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

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

by Dominic Jordan
     
 

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

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Overview

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.

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Product Details

ISBN-13:
9780199212033
Publisher:
Oxford University Press, USA
Publication date:
09/21/2007
Series:
Oxford Texts in Applied and Engineering Mathematics Series, #11
Edition description:
New Edition
Pages:
450
Product dimensions:
9.40(w) x 6.70(h) x 1.00(d)

Table of Contents

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, entrainment
8. Stability
9. Stability by solution perturbation: Mathieu's equation
10. Liapunov methods for determining stability of the zero equation
11. The existence of periodic solutions
12. Bifurcations and manifolds
13. Poincaré sequences, homoclinic bifurcation, and chaos

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