabulary/relators/aut 77035 Ordinary Differential Equations with Applications [electronic resource] / by Carmen Chicone. 3rd ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XXII, 729 p. 76 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Texts in Applied Mathematics, 2196-9949 ; 34 Ordinary Differential Equations -- Linear Systems and Stability of Nonlinear Systems -- Applications -- Hyperbolic Theory -- Continuation of Periodic Solutions -- Homoclinic Orbits, Melnikov’s Method, and Chaos -- Averaging -- Local Bifurcation. 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 theory, a discussion of optimal control, and a proof of a useful special case of the maximum principle. A key feature of earlier editions, a wide selection of original exercises, is respected in this edition with the inclusion of a wealth of new exercises. Reviews of the first edition: “As an applied mathematics text on linear and nonlinear equations, the book by Chicone is written with stimulating enthusiasm. It will certainly appeal to many students and researchers.”—F. Verhulst, SIAM Review “The author writes lucidly and in an engaging conversational style. His book is wide-ranging in its subject matter, thorough in its presentation, and written at a generally high level of generality, detail, and rigor.” —D. S. Shafer, Mathematical Reviews. Mathematical analysis. 64178 Dynamical systems. System theory. 66519 Mathematical physics. Analysis. Dynamical Systems. Complex Systems. 66520 Analysis. Theoretical, Mathematical and Computational Physics. 65563 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031516511 Printed edition: 9783031516535 Printed edition: 9783031516542 Texts in Applied Mathematics, 2196-9949 ; 34 76354 https://doi.org/10.1007/978-3-031-51652-8 ZDB-2-SMA ZDB-2-SXMS 59960 59960