Ordinary differential equations and dynamical systems
 Author/Creator
 Teschl, Gerald, 1970
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xi, 356 p. : ill. ; 26 cm.
 Series
 Graduate studies in mathematics ; v. 140.
Access
Available online

Stacks

Unknown
QA371 .T43 2012

Unknown
QA371 .T43 2012
More options
Contributors
 Contributor
 American Mathematical Society.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 345347) and index.
 Publisher's Summary
 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 PoincareBendixson 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Differential equations > Textbooks.
 Dynamics > Textbooks.
Bibliographic information
 Publication date
 2012
 Responsibility
 Gerald Teschl.
 Series
 Graduate studies in mathematics ; v. 140
 ISBN
 9780821883280 (alk. paper)
 0821883283 (alk. paper)