Ordinary Differential Equations (Hardcover)

I. First Order Equations: Some Integrable Cases.- 1. Explicit First Order Equations.- 2. The Linear Differential Equation. Related Equations.- Supplement: The Generalized Logistic Equation.- 3. Differential Equations for Families of Curves. Exact Equations.- 4. Implicit First Order Differential Equations.- II: Theory of First Order Differential Equations.- 5. Tools from Functional Analysis.- 6. An Existence and Uniqueness Theorem.- Supplement: Singular Initial Value Problems.- 7. The Peano Existence Theorem.- Supplement: Methods of Functional Analysis.- 8. Complex Differential Equations. Power Series Expansions.- 9. Upper and Lower Solutions. Maximal and Minimal Integrals.- Supplement: The Separatrix.- III: First Order Systems. Equations of Higher Order.- 10. The Initial Value Problem for a System of First Order.- Supplement I: Differential Inequalities and Invariance.- Supplement II: Differential Equations in the Sense of Caratheodory.- 11. Initial Value Problems for Equations of Higher Order.- Supplement: Second Order Differential Inequalities.- 12. Continuous Dependence of Solutions.- Supplement: General Uniqueness and Dependence Theorems.- 13. Dependence of Solutions on Initial Values and Parameters.- IV: Linear Differential Equations.- 14. Linear Systems.- 15. Homogeneous Linear Systems.- 16. Inhomogeneous Systems.- Supplement:L1-Estimation of C-Solutions.- 17. Systems with Constant Coefficients.- 18. Matrix Functions. Inhomogeneous Systems.- Supplement: Floquet Theory.- 19. Linear Differential Equations of Order n.- 20. Linear Equations of Order nwith Constant Coefficients.- Supplement: Linear Differential Equations with Periodic Coefficients.- V: Complex Linear Systems.- 21. Homogeneous Linear Systems in the Regular Case.- 22. Isolated Singularities.- 23. Weakly Singular Points. Equations of Fuchsian Type.- 24. Series Expansion of Solutions.- 25. Second Order Linear Equations.- VI: Boundary Value and Eigenvalue Problems.- 26. Boundary Value Problems.- Supplement I: Maximum and Minimum Principles.- Supplement II: Nonlinear Boundary Value Problems.- 27. The Sturm-Liouville Eigenvalue Problem.- Supplement: Rotation-Symmetric Elliptic Problems.- 28. Compact Self-Adjoint Operators in Hilbert Space.- VII: Stability and Asymptotic Behavior.- 29. Stability.- 30. The Method of Lyapunov.- A. Topology.- B. Real Analysis.- C. C0111plex Analysis.- D. Functional Analysis.- Solutions and Hints for Selected Exercises.- Literature.- Notation.