Ordinary Differential Equations with Applications

Carmen Chicone (Autor)

Buch | Softcover

XXII, 729 Seiten

2025 | 3. Third Edition 2024
Springer International Publishing (Verlag)
978-3-031-51654-2 (ISBN)

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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

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.

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.

The books of C. Chicone have proved to be excellent text books for teaching ordinary differential equations with emphasize on applications for graduate level courses, additionally they are frequently cited in recent research papers. The new material is related to optimization, control theory, optimal control and global continuation by bifurcation. Additional subject matter is meant to attract student interest for self study, topics courses and master s projects. (Klaus R. Schneider, zbMATH 1559.34002, 2025)

Erscheint lt. Verlag	20.5.2025
Reihe/Serie	Texts in Applied Mathematics
Zusatzinfo	XXII, 729 p. 76 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Derivative • differential equation • Implicit function • ordinary differential equation • Smooth function
ISBN-10	3-031-51654-0 / 3031516540
ISBN-13	978-3-031-51654-2 / 9783031516542
Zustand	Neuware