Ordinary Differential Equations with Applications de Carmen Chicone

Ordinary Differential Equations with Applications: Texts in Applied Mathematics, cartea 34

Carmen Chicone

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

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Paperback (1)	516^.08 lei 6-8 săpt.
Springer – 23 noi 2010	516^.08 lei 6-8 săpt.
Hardback (1)	430^.22 lei 3-5 săpt.	+58^.29 lei 7-13 zile
Springer International Publishing – 20 mai 2024	430^.22 lei 3-5 săpt.	+58^.29 lei 7-13 zile

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Notă biografică

Carmen Chicone is an emeritus professor of mathematics at the University of Missouri. He has authored two books, coauthored a third, and published over 100 research articles. His recent research interests are in the qualitative theory of ordinary and partial differential equations, applications of differential equations to mathematical models in science and engineering, and the development of numerical methods to obtain viable predictions from physically realistic model problems.

Textul de pe ultima copertă

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:

Caracteristici

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, optimization, control, averaging, and chaos Includes a wealth of original exercises, graduate level topics for self study or master’s level projects

Ordinary Differential Equations with Applications: Texts in Applied Mathematics, cartea 34

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