Nonlinear ordinary differential equations Problems and solutions 1st Edition by Jordan, Peter Smith ISBN 0199212031 978-0199212033

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Product details: 

ISBN 10: 0199212031

ISBN 13:  978-0199212033

Author: D. W. Jordan, Peter Smith

An ideal companion to the new 4th Edition of Nonlinear Ordinary Differential Equations 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 phase diagrams 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 Nonlinear Ordinary Differential Equations 4th Edition, and in most cases can be adapted for coursework or self-study.

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.

Table of contents: 

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:Poincaré sequences, homoclinic bifurcation, and chaos
Answers to the exercises

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