Ordinary Differential Equations with Applications

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 t

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Editors J.E. Marsden L. Sirovich S.S. Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton

Texts in Applied Mathematics 1. Sirovich: Introduction to Applied Mathematics. 2. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed. 3. Hale/Koc¸ak: Dynamics and Bifurcations. 4. Chorin/Marsden: A Mathematical Introduction to Fluid Mechanics, 3rd ed. 5. Hubbard/Weist: Differential Equations: A Dynamical Systems Approach: Ordinary Differential Equations. 6. Sontag: Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed. 7. Perko: Differential Equations and Dynamical Systems, 3rd ed. 8. Seaborn: Hypergeometric Functions and Their Applications. 9. Pipkin: A Course on Integral Equations. 10. Hoppensteadt/Peskin: Modeling and Simulation in Medicine and the Life Sciences, 2nd ed. 11. Braun: Differential Equations and Their Applications, 4th ed. 12. Stoer/Bulirsch: Introduction to Numerical Analysis, 3rd ed. 13. Renardy/Rogers: An Introduction to Partial Differential Equations. 14. Banks: Growth and Diffusion Phenomena: Mathematical Frameworks and Applications. 15. Brenner/Scott: The Mathematical Theory of Finite Element Methods, 2nd ed. 16. Van de Velde: Concurrent Scientific Computing. 17. Marsden/Ratiu: Introduction to Mechanics and Symmetry, 2nd ed. 18. Hubbard/West: Differential Equations: A Dynamical Systems Approach: Higher-Dimensional Systems. 19. Kaplan/Glass: Understanding Nonlinear Dynamics. 20. Holmes: Introduction to Perturbation Methods. 21. Curtain/Zwart: An Introduction to Infinite-Dimensional Linear Systems Theory. 22. Thomas: Numerical Partial Differential Equations: Finite Difference Methods. 23. Taylor: Partial Differential Equations: Basic Theory. 24. Merkin: Introduction to the Theory of Stability of Motion. 25. Naber: Topology, Geometry, and Gauge Fields: Foundations. 26. Polderman/Willems: Introduction to Mathematical Systems Theory: A Behavioral Approach. 27. Reddy: Introductory Functional Analysis with Applications to BoundaryValue Problems and Finite Elements. 28. Gustafson/Wilcox: Analytical and Computational Methods of Advanced Engineering Mathematics. 29. Tveito/Winther: Introduction to Partial Differential Equations: A Computational Approach. 30. Gasquet/Witomski: Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets.

(continued after index)

Carmen Chicone

Ordinary Differential Equations with Applications

With 73 Illustrations

Carmen Chicone Department of Mathematics University of Missouri Columbia, MO 65211

Series Editors J.E. Marsden Control and Dynamical Systems, 107–81 California Institute of Technology Pasadena, CA 91125 USA [email protected]

L. Sirovich Laboratory of Applied Mathematics and Department of Biomathematics Mt. Sinai School of Medicine New York, NY 10029-6574 [email protected]

S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA [email protected]

Mathematics Subject Classification

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