03723nam a22005175i 4500 978-0-387-35794-2 DE-He213 20260521091910.0 cr nn 008mamaa 100301s2006 xxu| s |||| 0|eng d 9780387357942 99780387357942 10.1007/0-387-35794-7 doi CICY 515.352 23 Chicone, Carmen. author. Ordinary Differential Equations with Applications [recurso electrónico] / by Carmen Chicone. 2. New York, NY : Springer New York, 2006. XIX, 636 p. 73 illus. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Texts in Applied Mathematics, 0939-2475 ; 34 to 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 over 20 years of the author teaching the course at his own university. It serves as a text for a graduate level course in the theory of ordinary differential equations, written from a dynamical systems point of view. It contains both theory and applications, with the applications interwoven with the theory throughout the text. The author also links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and even abstract algebra. The second edition incorporates corrections and improvements of the original text. New material includes a proof of the Grobman-Hartman theorem for flows based on the Lie derivative, more extensive treatment of the Euler-Lagrange equation and its applications, a proof of Noether's theorem on the existence of first integrals in the presence of symmetries and a new section on dynamic bifurcation with a proof of Pontryagin's formula. The impressive array of existing exercises has been more than doubled in size and further enhanced in scope, providing mathematics, physical science and engineering graduate students with a thorough introduction to the theory and application of ordinary differential equations. 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 MATHEMATICS. GLOBAL ANALYSIS (MATHEMATICS). DIFFERENTIABLE DYNAMICAL SYSTEMS. DIFFERENTIAL EQUATIONS. PHYSICS. ENGINEERING. MATHEMATICS. ORDINARY DIFFERENTIAL EQUATIONS. DYNAMICAL SYSTEMS AND ERGODIC THEORY. COMPLEXITY. ANALYSIS. SpringerLink (Online service) Springer eBooks Printed edition: 9780387307695 Texts in Applied Mathematics, 0939-2475 ; 34 http://dx.doi.org/10.1007/0-387-35794-7 Ver el texto completo en las instalaciones del CICY ddc ER 33400 33400 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 515.352 2025-07-10 08:39:55 2025-07-10 ER