Developed over 20 years of course instruction, this book links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and abstract algebra. Application is interwoven with theory throughout the text. This revised edition includes considerable new material; the impressive array of exercises has been more than doubled in size and enhanced in scope.

This book is developed primarily from the author's 20 years of teaching the course at his own university. It addresses both theory and applications, interweaving application with theory throughout the text. The author 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 revised edition includes considerable new material; the impressive array of exercises has been more than doubled in size and enhanced in scope.

Many new exercises added Includes supplementary material: sn.pub/extras

Autorentext

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.

Klappentext

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

Inhalt
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.