Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers / Edition 4

by Dominic Jordan, Peter Smith

Overview

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 while keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Product Details

ISBN-13:	9780199208258
Publisher:	Oxford University Press
Publication date:	10/11/2007
Series:	Oxford Texts in Applied and Engineering Mathematics , #10
Edition description:	REV
Pages:	544
Product dimensions:	9.60(w) x 6.70(h) x 1.20(d)

About the Author

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.

Table of Contents

Preface1. Second-order differential equations in the phase plane2. Plane autonomous systems and linearization3. Geometrical aspects of plane autonomous systems4. Periodic solutions; averaging methods5. Perturbation methods6. Singular perturbation methods7. Forced oscillations: harmonic and subharmonic response, stability, and entrainment8. Stability9. Stability by solution perturbation: Mathieu's equation10. Liapurnov methods for determining stability of the zero solution11. The existence of periodic solutions12. Bifurcations and manifolds13. Poincaré sequences, homoclinic bifurcation, and chaosAnswers to the exercisesAppendicesA. Existence and uniqueness theoremsB. Topographic systemsC. Norms for vectors and matricesD. A contour integralE. Useful identitiesReferences and further readingIndex

Editorial Reviews

"The book should be recommended to scientists and engineers."—Mathematical Reviews

From the Publisher