| Preface Ⅰ. Preliminary Questions 1. Elements of topology 2. Vectors and matrices 3. Analytic functions of several variables 4. Differentiable manifolds Ⅱ. Existence Theorems. General Properties of the Solutions 1. Generalities 2. The fundamental existence theorem 3. Continuity properties 4. Differentiability properties 5. Analyticity properties 6. Equations of higher order 7. Autonomous systems Ⅲ. Linear Systems 1. Various types of linear systems 2. Homogeneous systems 3. Non-homogeneous systems 4. Linear systems with constant coefficients 5. Linear systems with periodic coefficients: Theory of Floquet Ⅳ. Stability 1. Historical considerations 2. Stability of critical points 3. Stability in linear homogeneous systems 4. Uniformly regular transformations 5. Stability of trajectories 6. Stability of mappings 7. Further definitions of stability Ⅴ.The Differential Eqation Ⅵ.The Differential Eqation Ⅶ.The Differential Eqation Ⅷ.Periodic Systems and Their Stability Ⅸ.Two Dimensional Systems.Simple Critical Points.The Index.Behavior and Infinity Ⅹ.Two Dimensional Systems(continued) Ⅺ.Differential Equations of the Second Order Ⅻ.Oscillations in Systems of theh Second order.Methods of Approximation Appendix Problems Biblisgraphy List of Principal Symbols Index |
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