Nonlinear Ordinary Differential Equations: Problems and Solutions A Sourcebook for Scientists and Engineers

by Jordan, Dominic; Smith, Peter

• ISBN13: 9780199212033
• ISBN10: 0199212031
• Format: Paperback
• Copyright: 2007-10-11
• Publisher: Oxford University Press

Summary

An ideal companion to the new 4th Edition of em/Nonlinear Ordinary Differential Equations /em by Jordan and Smith (OUP, 2007), this text contains over 500 problems and fully-worked solutions in nonlinear differential equations. With 272 figures and diagrams, subjects covered include phasediagrams in the plane, classification of equilibrium points, geometry of the phase plane, perturbation methods, forced oscillations, stability, Mathieu's equation, Liapunov methods, bifurcations and manifolds, homoclinic bifurcation, and Melnikov's method. The problems are of variable difficulty; some are routine questions, others are longer and expand on concepts discussed in em/Nonlinear Ordinary Differential Equations /em 4th Edition, and in most cases can be adapted for coursework or self-study. 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.

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,entrainment

Stability

Stability by solution perturbation: Mathieu's equation

Liapunov methods for determining stability of the zero equation

The existence of periodic solutions

Bifurcations and manifolds

Poincarand#233; sequences, homoclinic bifurcation, and chaos

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