
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Graduate Studies in Mathematics 2012; 356 pp; hardcover Volume: 140 ISBN10: 0821883283 ISBN13: 9780821883280 List Price: US$64 Member Price: US$51.20 Order Code: GSM/140 See also: Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators  Gerald Teschl Ordinary Differential Equations: Qualitative Theory  Luis Barreira and Claudia Valls Classical Methods in Ordinary Differential Equations: With Applications to Boundary Value Problems  Stuart P Hastings and J Bryce McLeod  This book provides a selfcontained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and SturmLiouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The PoincaréBendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the HartmanGrobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the SmaleBirkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations. Request an examination or desk copy. Readership Graduate students interested in ordinary differential equations and dynamical systems. 


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