Nonlinear ordinary differential equations : an introduction for scientists and engineers

✍ Scribed by D W Jordan; Peter Smith

Publisher: Oxford University Press
Year: 2007
Leaves: 540
Series: Oxford applied and engineering mathematics
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

Content: 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. Poincare 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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