Ordinary Differential Equations: Introduction and Qualitative Theory, Third EditionCRC Press, 15 февр. 1994 г. - Всего страниц: 392 This text, now in its second edition, presents the basic theory of ordinary differential equations and relates the topological theory used in differential equations to advanced applications in chemistry and biology. It provides new motivations for studying extension theorems and existence theorems, supplies real-world examples, gives an early introduction to the use of geometric methods and offers a novel treatment of the Sturm-Liouville theory. |
Содержание
Preface to Second Edition | 1 |
Examples | 55 |
Linear Systems | 65 |
Autonomous Systems | 127 |
Stability | 161 |
The Lyapunov Second Method | 197 |
Periodic Solutions | 217 |
Bifurcation and Branching | 261 |
Appendix | 321 |
| 357 | |
| 365 | |
Часто встречающиеся слова и выражения
Algebra analysis applications assume asymptotically stable autonomous system bounded open set c₁ c₂ Chapter characteristic exponents characteristic multipliers completes the proof computation continuous function converges defined definition deg[ƒ denote described domain eigenvalues equa equilibrium point example Existence Theorem Existence Theorem 1.1 finite follows fundamental matrix h₁ Hence Hopf Bifurcation Theorem Jordan canonical form K₁ Linear Systems linearly independent Lipschitz condition Lyapunov mathematical n-dimensional neighborhood nonlinear nonsingular matrix nonzero obtain open set orbit periodic solutions phase asymptotically stable physical system Poincaré-Bendixson Theorem positive number proof of Existence proof of Lemma prove real number S-L problem satisfies a Lipschitz sequence simple closed curve solution x(t ẞs ẞt Stability Theorem stable solution Sturm-Liouville theory sufficiently small Suppose t₁ t₂ tion topological degree uniformly v₁ variables x(to zero