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

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

by Dominic Jordan, P. Smith, Peter Smith
     
 

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ISBN-10: 0199208255

ISBN-13: 9780199208258

Pub. Date: 09/21/2007

Publisher: Oxford University Press, USA


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

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, USA
Publication date:
09/21/2007
Series:
Oxford Texts in Applied and Engineering Mathematics Series, #10
Edition description:
REV
Pages:
560
Product dimensions:
9.60(w) x 6.60(h) x 1.10(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, 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
Appendices
A. Existence and uniqueness theorems
B. Topographic systems
C. Norms for vectors and matrices
D. A contour integral
E. Useful identities
References and further reading
Index

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