Nonlinear Ordinary Differential Equations An Introduction for Scientists and Engineers

by Jordan, Dominic; Smith, Peter

• ISBN13: 9780199208241
• ISBN10: 0199208247
• Edition: 4th
• Format: Hardcover
• Copyright: 2007-10-11
• Publisher: Oxford University Press

Summary

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.

Author Biography

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

Preface

Second-order differential equations in the phase plane

Plane autonomous systems and linearization

Geometrical aspects of plane autonomous systems

Periodic solutions; averaging methods

Perturbation methods

Singular perturbation methods

Forced oscillations: harmonic and subharmonic response, stability, and entrainment

Stability

Stability by solution perturbation: Mathieu's equation

Liapurnov methods for determining stability of the zero solution

The existence of periodic solutions

Bifurcations and manifolds

Poincaré sequences, homoclinic bifurcation, and chaos

Answers to the exercises

Appendices

Existence and uniqueness theorems

Topographic systems

Norms for vectors and matrices

A contour integral

Useful identities

References and further reading

Index

Table of Contents provided by Publisher. All Rights Reserved.