Nonlinear Ordinary Differential Equations
(Sprache: Englisch)
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...
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Klappentext zu „Nonlinear Ordinary Differential Equations “
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.
Inhaltsverzeichnis zu „Nonlinear Ordinary Differential Equations “
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
Autoren-Porträt von Dominic Jordan, Peter Smith
Peter Smith is a professor in the Mathematics Department of Keele University. He has taught courses in mathematical methods, applied analysis, dynamics, stochastic processes, and nonlinear differential equations, and his research interests include fluid dynamics and applied analysis.
Bibliographische Angaben
- Autoren: Dominic Jordan , Peter Smith
- 4 Rev ed, 544 Seiten, mit Schwarz-Weiß-Abbildungen, Maße: 17,3 x 24,6 cm, Kartoniert (TB), Englisch
- Verlag: Oxford University Press
- ISBN-10: 0199208255
- ISBN-13: 9780199208258
- Erscheinungsdatum: 23.08.2007
Sprache:
Englisch
Rezension zu „Nonlinear Ordinary Differential Equations “
UNEDITED UK REVIEW: "Review from previous edition ."..classic book...The book succeeds as an exceptionally well written test fot its intended audience...No doubt one of its strongest features is over 500 problems...throughout the entire book only important physical processes are described... The new edition is greatly enhanced...I strongly recommend that you take a look. The presentation is exquisitely straightforward with numerous physically interesting examples, and it is carefully and well written""--SIAM"The book should be recommended to scientists and engineers."--Mathematical Reviews
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