Ordinary Differential Equations
Introduction and Qualitative Theory, Third Edition
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Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition provides a detailed account, based on the work of Lefschetz, of the Bendixson theory of solutions of two-dimensional autonomous systems in a neighborhood of a singular point. Updated and revised, this third edition presents a unified treatment of the perturbation problem for periodic solutions, covering nonautonomous equations and bifurcation problems. The text includes a self-contained account of topological degree and its use as well as a detailed description of how the averaging method can be used to examine the problem of periodic solutions. It also contains additional exercises, applications, and solutions.
Exploring the qualitative aspects of periodic solutions of ODEs, this edition extends the treatment of two-dimensional systems as well as periodic solutions in small parameter problems. It illustrates existence theorems with various examples, provides a detailed account of the Bendixson theory of solutions of two-dimensional autonomous systems, and presents a unified treatment of the perturbation problem for periodic solutions. The text also shows how topological degree is used to obtain significant extensions of perturbation theory and describes how the averaging method is used to study periodic solutions. It contains numerous exercises.
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