Nonlinear Ordinary Differential Equations (4^th Ed.) An Introduction for Scientists and Engineers Oxford Texts in Applied and Engineering Mathematics Series

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007). Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Preface. 1. Second-order differential equations in the phase plane. 2. Plane autonomous systems and linearization. 3. Geometrical aspects of plane autonomous systems. 4. Periodic solutions, averaging methods. 5. Perturbation methods. 6. Singular perturbation methods. 7. Forced oscillations: harmonic and subharmonic response, stability, and entrainment. 8. Stability. 9. Stability by solution perturbation: Mathieu's equation. 10. Liapurnov methods for determining stability of the zero solution. 11. The existence of periodic solutions. 12. Bifurcations and manifolds. 13. Poincara#233, sequences, homoclinic bifurcation, and chaos. Answers to the exercises. Appendices. A. Existence and uniqueness theorems. B. Topographic systems. C. Norms for vectors and matrices. D. A contour integral. E. Useful identities. References and further reading. Index.

Prior to his retirement, Dominic Jordan was a professor in the Mathematics Department at Keele University. His research interests include applications of applied mathematics to elasticity, asymptotic theory, wave and diffusion problems, as well as research on the development of applied mathematics in its close association with late 19th century engineering technologies. Peter Smith is a professor in the Mathematics Department of Keele University. He has taught courses in mathematical methods, applied analysis, dynamics, stochastic processes, and nonlinear differential equations, and his research interests include fluid dynamics and applied analysis.