Nonlinear Ordinary Differential Equations
Oxford University Press (Verlag)
978-0-19-856562-8 (ISBN)
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Nonlinear ordinary differential equations was first published in 1977 and has since become a standard text in the teaching of the subject. It takes a qualitative approach, and is designed for advanced undergraduate and graduate students of dynamical systems in mathematics or mathematics-related subjects. The text of this third edition has been completely revised to bring it into line with current teaching, including an expansion of the material on bifurcations and chaos. The book is directed towards practical applications of the theory, with several hundred examples and problems covering a wide variety of applications. Prerequisites are kept to a minimum, with appendices containing the necessary mathematical theory new to this edition. From reviews of the first edition: The book can profitably be used in a senior undergraduate course. It is well written, well motivated and contains some recent developments of interest which have not been readily accessible before at this level. V.Lakshmikantham in Mathematical Reviews From reviews of the second edition: The subject has wide applications in physical, biological, and social sciences which continuously supply new problems of practical and theoretical importance.
The book does a good job in motivating the reader in such pursuits, and presents the subject in a simple but elegant style. P. K. Kythe in Applied Mechanics Reviews
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. Determination of stability by solution perturbation; 10. Liapunov methods for determining stability of the zero solution; 11. The existence of periodic solutions; 12. Bifurcations and manifolds; 13. Poincare series, homoclinic bifurcations and chaos; HINTS AND ANSWERS TO THE PROBLEMS; Appendix A. Existence and uniqueness theorems; Appendix B. Topographic systems; Appendix C. Norms for vectors and matrices; Appendix D. A contour integral; References and further reading; Index
| Erscheint lt. Verlag | 1.9.1999 |
|---|---|
| Co-Autor | P. Smith |
| Zusatzinfo | numerous figures and tables |
| Verlagsort | Oxford |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 0-19-856562-3 / 0198565623 |
| ISBN-13 | 978-0-19-856562-8 / 9780198565628 |
| Zustand | Neuware |
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